Copyright Psion PLC 1989
All rights reserved. This manual and the programs referred to herein are copyrighted works of Psion PLC, London, England. Reproduction in whole or in part including utilisation in machines capable of reproduction or retrieval, without the express written permission of Psion PLC is prohibited. Reverse engineering is also prohibited.
The information in this document is subject to change without notice.
Psion and the Psion logo are registered
trademarks of Psion PLC.
Psion Organiser II, Datapak and Rampak are trademarks of Psion PLC.
Please note that formulae provided in this product are designed to illustrate the utility and application of the Formulator. Users must satisfy themselves as to the validity and applicability of any individual formula before use.
Psion accepts no liability for loss, including consequential loss, arising from the use of the formulae contained herein.
Part No. 6100-0074
1 Getting started Running the formulator A single-calculation formula A multiple-calculation formula Valid expressions Leaving the formulator 2 finding and saving formulae Saving a formula Finding a formula Erasing a formula 3 Advanced features Decimal places Intermediate results Titles 4 Using the supplied formulae Finding the formula you want Copying a formula to device A: Analysing a formula Functions provided 5 Using the formulator from opl Appendices A Error messages B Supplied formulae INDEX
The Formulator can work out almost any calculation that can be expressed as a formula. On the Formulator pack there are over 250 formulae. You can use these supplied formulae and you can also enter your own extra ones.
The supplied formulae cover a huge range of common calculation areas, including:
To enter an extra formula of your own, you just type it in on one line. You only have to type it once - as you save it and use it again later. As a simple example, you could enter a formula to convert litres to pints:
Whenever you used this formula, the Formulator would ask you for a value in litres, and display the result in pints.
The Formulator occupies about 4K of Organiser memory, It works on all models.
Chapter 1 explains how to run the Formulator and how to enter and use your own formulae. Chapter 2 explains how to find, save and erase formulae. Chapter 3 has more detail about the format of complex formulae.
Chapter 4 explains how to use the supplied formulae, which are listed in Appendix B.
Chapter 5 explains how to use the Formulator in conjuction with OPL.
Note: The screen messages on the different Organiser models vary slightly - so your screen may not show exactly the same words as the examples in this manual.
To run the program:
This adds the option "XFORM" near the end of the main menu.
The prompt XFORM: appears, and you can use the Formulator. The screen shows:
Model CM or XP:
Model LZ or LZ64:
f 3:00p XFORM:_
Using the Formulator is similar to using the Organiser calculator. However, since you type words as well as numbers, the keyboard is normally set to letters.
Once you have added the "XFORM" option, you can if you wish remove the Formulator pack. If you do this, don't press ON/CLEAR when the main menu is displayed, as this removes the "XFORM" option and you then have to reload it from the pack.
In the introduction, there was a simple example formula to convert litres to pints:
You are then prompted for the number of litres to convert to pints, like this:
When you press EXE to enter the number, the screen shows the result. So if you entered the number 3, the screen shows:
Normally, when you type in one of your own formulae you would save it for future use. This is covered in the next chapter.
When the Formulator runs a simple formula it evaluates the sum on the right of the equals sign, here LITRES*1.76, prompting you for the necessary values, here LITRES.
It then displays the result name (the text on the left of the equals sign), here PINTS, followed by the result it has calculated.
The litres-to-pints formula from the previous section can be altered to produce a second result in gallons, as follows:
This formula now contains two calculations, separated by a semicolon.
If the formula from the previous section is still there, you can edit it in the usual way. Move around with the cursor keys (↑ and ↓ take you straight to the beginning and end of the line). Use DEL to delete characters, and just type in extra ones.
As before, you are prompted to enter the number of litres to convert to pints. In the second calculation, GALLONS=PINTS/8, the value for PINTS from the first calculation is automatically used.
The results - in this case, PINTS and GALLONS - are displayed one to a line.
This example shows how any result or input value in a formula, here the value of PINTS, can be used anywhere else in the formula. It is not even necessary to arrange the calculations in the correct order, the example could have been entered like this:
When two or more prompts are required, they appear on the screen in turn, according to their position from left to right in the formula. This means that you can swap formulae around to change the order in which prompts appear.
A formula may contain up to 16 different prompts and result names, and up to 16 separate calculations.
You can abbreviate any prompt or result name when you re-use it in a formula, as long as you use at least the first three characters of the name.
In the previous example, the second occurrence of PINTS could have been typed as PIN or PINT, like this;
The Formulator matches things like PIN and PINTS, whatever order they are in.
Take care not to accidentally use prompt names whose first three characters match. If, for example, you tried to run a formula containing prompts for both COST and COST2, the Formulator would treat them as one, and only prompt for COST2.
When entering a formula, or typing a number in response to a prompt, you can use any expression which OPL allows, just as you can in the calculator. For example:
2 2+3 $18 a hexadecimal number SIN(5) an OPL function PI**2 an OPL function DATAGET%:(2,3) a call to an OPL procedure
You should ensure that none of your prompts conflict with the numeric OPL functions "PI", "SECOND", "MINUTE", "HOUR", "DAY", "WEEK", "MONTH", "YEAR", and "RND", or with the logical operators "AND", "OR", and "NOT". The Formulator would evaluate these in the same way that OPL does.
Similarly, you should not use "M0" to "M9" as prompts as these clash with the names of the calculator memories.
See the chapter on operators in the OPL section of your Organiser manual for more detail of the mathematical syntax in OPL.
You can cancel the execution of a formula by just pressing ON/CLEAR when you are prompted for a number.
Note that pressing ON/CLEAR while the Formulator is running a formula may cause the Organiser to pause, just as it does in OPL. If you then press Q to Quit, you cancel the calculation; if you press any other key the calculation continues.
To leave the Formulator, just press ON/CLEAR at the XFORM: prompt. This returns to the Organiser's main menu.
If you then wish to free the memory used by the Formulator, remove the datapak and press ON/CLEAR.
You can save formulae and find them again to re-run at any time. Just as Find and Save on the main menu use a data file called MAIN, Find and Save in the Formulator use a data file called XFORM.
To try saving a formula, return to the XFORM: prompt and type:
Find Save Erase
You can now run the formula again, edit it, or press ON/CLEAR to clear it
You can't have more than one formula in the XFORM data file which has the same left-hand side.
For example, if you have already saved the metres-to-feet formula above on A:, try typing in and saving this formula on A: too:
As the first formula you saved also begins with FEET=, you aaked:
If you press Y, you delete the first formula and save this new one in its place. If you press N, you keep the first formula and do not save the new one.
There are two ways of finding formulae - a quick method and a menu method.
The quickest way to find a formula which has been saved is to:
The XFORM: prompt changes to a FIND prompt, followed by the device name, and the search starts on that device.
For example, if you saved the metres-to- feet formula in the previous section:
If the device in use is not A:, use MODE to change device, and search there.
When a formula containing the search text that you typed if found it is displayed.
If the formula is the right one:
If the formula is the not right one:
Pressing ↑ returns to the previous matching formula. Once the end of the XFORM data filehas been reached, the search starts again at the beginning. If there are no formulae containing the search clue, this message is displayed:
Pressing ON/CLEAR will in this case return to the XFORM: prompt with the search text.
To see all the formulae on a device, just press EXE at the XFORM: prompt and keep pressing ↓.
There is also a "FIND" option on the Formulator menu, which may be used as an alternative to the quick method.
It operates in th same way as Find on the main menu. You should use this option instead of the quick method if your search text contains an equals sign, or if you prefer to be able to use EXE instead of ↓ to search down the data file for further matches.
LZ users should note that you cannot use the wild cards * and + to search in the Formulator.
The "ERASE" option on the menu acts in a similar way to the "Find" option.
For example, to erase the metres-to-feet formula if you saved it earlier, make suure you're on device A: then type METRES or FEET.
The first matching formula is displayed.
When you have found the formula:
You can specify that a result from a formula is displayed to a certain number of decimal places.
For example, the following formula converts litres to pints, and displays the result to two decimal places:
This only affects the final display of the results, not the calculations, which are always performed to 12 digit accuracy.
You can also specify that a result is just to be used for intermediate calculations and not shown in the final display of results.
For example, when calculating the area of a triangle from the lengths of its sides, the value of half the sum of the lengths must be calculated, and then used several times in the final calculation. A suitable formula for this is as follows (but all on one line):
HS:=(S1+S2+S3)/2; AREA=SQR(HS* (HS-S1) *(HS-S2)*(HS-S3))
HS stands for half the sum of the sides. As it is followed by a colon it is only an intermediate result, and is not shown in the final display of results. S1, S2 and S3 are the three sides which are prompted for.
As mentioned in chapter 2, you can change the order in which values are prompted for by rearranging the formula. There may be cases, however, where it is difficult do this. You can then use a dummy intermediate result instead.
For example, to cause the value UNITS, to be the first prompt, even if normally it would appear near the end of the formula, you can begin your formula like this:
This dummy calculation uses an intermediate result with no name, purely to ensure that the name on the right of the equals sign (which would be used later in the formula) is the first value prompted for.
You can begin a formula with a title which is displayed before the list of results. This is very helpful as a confirmation to you when you find the formula, and it is ideal to use as search clue.
In the supplied formulae, ">" is used to mean "to" in conversions. Following this style, you could rewrite the litres-to-pints formula like this:
When the formula is run, the title LITRES>PINTS is displayed before the list of results.
The formulae supplied on the Formulator pack are stored in an ordinary data file, called "XFORM". There is a list of them in Appendix B.
Most of the formulae begin ith a title, and if a formula is a conversion, "to" is represented by ">". For example, there are several formulae to convert between different units of volume, including one to convert from litres to other liquid unit; its title is Litres>. To find this formula:
If the current device is not the one containing the Formulator pack, use MODE to change to a different device and start using it.
The formula is displayed, scrolling round - you can use ← and → to control this.
The list includes the number of litres you specified, so you can check the value you typed. There are brackets round the word Litres. This is because Litres=Litres can't be used to force the Formulator to display Litres as a result, as this would be a "circular reference" (see Appendix A), so (Litres)=Litres is used instead.
You may want to copy some of the supplied formulae from the Formulator pack to the internal memory (device A:).
Even if your Organiser has a lot of free memory, it is not a good idea to copy the entire "XFORM" data file to A:, since filling up memory will affect calculation speed. It is better to copy the formulae you want, one by one. For example, you could copy the supplied formula which converts litres to other liquid units.
The formula is displayed.
At this stage you can, if you wish, modify it to your own requirements.
You can now run or edit the formula again. You can freely modify formulae on A:, since the originals still exist as backup on the Formulator datapak.
A few of the supplied formulae use OPL programs which are supplied on the Datapak. To copy these formulae to device A: and run them from there, either copy their OPL programs as well or leave the Datapak plugged in when you run them.
See chapters 1 and 3 for more details.
If you wished to make substantial changes to the formulae, you could use the Psion Comms Link to transfer the XFORM data file to a desktop computer for editing. You can also modify the XFORM data file using OPL.
This is a list of the functions provided by the supplied formulae. The actual formulae are printed in the appendix.
The titles and key words which are useful as search clues are printed in bold here.
If a formula does not quite suit your requirments, you can easily modify it and save the changed version on A:.
Note that although all calculations are performed to 12 digit accuracy, many of the constants used in the formulae have less than 12 digits, adjust them if you require greater accuracy
The data file begins with financial formulae. Some of these are specific to the U.K., but you can adjust them, if necessary.
They include conversion between price, net and VAT (UK 15% sales tax); mark up and discount; compound interest, current value, annuity future and current, loan repayment and APR, repayment mortgage, endowment mortgage and take home pay.
The UK 15% sales tax formulae (for VAT) are followed by the corresponding formulae for France 18.6%, France 33%, Germany 14%, Austria 20%, Portugal 16%, Spain 12%, Italy 18%, Belgium 19%, Holland 20%, Turkey 12% and Morocco 19%.
You can adapt the UK formulae for use with a US sales tax by replacing every occurrence of 15 in the formula by the correct percentage.
For the formulae involving interest rates, the prompt Incrs Per Year refers to the number of times per year the accrued interest is added to the capital sum - daily, weekly, monthly, quarterly or yearly.
The mortgage repayments calculate the repayments first with no allowance for tax, then under MIRAS, assuming a tax rate of 25%. Additional payments may be required, so you should consult the lending institution for the total cost.
The take home pay formulaa apply to the UK, in the years 1989/90, assuming non-contracted out N.I. contributions and tax in the 25% tax bracket - however, you can adjust it. Because of rounding errors and discrepancies between weekly and monthly N.I. contributions, the result may be out by a few pence.
Note that when a prompt ends with a % sign you should type in a percentage, not a fraction: e.g. to specify 75%, type 75, not 0.75.
The next formula is a number converter. You can only give it as input a simple decimal number, octal number (prefixed by the letter 'O'), or hexadecimal number (prefixed by '$'). It then lists the number in all three notations.
Then comes a group of mathematical and statistical functions and formulae.
This includes factorial, Gamma function, Beta function, Bessel function of the 1st kind, Euler numbers, Bernoulli numbers, Rieman Zeta function, and Chebyshev polynomial (1st and 2nd) for values between zero and one; binomial distribution, binomial probability, Poisson probability, chi-squared distribution, Student's t distribution and normal probability.
Some of the above formulae may take some time to execute since they rely on the convergence of series.Remember that you can always exit from a calculation by pressing ON/CLEAR and Q.
The next group contains geometry formulae. These are triangle sizes (SAS for specifying side-angle-side, SAA for side-angle-angle and SSS for side-side-side), triangle area, regular polygon (from edge length, short radius and long radius), circle, sphere, and cone (from height and slant).
There then follow conic formulae: two formulae for calculating the Y and X of a parabola, three for the Y, X and eccentricity of an ellipse, and three for the Y, X and eccentricity of a hyperbola.
Next come asin, acos, hyperbolic functions, sum arithmetic series, sum geometric series, real quadratic (equation with real solutions), complex quadratic (equation with imaginary solutions), complex arithmetic (add, subtract, multiply, divide, exp, sinh and cosh), polar coords (to and from cartesian), polar arithmetic (add, multiply and divide), spherical coords (to and from cartesian), vector dot product and vector cross product.
The following formulae are conversions. In each case, the units which are converted from are also the title of the formula, followed by a ">" character meaning "to". The titles are in groups here, each group separated by a "/".
If, for example, you want to convert from metres to microns, you need the third formula whose title is "metres>", the one in the group which converts microns, angstroms, and fermis.
inches>, feet>, yards>, miles>, nautical
miles (nmiles>), metres> and km>/
fathoms>, yards> and metres>/
microns>, angstroms>, fermis> and
Au>(astronomic units), light years>, parsec> and metres>/
BMU>, points>, picas>, inches> and cm>/
sq inches>, sq feet>, sq yards>, acres>, sq miles>, sq metres>, hectares> and sq km>/
fl oz>, pints>, gallons>, litres>, US gallons> and barrels>/
cu inches>, cu feet>, cu yards>, cc> and litres/
oz>, pounds>, stone>, CWT>, short tons>, long tons>, kg> and tonnes>/
oz fine or troy>, oz avoirdupois>, and gram>/
sec of arc>, min of arc>, degrees> and radians>/
seconds>, minutes>, hours>, days>, weeks> and years>/
MPH>, FPS> (feet per second), KPH>, metres/sec> and knots>/
milesUKg>, milesUSg>, and kmLitres>/
poundals>, lbf> and newtons>/
dynes> and newtons>/
joules>, ergs>, calories>, therms>, btu> and KWH>/
joules>, eVolt>, Hertz>, Kelvin> and kg>/
PSI> (pounds per square inch), Pascals>, mmHg>, inHg>, Millibars> and atmosphere>/
Tesla> and Gauss>/
Curie> and Becquerel>/
Rads> and Gray>/
Horsepower> and Watts>/
RPM> and Hertz>/
Fahrenheit>, Celsius(centigrade)> and Kelvin>/
electron masses (em>), proton masses (pm>), neutron masses (nm>) and Kg>.
UK nautical miles have been used, which are equal to 6080 ft. International nautical miles are 1852 metres, so one UK nautical mile is approximately equal to 1.00064 international nautical miles.
IT calories have been used, equal to 4.1868 joules. Thermodynamic calories are 4.1840 joules.
The next section is concerned with physical and chemical formulae. It covers Watts (from Amps and Volts, Amps and Ohms, and Volts and Ohms), Joules (from farads and volts), Farads (from Joules and volts), Volts (from amps and ohms), Amps (from volts and ohms) and Ohms (from volts and amps); constant acceleration formulae (where units are unspecified they should be determined by the user), including velocity (from either time or distance), distance (from either time or final velocity), and energy (from initial and final velocity); some fundamental relationships including force (from mass and acceleration), momentum (from velocity and mass), final speed when two objects moving in the same direction collide, circular motion acceleration (from velocity and radius) and centripetal force (from velocity, radius and mass); unit definitions for Joules (from newtons and metres) and newtons (from Kilograms and acceleration); lens focal length (from image and object distance) and image distance (from object distance and focal length); pendulum period (from pendulum length); earth satellite velocity and period (from height); Resistance value of two resistors in parallel; charge growth and charge decay for an RC circuit; Amps growth and Amps decay for an RL circuit; Volts, Amps and Impedance for an AC series circuit, resonant frequency for a LC circuit and Coulombs Law for force, energy and voltage; pressure and volume from Boyles law; Adiabatic gas law and Ideal gas law; Joules from expanding gas (isothermal) and expanding gas (adiabatic); denier (from Kilograms and metres), Kg (from deniers and metres) and metres (from deniers and Kilograms). Rads/hour (from Curies, MeVolts and metres) and radiation decay (from initial radiation, half life of source and time).
Next come navigational formulae including radar range, sea horizon, extreme range and approximate barometer correction (each from feet and metres), true speed and bearing (from apparent speed, apparent bearing, drift speed and drift bearing) and apparent speed and bearing (from true speed, true bearing, drift speed and drift bearing).
The list of formulae ends with new exposure time for photo printing (from old exposure, old distance from lens and new distance from lens), and wall area, ceiling and total area of a rectangular room (from width, length and height).
A few of the formulae (the APR formula, the number converter and some of those concerning statistics and probability) use OPL programs which are supplied on the Datapak.
When the XFORM option has been added to the main menu, an additional instruction, XFORM:, is added to OPL.
Using XFORM: is like calling one of your own OPL procedures - so remember the final colon.
You can use it to simply run a formula:
Or to find then run one:
You can use XFORM: to run formulae stright from the main menu. For example, you could enter a simple one-line OPL procedure called P:
When you've translated and saved the procedure, you could insert its name as an option on the main menu. Whenever you select this option, it will run the formula.
To search for a formula from within a procedure, pass XFORM: a search clue instead of a formula. (The clue can't contain "=".) For example:
This will search "XFORM" data file for a formula which contains the search text and you can then use ↑ and ↓ to search for different formulae, or MODE to change the device.
When you press EXE, the Formulator will execute the formula, and then return to wherever you ran the procedure from.
If you press ON/CLEAR you return to OPL without having run a formula.
See the OPL section of your Organiser manual for how to enter, translate and save an OPL procedure.
If a formula contains an error, a message is displayed when you run it. The message may come from the Formulator or OPL.
The formula contains a "circular reference", such as the LITRES result depending on PINTS while the PINTS result depends on LITRES. The Formulator is unable to find a place to begin calculation. One of the names in the circle is displayed after the message.
TOO MANY NAMES
The formula has more than 16 different prompts and result names.
TOO MANY CALCS
The formula contains more than 16 separate calculations.
The formula assigns to the same result name twice.
STRING TOO LONG
The result list is more than 254 characters in length (add one character for the end of every line).
OUT OF MEMORY
The Formulator has run out of memory while trying to calculate a formula.
DIVIDE BY ZERO
Division by zero was attempted - e.g. you specified 0 payments per year in the loan repayments formula.
The formula contains an error and could not be calculated.
BAD FN ARGS
The arguments to an OPL function are of the wrong type, such as sin(x,y).
A formula referred to a procedure which does not exist anywhere on the Organiser. This happens if you copy a formula which calls an OPL program to A: and run it from there when the datapak containing the OPL program has been removed.
FN ARGUMENT ERR
An invalid input combination was used, such as entering 2 as input to the ACOS formula, or specifying the three sides of a triangle as lengths 1, 1 and 3.
An invalid character such as % has been used.
A meaningless number, such as 2.3.4 has been used, or an invalid number of decimal places was specified for the display of a result
The left and right brackets in a formula do not match up.
A number is too large to be held, e.g. the factorial of 100.
BAD DEVICE CALL
An attempt has been made to call the Formulator either from within itself or from within the calculator.
TYPE MISMATCH or MISMATCHED "
One or more quote characters (") have been used in a calculation.
If you come across such an error press SPACE to re-edit the formula at the "XFORM:" prompt.
All the formulae supplied on the Formulator Datapak are printed in this appendix.
Note that although each formula is one line only on the Organiser, many of them here carry over on to more.
UK 15%,VAT:2=Price*(.15/1.15);Net:2=Price-VAT;(Price):2=Price UK 15%,Price:2=Net*1.15;VAT:2=Price-Net;(Net):2=Net France 18.6%,TVA:2=Prix*(.186/1.186);Net:2=Prix-TVA;(Prix):2=Prix France 18.6%,Prix:2=Net*1.186;TVA:2=Prix-Net;(Net):2=Net France 33%,TVA:2=Prix*(.33/1.33);Net:2=Prix-TVA;(Prix):2=Prix France 33%,Prix:2=Net*1.33;TVA:2=Prix-Net;(Net):2=Net Germany 14%,MWSt:2=Preis*(.14/1.14);Netto:2=Preis/1.14;(Preis):2=Preis Germany 14%,Preis:2=Netto*1.14;MWSt:2=Preis-Netto;(Netto):2=Netto Austria 20%,MWSt:2=Preis*(.20/1.20);Netto:2=Preis/1.20;(Preis):2=Preis Austria 20%,Preis:2=Netto*1.20;MWSt:2=Preis-Netto;(Netto):2=Netto Portugal 16%,IVA:2=Preco*(.16/1.16);Liquido:2=Preco/1.16;(Preco):2=Preco Portugal 16%,Preco:2=Liquido*1.16;IVA:2=Preco-Liquido;(Liquido):2=Liquido Spain 12%,IVA:2=Precio*(.12/1.12);Neto:2=Precio/1.12;(Precio):2=Precio Spain 12%,Precio:2=Neto*1.12;IVA:2=Precio-Neto;(Neto):2=Neto Italy 18%,IVA:2=Prezzo*(.18/1.18);Netto:2=Prezzo/1.18;(Prezzo):2=Prezzo Italy 18%,Prezzo:2=Netto*1.18;IVA:2=Prezzo-Netto;(Netto):2=Netto Belgium 19%,BTW:2=Prijs*(.19/1.19);Netto:2=Prijs/1.19;(Prijs):2=Prijs Belgium 19%,Prijs:2=Netto*1.19;BTW:2=Prijs-Netto;(Netto):2=Netto Holland 20%,BTW:2=Prijs*(.20/1.20);Netto:2=Prijs-BTW;(Prijs):2=Prijs Holland 20%,Prijs:2=Netto*1.20;BTW:2=Prijs-Netto;(Netto):2=Netto Turkey 12%,KDV:2=Fiat*(.12/1.12);Net:2=Fiat-KDV;(Fiat):2=Fiat Turkey 12%,Fiat:2=Net*1.12;KDV:2=Fiat-Net;(Net):2=Net Morocco 19%,TVA:2=Prix*(.19/1.19);Net:2=Prix-TVA;(Prix):2=Prix Morocco 19%,Prix:2=Net*1.19;TVA:2=Prix-Net;(Net):2=Net Price:2=Cost*(1+Mark Up%/100);(Cost):2=Cost Sale Price:2=Price*(1-Discount%/100);(Price):2=Price Compound Interest,Balance:2=Deposit*(1+Annual Rate%/(100*Incrs Per Year))**(Years*Inc) Current Value,:2=Future Value*(1+Annual Rate%/(100*Incrs Per Year))**(-Years*Inc) Annuity Value,Future:2=Annual Amount*(((1+Annual Rate%/(100*Incrs per Year))**(Years*Incr)-1) /(Annual R/100));Current:2=Annual A*((1-(1+Annual R/(100*Incr))**(-Years*Incr))/(Annual R/100)) Loan Repayment,:=Loan;Rate:=Annual Rate%/(100*Number Payments per Year); :2=Loan*Rate/(1-(1+Rate)**-(Years*Number)) Loan Repayment(APR),:=Loan;Rate:=(1+APR%/100)**(-1/Number Payments per Year); :2=Loan*((1-Rate)/(1-Rate**(Years*Number))/Rate) APR%:1=apr:(Loan/Payment,Number Payments per Year,Years) Repayment Mortgage,:=Loan;Rate:=Annual Rate%/100;X:=(1+Rate)**Years;Monthly :2=Loan*Rate*X/(12*(X-1)); Z:=1+Rate*.75;Z1:=Z**Years;Monthly(MIRAS):2=-(Loan<=30000)*(Loan*Z1*(Z-1)/(Z1-1)/12)-(Loan>30000)* (Monthly -625*Rate) Endowment Mortgage - does not include policy premiums,:=Loan;Rate:=Annual Rate%/1200;Monthly :2=Rate*Loan; Z:=Loan+(Loan>30000)*(Loan-30000);Monthly(MIRAS):2=(Loan-.25*(Loan+(Loan>30000)*(Loan-30000)))*Rate Take Home Pay(to 10/89),A:=Annual Salary*(1-Pension%/100); NI:=-A*.05*(A>=2236)-.02*A*((A>=3900)+(A>=5980))+.09*(A-16900)*(A>16900);Y:=A-Allowance; Z:=-.25*Y*(Y>0)-.15*(Y-20700)*(Y>20700);Pay:2=(A-NI-Z)/12;Tax:2=Z/12;N.I.:2=NI/12;Pension :2=(Annual-A)/12 Take Home Pay(from 10/89 to 4/90),A:=Annual Salary*(1-Pension%/100); NI:=-(A>2236)*(.09*(A+(A-16900)*(A>16900))-156.52);Y:=A-Allowance;Z:=-.25*Y*(Y>0)-.15*(Y-20700)*(Y>20700); Pay:2=(A-NI-Z)/12;Tax:2=Z/12;N.I.:2=NI/12;Pension :2=(Annual-A)/12
Factorial,=fact:(int(r));(r)=int(r) Gamma:4=Gamma:(n);(n)=n Beta:4=Gamma:(n)*Gamma:(m)/Gamma:(n+m);(n)=n;(m)=m Bessel:4=JBessel:(n,x);(n)=n;(x)=x Euler=euler:(int(n));(n)=int(n) Bernoulli=bernli:(int(n));(n)=int(n) Zeta=zeta:(int(n));(n)=int(n) Chebyshev Poly 1st,Y:=atan(sqr((1/(x*x))-1));:8=cos(n*Y) Chebyshev Poly 2nd,Y:=atan(sqr((1/(x*x))-1));:8=sin((n+1)*Y)/sin(Y) Binomial Coefs,=binomial:(int(n),int(r));(n)=int(n);(r)=int(r) Binomial Dist,=binomial:(int(n),int(r))*(p**r)*((1-p)**(n-r));(n)=int(n);(r)=int(r);(p)=p Poisson Prob,=exp(-a)*(a**int(r)/fact:(int(r)));(a)=a;(r)=int(r) Chi:4=Chi:(p%,n);(p%)=p%;(n)=n t Dist,Certainty%:4=100*Tdist:(int(n),x);(n)=int(n);(x)=x Normal Prob:4=normal:(x);Ordinates:4=exp(-x*x/2)*.39894;(x)=x
Triangle SAS,Side1=S1;:=A3;Side2=S2;Side3=sqr(S1*S1+S2*S2-2*S1*S2*cos(rad(A3))); t:=deg(atan(sqr((1/(1-(sin(rad(A3))/Side3*S1)**2))-1)));Angle1:2=t-(s1*s1>s2*s2+Side3*Side3)*(180-t-t); Angle2:2=180-A3-Angle1;Angle3:2=A3;Area=S1*S2*sin(rad(A3))/2 Triangle SAA,Side1=S1;:=A1;:=A2;Side2=S1/sin(rad(A1))*sin(rad(A2));Side3=S1/sin (rad(A1))*sin(rad(180-A1-A2));Angle1:2=A1;Angle2:2=A2;Angle3:2=180-A1-A2;Area=S1*Side2*sin(rad(Angle3))/2 Triangle SSS,Side1=S1;Side2=S2;Side3=S3;X:=(S1+S2+S3)/2;Y:=sqr((X*(X-S1))/(S2*S3)); Z:=sqr((X*(X-S2))/(S1*S3));Angle1:2=2*deg(atan(sqr((1/(Y*Y))-1)));Angle2:2=2*deg(atan(sqr((1/(Z*Z))-1))); Angle3:2=180-Angle1-Angle2;Area=S1*S2*sin(rad(Angle3))/2 Triangle Area,P:=(S1+S2+S3)/2;=SQR(P*(P-S1)*(P-S2)*(P-S3)) Regular Polygon,Area=Edge Len*Edge*No Sides*cos(pi/No S)/(sin(pi/No S)*4);Perimeter=Edge*No S; (Edge Len)=Edge;Long Radius=sqr(Short Radius*Short+Edge*Edge/4);Short=2*Area/(No S*Edge) Regular Polygon,Area=Long Radius*Long*No Sides*sin(2*pi/No S)/2;Perimeter=2*No S*Long*sin(pi/No S); Edge Len=Perimeter/No S;(Long Radius)=Long;Short Radius=sqr(Long*Long-Edge*Edge/4) Regular Polygon,Area=Short Radius*Short*No Sides*tan(pi/No S);Perimeter=2*No S*Short*tan(pi/No S); Edge Len=Perimeter/No S;Long Radius=sqr(Short*Short+Edge*Edge/4);(Short Radius)=Short Circle,Circumference:2=2*pi*Radius;Area:2=pi*Radius*Radius Sphere,Surface:2=Radius*Radius*4*pi;Volume:2=Radius*Radius*Radius*pi*4/3 Cone,:=Height;Slant:2=sqr(Radius*Radius+Height*Height);Surface:2=Radius*(Slant+Radius)*pi; Volume:2=Radius*Radius*Height*pi/3;(Height)=Height;(Radius)=Radius Cone,:=Slant;Height:2=sqr(-Radius*Radius+Slant*Slant);Surface:2=Radius*(Slant+Radius)*pi; Volume:2=Radius*Radius*Height*pi/3;(Slant)=Slant;(Radius)=Radius Parabola,Y(+/-)=sqr(4*Focus*X);Directrix X=-Focus;(Focus)=Focus;(X)=X Parabola,X=1/(4*Focus)*Y*Y;Directrix X=-Focus;(Focus)=Focus;(Y)=Y Ellipse,Y(+/-)=sqr(1-X*X/(a*a))*b;(X)=X;(a)=a;(b)=b Ellipse,X(+/-)=sqr(1-Y*Y/(b*b))*a;(Y)=Y;(a)=a;(b)=b Ellipse,Eccentricity=sqr(1-(1/(a*a)*b*b));Focus(+/-)=Ecc*a;Directrix X(+/-)=a/Ecc;Area=pi*a*b;(a)=a;(b)=b Hyperbola,Y(+/-)=sqr((X*X/(a*a))-1)*b;(X)=X;(a)=a;(b)=b Hyperbola,X(+/-)=sqr(1+(Y*Y/(b*b)))*a;(Y)=Y;(a)=a;(b)=b Hyperbola,Eccentricity=sqr((1/(a*a)*b*b)+1);Focus(+/-)=Ecc*a;Directrix X(+/-)=a/Ecc;(a)=a;(b)=b
Asin:2=deg(atan(x/sqr(1-x*x)));(x)=x Acos,t:=deg(atan(sqr((1/(x*x))-1)));Acos:2=t-(x<0)*(180-t-t);(x)=x Hyperbolics,Y:=exp(x);Z:=exp(-x);COSH=(Y+Z)/2;SINH=(Y-Z)/2;TANH=1-2/(exp(2*X)+1);(x)=x Sum Arithmetic Series,=(First Term+Last Term)*No of Terms/2 Sum Arithmetic Series,=First*No of Terms+Increment*No of T*(No of T-1)/2 Sum Geometric Series,:2=First*(1-R**No of Terms)/(1-R) Real Quadratic,:=a;R:=sqr(b*b-4*a*c);X1:8=(-b+R)/(2*a);X2:8=(-b-R)/(2*a);(a)=a;(b)=b;(c)=c Complex Quadrtic,:=a;I:=sqr(-b*b+4*a*c);Real:8=-b/(2*a);Imag(+/-):8=I/(2*a);(a)=a;(b)=b;(c)=c Complex Add,:=a;:=b;:=c;:=d;Real=a+c;Imag=b+d Complex Subtact,:=a;:=b;:=c;:=d;Real=a-c;Imag=b-d Complex Multiply,:=a;:=b;:=c;:=d;Real=a*c-b*d;Imag=a*d+b*c Complex Divide,:=a;:=b;:=c;:=d;X:=c*c+d*d;Real=(a*c+b*d)/X;Imag=(b*c-a*d)/X Complex Exp,X:=exp(a);Real:9=X*cos(b);Imag:9=X*sin(b) Complex Sinh,X:=exp(a);Y:=exp(-a);Real:9=(X*cos(b)-Y*cos(-b))/2;Imag:9=(X*sin(b)-Y*sin(-b))/2 Complex Cosh,X:=exp(a);Y:=exp(-a);Real:9=(X*cos(b)+Y*cos(-b))/2;Imag:9=(X*sin(b)+Y*sin(-b))/2 Polar Coords,r=sqr(x*x+y*y);Z:=deg(atan(y/x))-180*(x<0);theta:4=Z-(Z<0)*360;(x)=x;(y)=y Polar Coords,x=r*cos(rad(theta));y=r*sin(rad(theta));(r)=r;(theta)=theta Polar Add,:=r1;T1:=theta 1;:=r2;T2:=theta 2;Z:=pi-rad(T1-T2);r3=sqr(r1*r1+r2*r2-2*r1*r2*cos(Z)); X:=T1+(1+2*(((T2<T1)and((T2+180)>T1))or((T2>T1)and(T2>(T1+180))))) *deg(atan(sqr((1/(1-(sin(Z)/r3*r2)**2))-1)));theta 3:4=X+360*((X>=360)-(X<0)) Polar Multiply,:=r1;T1:=theta 1;:=r2;T2:=theta 2;r3=r1*r2;Z:=T1+T2;theta 3:4=Z+(Z>360)*360 Polar Divide,:=r1;T1:=theta 1;:=r2;T2:=theta 2;r3=r1/r2;Z:=T1-T2;theta 3:4=Z-(Z<0)*360 Spherical Coords,:=x;:=y;:=z;r=sqr(x*x+y*y+z*z);A:=deg(atan(y/x))-180*((Y<0)and(X<0)); phi:4=A-360*(A<0);B:=z/r;C:=deg(atan(sqr((1/(B*B))-1)));Theta:4=(C-180)*(z<0)-C*(z>0);(x)=x;(y)=y;(z)=z Spherical Coords,:=r;P:=rad(phi);T:=rad(theta);x=r*sin(T)*cos(P); y=r*sin(T)*sin(P);z=r*cos(T);(r)=r;(phi)=phi;(theta)=theta Dot Product,:=A1;:=A2;:=A3;:=B1;:=B2;:=B3;=A1*B1+A2*B2+A3*B3 Cross Product,:=A1;:=A2;:=A3;:=B1;:=B2;:=B3;i=A2*B3-A3*B2;j=A3*B1-A1*B3;k=A1*B2-A2*B1
Inches>,(Inches):2=Inches;Feet:2=Inches/12;Yards:2=Feet/3;Miles:2=Yards/1760;Naut Miles:2=Feet/6080; metres:2=Inch*.0254;Kilometres:2=metres/1000 Feet>,Inches:2=Feet*12;(Feet):2=Feet;Yards:2=Feet/3;Miles:2=Yards/1760;Naut Miles:2=Feet/6080; metres:2=Feet*.3048;Kilometres:2=metres/1000 Yards>,Inches:2=Yards*36;Feet:2=Yards*3;(Yards):2=Yards;Miles:2=Yards/1760;Naut Miles:2=Feet/6080; metres:2=Yards*.9144;Kilometres:2=metres/1000 Miles>,Inches:2=Miles*63360;Feet:2=Miles*5280;Yards:2=Miles*1760;(Miles):2=Miles;Naut Miles:2=Feet/6080; metres:2=Miles*1609.343;Kilometres:2=metres/1000 NMiles>,Inches:2=NMiles*72960;Feet:2=NMiles*6080;Yards:2=Feet/3;Miles:2=Yards/1760;(Naut Miles):2=NMiles; metres:2=NMiles*1853.183;Kilometres:2=metres/1000 Metres>,Inches:2=metres*39.3701;Feet:2=metres*3.28084;Yards:2=metres*1.0936146;Miles:2=metres*6.213717e-4; Naut Miles:2=metres*5.39612e-4;(metres):2=metres;Kilometres:2=metres/1000 Km>,Inches:2=Km*39370.1;Feet:2=Km*3280.84;Yards:2=Km*1093.6146;Miles:2=Km*.6213717; Naut Miles:2=Km*.539612;metres:2=Km*1000;(Kilometres):2=Km Fathoms>,(Fathom)=Fathoms;Yards=Fathoms*2;Metres:2=Fathoms*1.8288 Yards>,Fathom=Yards/2;(Yards)=Yards;Metres:2=Yards*.9144 Metres>,Fathom:2=metres*.5468;Yards:2=Fathom*2;(metres)=metres Microns>,(Microns):4=Microns;Angstroms:4=Microns*1e4;Fermis:4=Microns*1e9;Metres:4=Microns*1e-6 Angstroms>,Microns:4=Angstroms*1e-4;(Angstroms):4=Angst;Fermis:4=Angst*1e5;Metres:4=Angst*1e-10 Fermis>,Microns:4=Fermis*1e-9;Angstroms:4=Fermis*1e-5;(Fermis):4=Fermis;Metres:4=Fermis*1e-15 Metres>,Microns:4=metres*1e6;Angstroms:4=metres*1e10;Fermis:4=metres*1e15;(metres):4=metres Au>,(Astronomic units)=Astronomic units;Light Years=Astro*1.58e-5;Parsecs=Astro*4.85e-6; Metres=Astro*1.496e11 Light Years>,Au=Light Years*63242;(Light Years)=Light;Parsecs=Light*.3068;Metres=Light*9.461e15 Parsecs>,Au=Parsecs*206150;Light Years=Parsecs*3.26;(Parsecs)=Parsecs;Metres=Parsecs*3.084e16 Metres>,Au=Metres*6.6845e-12;Light Years=Metres*1.057e-16;Parsecs=Metres*3.24e-17;(Metres)=Metres BMU>,(Basic Measurement Units):2=BMU;Points:2=BMU/6;Picas:2=BMU/72;Inches:2=BMU/1440; Centimetres:2=BMU*1.7639e-3 Points>,BMU:2=Points*6;(Points):2=Points;Picas:2=Points/12;Inches:2=Points/240;Centimetres:2=Points*.0105833 Picas>,BMU:2=Picas*72;Points:2=Picas*12;(Picas):2=Picas;Inches:2=Picas/20;Centimetres:2=Picas*.127 Inches>,BMU:2=Inches*1440;Points:2=Inches*240;Picas:2=Inches*20;(Inches):2=Inches;Centimetres:2=Inches*2.54 cm>,BMU:2=cm*566.93;Points:2=cm*94.488;Picas:2=cm*7.874;Inches:2=cm*.3937;(Centimetres):2=cm Sq Inches>,(Sq Inches):2=Sq Inches;Sq Feet:2=Sq I/144;Sq Yards:2=Sq F/9;Acres:2=Sq Y/4840; Sq Miles:2=Acres/640;Sq Metres:2=Sq I*6.4516E-4;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Sq Feet>,Sq Inches:2=Sq Feet*144;(Sq Feet):2=Sq F;Sq Yards:2=Sq F/9;Acres:2=Sq Y/4840; Sq Miles:2=Acres/640;Sq Metres:2=Sq F*.092903;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Sq Yards>,Sq Inches:2=Sq Yards*1296;Sq Feet:2=Sq Y*9;(Sq Yards):2=Sq Y;Acres:2=Sq Y/4840; Sq Miles:2=Acres/640;Sq Metres:2=Sq Y*.836126;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Acres>,Sq Inches:2=Acres*6272640;Sq Feet:2=Acres*43560;Sq Yards:2=Acres*4840;(Acres):2=Acres; Sq Miles:2=Acres/640;Sq Metres:2=Acres*4046.85;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Sq Miles>,Sq Inches:2=Sq Miles*4.01449E9;Sq Feet:2=Sq Mi*27878400;Sq Yards:2=Sq Mi*3097600; Acres:2=Sq Mi*640;(Sq Miles):2=Sq Mi;Sq Metres:2=Sq Mi*2589984;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Sq Metres>,Sq Inches:2=Sq Metres*1550.01;Sq Feet:2=Sq Me*10.7639;Sq Yards:2=Sq Me*1.196; Acres:2=Sq Y/4840;Sq Miles:2=Acres/640;(Sq Metres):2=Sq Me;Hectares:2=Sq Me*1e-4;Sq km:2=Hect/100 Hectares>,Sq Inches:2=Hectares*1.5501e7;Sq Feet:2=Sq I/144;Sq Yards:2=Sq F/9;Acres:2=Sq Y/4840; Sq Miles:2=Acres/640;Sq Metres:2=Hect*1e4;(Hectares):2=Hect;Sq km:2=Hect/100 Sq km>,Sq Inches:2=Sq km*1.5501e9;Sq Feet:2=Sq I/144;Sq Yards:2=Sq F/9;Acres:2=Sq Y/4840; Sq Miles:2=Sq km*.3861;Sq Metres:2=Sq K*1e6;Hectares:2=Sq K*1e4;(Sq km):2=Sq K Fl oz>,(Fl oz):2=Fl oz;Pints:2=Fl O/20;Gallons:2=Pints/8;Litres:2=FL O*.028413; US Gallon:2=FL O*.0075059;Barrels:2=US G/42 Pints>,Fl oz:2=Pints*20;(Pints):2=Pints;Gallons:2=Pints/8;Litres:2=Pints*.56826; US Gallon:2=Pints*.1501187;Barrels:2=US G/42 Gallons>,Fl oz:2=Gallons*160;Pints:2=Gallons*8;(Gallons):2=Gallons;Litres:2=Gallons*4.54609; US Gallon:2=Gallons*1.20095;Barrels:2=US G/42 Litres>,Fl oz:2=Litres*35.195;Pints:2=Litres*1.75975;Gallons:2=Litres*.21997;(Litres):2=Litres; US Gallon:2=Litres*.26417;Barrels:2=US G/42 US Gallons>,Fl oz:2=US Gallons*133.228;Pints:2=US G*6.6614;Gallons:2=US G*.83267; Litres:2=US G*3.7854;(US Gallon):2=US G;Barrels:2=US G/42 Barrels>,Fl oz:2=Barrels*5595.6;Pints:2=Barrels*279.78;Gallons:2=Barrels*34.972; Litres:2=Barrels*158.987;US Gallon:2=Barrels*42;(Barrels):2=Barrels Cu Inches>,(Cubic Inches):2=Cu Inches;Cubic Feet:2=Cu I/1728;Cubic Yards:2=Cu I/46656; Cubic Centimetres:2=Cu I*16.387;Litres:2=Cu I*.016387 Cu Feet>,Cubic Inches:2=Cu Feet*1728;(Cubic Feet):2=Cu F;Cubic Yards:2=Cu F/27; Cubic Centimetres:2=Cu F*28317;Litres:2=Cu F*28.317 Cu Yards>,Cubic Inches:2=Cu Yards*46656;Cubic Feet:2=Cu Y*27;(Cubic Yards):2=Cu Y; Cubic Centimetres:2=Cu Y*764555;Litres:2=Cu Y*764.555 CC>,Cubic Inches:2=CC*.061024;Cubic Feet:2=CC*.3531467e-4;Cubic Yards:2=CC*.130795e-5; Cubic Centimetres:2=CC;Litres:2=CC/1000 Litres>,Cubic Inches:2=Litres*61.024;Cubic Feet:2=Litres*.03531476;Cubic Yards:2=Litres*.130795e-2; Cubic Centimetres:2=Litres*1000;(Litres):2=Litres oz>,(oz):2=oz;Pounds:2=oz/16;Stone:2=Pounds/14;CWT:2=Stone/8; Ton(short):2=Pounds/2000;Ton(long):2=CWT/20;Kg:2=oz*.0283495;Tonnes:2=Kg/1000 Pounds>,oz:2=Pounds*16;(Pounds):2=Pounds;Stone:2=Pounds/14;CWT:2=Stone/8; Ton(short):2=Pounds/2000;Ton(long):2=CWT/20;Kg:2=Pounds*.453592;Tonnes:2=Kg/1000 Stone>,oz:2=Stone*224;Pounds:2=Stone*14;(Stone):2=Stone;CWT:2=Stone/8; Ton(short):2=Pounds/2000;Ton(long):2=CWT/20;Kg:2=Stone*6.35029;Tonnes:2=Kg/1000 CWT>,oz:2=CWT*1792;Pounds:2=CWT*112;Stone:2=CWT*8;(CWT):2=CWT; Ton(short):2=Pounds/2000;Ton(long):2=CWT/20;Kg:2=CWT*50.8023;Tonnes:2=Kg/1000 Short Tons>,oz:2=Short Tons*32000;Pounds:2=Short*2000;Stone:2=Pounds/14;CWT:2=Stone/8; (Ton(short)):2=Short;Ton(long):2=Short*25/28;Kg:2=Short*907.184;Tonnes:2=Kg/1000 Long Tons>,oz:2=Long Tons*35840;Pounds:2=Long*2240;Stone:2=Long*160;CWT:2=Long*20; Ton(short):2=Pounds/2000;(Ton(long)):2=Long;Kg:2=Long*1016.047;Tonnes:2=Kg/1000 Kg>,oz:2=kg*35.27395;Pounds:2=Kg*2.20462;Stone:2=Kg*.157473;CWT:2=Kg*.0196841; Ton(short):2=Pounds/2000;Ton(long):2=Kg*9.84206e-4;(Kg):2=Kg;Tonnes:2=Kg/1000 Tonnes>,oz:2=Tonnes*35273.95;Pounds:2=Tonnes*2204.62;Stone:2=Tonnes*157.473;CWT:2=Tonnes*19.6841; Ton(short):2=Pounds/2000;Ton(long):2=Tonnes*.984206;Kg:2=Tonnes*1000;(Tonnes):2=Tonnes oz Fine or Troy>,(oz tr)=oz tr;oz av=oz tr*1.09714;Gram=oz tr*31.1035 oz Avoirdupois>,oz tr=oz av*.911458;(oz av)=oz av;Gram=oz av*28.3495 Gram>,oz tr=Gram*.0321507;oz av=Gram*.03527395;(Gram)=Gram Sec of Arc>,(Sec of Arc):2=Sec Of Arc;Min of Arc:2=Sec/60;Degrees:2=Min/60;Radians:2=Sec*pi/648000 Min of Arc>,Sec of Arc:2=Min Of Arc*60;(Min of Arc):2=Min;Degrees:2=Min/60;Radians:2=Min*pi/10800 Degrees>,Sec of Arc:2=Degrees*3600;Min of Arc:2=Degrees*60;(Degrees):2=Degrees;Radians:2=Degrees*pi/180 Radians>,Sec of Arc:2=Radians*648000/pi;Min of Arc:2=Radians*10800/pi; Degrees:2=Radians*180/pi;(Radians):2=Radians Seconds>,(Seconds):2=Seconds;Minutes:2=Seconds/60;Hours:2=Minutes/60;Days:2=Hours/24;Weeks:2=Days/7; Tropical Year:2=Seconds*3.1689e-8 Minutes>,Seconds:2=Minutes*60;(Minutes):2=(Minutes);Hours:2=Minutes/60;Days:2=Hours/24;Weeks:2=Days/7; Tropical Year:2=Minutes*1.9013e-6 Hours>,Seconds:2=Hours*3600;Minutes:2=Hours*60;(Hours):2=Hours;Days:2=Hours/24;Weeks:2=Days/7; Tropical Year:2=Hours*1.1408e-4 Days>,Seconds:2=Days*86400;Minutes:2=Days*1440;Hours:2=Days*24;(Days):2=Days;Weeks:2=Days/7; Tropical Year:2=Days*2.7379E-3 Weeks>,Seconds:2=Weeks*604800;Minutes:2=Weeks*10080;Hours:2=Weeks*168;Days:2=Weeks*7;(Weeks):2=Weeks; Tropical Year:2=Weeks*.019165 Years>,Seconds:2=Years*3.1557e7;Minutes:2=Years*525950;Hours:2=Years*8765.8;Days:2=Years*365.24; Weeks:2=Days/7;(Tropical Year):2=Years MPH>,(MPH):2=MPH;Feet/Sec:2=MPH*22/15;KPH:2=MPH*1.609343;Metres/Sec:2=KPH*5/18;Knots:2=MPH*33/38 FPS>,MPH:2=FPS*15/22;(Feet/Sec):2=FPS;KPH:2=FPS*1.09728;Metres/Sec:2=KPH*5/18;Knots:2=MPH*33/38 KPH>,MPH:2=KPH*.621372;Feet/Sec:2=MPH*22/15;(Km/Hour):2=KPH;Metres/Sec:2=KPH*5/18;Knots:2=MPH*33/38 Metres/Sec>,MPH:2=Metres per Sec*2.23694;Feet/Sec:2=MPH*22/15;KPH:2=Metres*18/5;(Metres/Sec):2=Metres; Knots:2=MPH*33/38 Knots>,MPH:2=Knots*38/33;Feet/Sec:2=MPH*22/15;KPH:2=Knots*1.8532;Metres/Sec:2=KPH*5/18;(Knots):2=Knots MilesUKg>,(MilesUKgall):2=MilesUKgallon;MilesUSgall:2=MilesUK*.83267;KmLitres:2=MilesUK*.35401 MilesUSg>,MilesUKgall:2=MilesUSgallon*1.20095;(MilesUSgall):2=MilesUS;KmLitres:2=MilesUS*.42514 KmLitres>,MilesUKgall:2=KmL*2.82481;MilesUSgall:2=KmL*2.35215;(KmLitres):2=KmLitres Poundals>,(Poundals)=Poundals;lbf=Poundals*.031081;Newtons=Poundals*.138255 lbf>,Poundals=lbf*32.17404;(lbf)=lbf;Newtons=lbf*4.448222 Newtons>,Poundals=Newtons*7.233011;lbf=Newtons*.224809;(Newton)=Newtons Dynes>,Newtons=Dynes*1e-5;(Dynes)=Dynes Newtons>,Dynes=Newtons*1e5;(Newtons)=Newtons Joules>,(Joules)=Joules;Ergs=Joules*1e7;Calories=Joules*.238846; Therms=Joules*9.4787e-9;Btu=Therms*1e5;KWH=Joules/3.6e6 Ergs>,Joules=Ergs*1e-7;(Ergs)=Ergs;Calories=Ergs*.238846e-7;Therms=Ergs*9.4787e-16; Btu=Therms*1e5;KWH=Joules/3.6e6 Calories>,Joules=Calories*4.1868;Ergs=Joules*1e7;(Calories)=Calories; Therms=Calories*3.9685e-8;Btu=Therms*1e5;KWH=Calories*1.163e-6 Therms>,Joules=Therms*1.055e8;Ergs=Joules*1e7;Calories=Therms*2.5198e7; (Therms)=Therms;Btu=Therms*1e5;KWH=Therms*29.306 Btu>,Joules=Btu*1.055e3;Ergs=Joules*1e7;Calories=Btu*251.98;Therms=Btu*1e-5;(Btu)=Btu;KWH=Btu*2.9306e-4 KWH>,Joules=KWH*3.6e6;Ergs=Joules*1e7;Calories=KWH*8.5986e5;Therms=KWH*.034123;Btu=Therms*1e5;(KWH)=KWH Joules>,(Joules)=Joules;eVolts=Joules*6.242e18;Hertz=Joules*1.509e33;Kelvin=Joules*7.244e22; Kg=Joules*1.113e-17 eVolts>,Joules=eVolts*1.602e-19;(eVolts)=eVolts;Hertz=eVolts*2.418e14;Kelvin=eVolts*1.16e4; Kg=eVolts*1.783e-36 Hertz>,Joules=Hertz*6.626e-34;eVolts=Hertz*4.136e-15;(Hertz)=Hertz;Kelvin=Hertz*4.8e-11;Kg=Hertz*7.375e-51 Kelvin>,Joules=Kelvin*1.381e-23;eVolts=Kelvin*8.62e-5;Hertz=Kelvin*2.084e10;(Kelvin)=Kelvin; Kg=Kelvin*1.537e-40 Kg>,Joules=kg*8.988e16;eVolts=kg*5.61e35;Hertz=kg*1.356e50;Kelvin=kg*6.511e39;(Kg)=kg PSI>,(Pounds/Sq Inch)=PSI;Pascals=PSI*6894.8;mmHg=PSI*51.714;inHg=PSI*2.036;Millibars=Pascal/100; Atmosphere=PSI*.06805 Pascals>,PSI=Pascals*1.4504e-4;(Pascals)=Pascals;mmHg=Pascals*7.501e-3;inHg=Pascals*2.953e-4; Millibars=Pascals/100;Atmosphere=Pascals*9.869e-6 mmHg>,PSI=mmHg*.01934;Pascals=mmHg*133.3;(mmHg)=mmHg;inHg=mmHg*.03937;Millibars=Pascals/100; Atmosphere=mmHg/760 inHg>,PSI=inHg*.4911;Pascals=inHg*3386;mmHg=inHg*25.4;(inHg)=inHg;Millibars=Pascals/100; Atmosphere=inHg*.03342 Millibars>,PSI=Millibars*.014504;Pascals=Millibars*100;mmHg=Millibars*.7501;inHg=Millibars*.02953; (Millibars)=Millibars;Atmosphere=Millibars*9.869e-4 Atmosphere>,PSI=Atmosphere*14.7;Pascals=Atmosphere*1.013e5;mmHg=Atmosphere*760;inHg=Atmosphere*29.9; Millibars=Atmosphere*1013;(Atmosphere)=Atmosphere Gauss>,(Gauss):2=Gauss;Tesla:2=Gauss*1e4 Tesla>,Gauss:2=Tesla*1e-4;(Tesla):2=Tesla Curies>,(Curies)=Curies;Becquerels:2=Curies*3.7e10 Becquerels>,Curies:2=Becquerels*2.7e-11;(Becquerels)=Becq Rads>,(Rads):2=Rads;Grays=Rads/100 Grays>,Rads:2=Grays*100;(Grays)=Grays Watts>,(Watts)=Watts;Horsepower=Watts*1.341E-3 Horsepower>,Watts=Horsepower*745.7;(Horsepower)=Horsepower RPM>,(RPM):2=Revs per Minute;Hertz:2=Revs/60 Hertz>,RPM:2=Hertz*60;(Hertz)=Hertz Fahrenheit>,(Fahrenheit)=Fahrenheit;Celsius:2=(Fahrenheit-32)*5/9;Kelvin:2=Celsius+273.15 Celsius(Centigrade)>,Fahrenheit:2=32+Celsius*9/5;(Celsius)=Celsius;Kelvin:2=Celsius+273.15 Kelvin>,Fahrenheit:2=32+(Kelvin-273.15)*9/5;Celsius:2=Kelvin-273.15;(Kelvin):2=Kelvin em>,(Electron Masses)=Electron M;pm=Electron M*5.4463e-4;nm=Electron M*5.4388e-4;kg=Electron M*9.1091e-31 pm>,em=Proton Masses*1836.1;(Proton Masses)=Proton M;nm=Proton M*.99863;kg=Proton M*1.6725e-27 nm>,em=Neutron Masses*1838.6;pm=Neutron M*1.001375;(Neutron Masses)=Neutron M;kg=Neutron M*1.6748e-27 Kg>,em=kg*1.0978E30;pm=kg*5.979e26;nm=kg*5.9708e26;(kg)=kg
Watts=Amps*Volts Watts=Amps*Amps*Ohms Watts=Volts*Volts/Ohms Joules=Farads*Volts*Volts/2 Farads=Coulombs/Volts Volts=Amps*Ohms Amps=Volts/Ohms Ohms=Volts/Amps Const Acc,Final Velocity=Initial Velocity+Acceleration*Time;Distance=Init*Time+Acc*Time*Time/2 Const Acc,Final Velocity=sqr(Initial Velocity*Initial V+2*Acceleration*Distance) Const Acc,Distance=(Initial Velocity+Final Velocity)*Time/2 Const Acc,Energy=Mass*(-Initial Velocity*Initial V+Final Velocity*Final V)/2 Force=Mass*Acceleration Momentum=Mass*Velocity Final Speed=(Initial Speed 1*Mass 1+Initial Speed 2*Mass 2)/(Mass 1+Mass 2) Circular Motion,Acceleration=Velocity*Velocity/Radius Circular Motion,Centripetal Force=Mass*Velocity*Velocity/Radius;Acceleration=Cent/Mass Joules=Newtons*Metres Newtons=kg*MetresPerSec2 Focal Length=1/(1/Object Dist+1/Image Dist) Image Dist=1/(1/Focal Length-1/Object Dist) Pendulum Period(sec),:2=2*pi*sqr(Metres/9.807) Pendulum Period(sec),:2=2*pi*sqr(Feet/32.17) Earth Satellite,R:=6370+Km Height;Speed(Kms/sec):2=6370*sqr(9.8e-3/R);Period(Hours):2=2*pi*R/Speed/3600 Resistance,:2=1/(1/R1+1/R2) RC Circuit constant V,Charge Growth=Farads*Voltage*(1-exp(-Seconds/(Ohms*Farads))) RC Circuit,Charge Decay=Farads*Init Voltage*exp(-Seconds/(Ohms*Farads)) RL Circuit constant V,Amps Growth=Voltage/Ohms*(1-exp(-Ohms*Seconds/Henrys)) RL Circuit,Amps Decay=Init Amps*(exp(-Ohms*Seconds/Henrys)) AC Series Circuit,Radians:=Frequency*2*pi;Volts=Peak Volts*sin(Radians*Seconds) AC Series Circuit,Radians:=Frequency*2*pi;Amps=Peak Volts/sqr(Ohms*Ohms+(Radians*Henrys-1 /(Radians*Farads))**2)*cos(Radians*Seconds-atan((Radians*Henrys-1/(Radians*Farads))/Ohms)) AC Series Circuit,Radians:=Frequency*2*pi;Impedance=sqr(Ohms*Ohms+(Radians*Henrys-1/(Radians*Farads))**2) Resonant Frequency=1/(sqr(Farads*Henrys)*2*pi) Coulombs Law,Force=-Charge 1*Charge 2*8.98e9/(Permittivity*Radius*Radius) Coulombs Law,Energy=Charge 1*Charge 2*8.98e9/Radius Coulombs Law,Voltage=Charge*8.98e9/(Permittivity*Radius) Boyles Law,Pressure=Gas Constant/Volume Boyles Law,Volume=Gas Constant/Pressure Adiabatic Gas Law,X:=Init Vol/Final Vol;Pressure=Init Pressure*(X**Gamma); Kelvin=Init Kelvin*(X**(Gamma-1));Work=(Final V*Pressure-Init V*Init P)/(1-Gamma) Ideal Gas Law,Cubic Metres:2=8.31*Moles*Kelvin/Pascal Ideal Gas Law,Pascal:2=8.31*Moles*Kelvin/Cubic Metres Expanding Gas (Isothermal),Joules=8.31*Moles*Kelvin*(ln(Final Cu M/Init Cu M)) Expanding Gas (Adiabatic),Joules=(Final Pascals*Final Cu M-Init Pascals*Init Cu M)/(Gamma-1) Deniers=9e6*Kg/Metres Kg=Deniers*Metres/9e6 Metres=9e6*Kg/Deniers Rads/Hour(approx),:2=Curies*MeVs/(2*Metres*Metres) Radiation:2=Init Radiation*exp(-ln(2)*Time/Half Life)
Radar range,Nmiles:1=2.21*sqr(Height in Metres);Km:1=1.85*Nmiles Sea Horizon,Nmiles:1=2.12*sqr(Height in Metres);Km:1=1.85*Nmiles Extreme range,Nmiles:1=2.12*(sqr(Observer Height in Metres)+sqr(Object Height in Metres));Km:1=1.85*Nmiles Barometer Correction to Mean Sea Level,approx:1=Metres/8-Celsius*Metres/2100 A:=App Speed;B:=App Bear;C:=Drift Speed;D:=Drift Bear;X:=pi-rad(B-D);True Speed:2=sqr(A*A+C*C-2*A*C*cos(X)); Y:=B+(1+2*(((D<B)and(D+180>B))or((D>B)and(D>B+180))))*deg(atan(sqr((1/(1-(sin(X)*C/True Speed)**2))-1))); True Bear:0=Y+360*((Y>=360)-(Y<0)) A:=True Speed;B:=True Bear;C:=Drift Speed;D:=Drift Bear;X:=rad(D-B);App Speed:2=sqr(A*A+C*C-2*A*C*cos(X)); Y:=B-(1+2*(((D<B)and(D+180>B))or((D>B)and(D>B+180))))*deg(atan(sqr((1/(1-(sin(X)/App Speed*C)**2))-1))); App Bear:0=Y+360*((Y>=360)-(Y<0))
Photo printing,New Exposure:2=Old exposure*(New Height/Old Height)**2 Rectangular room,Wall Area=2*Height*(Width+Length);Ceiling/Floor=Width*Length;Total Area=Wall+2*Ceiling
Abbreviating names Aborting a Calculation, (2) Accuracy Analysing a Formula
BAD CHARACTER error BAD DEVICE CALL error BAD FN ARGS error BAD NUMBER error
Calculation order CIRCULAR REF error Circular refs, (2) Colons Commas Comms Link Copying Formulae
Data File (XFORM) copying from Datapak copying data from removing Decimal Places DIVIDE BY ZERO error
Editing Formulae Equals Sign Erasing Formulae Error messages EXPONENT RANGE error Expressions
Finding Formulae find all find next menu method quick method FN ARGUMENT error Formulae analysing cancelling calculation editing erasing finding multiple-calculation saving single-calculation supplied, list supplied, using
Keyboard mode, (2) ON/CLEAR
main menu running formulae from Memory occupied MISMATCHED " error MISMATCHED ()'s error MISSING PROC error
OPL functions in formulae XFORM: instruction Order of calculation OUT OF MEMORY error Overwriting Formulae
Prompt names abbreviating
Quick find method Quitting the Program
Removing the Datapak REPEATED RESULT error Result List Result Names abbreviating Running the Program
Saving Formulae Search clue, (2) Semicolons Speed of Calculation STRING TOO LONG error Supplied formulae copying functions provided listed using SYNTAX ERROR error
Titles TOO MANY CALCS error TOO MANY NAMES error TYPE MISMATCH error
XFORM data file XFORM: entry prompt OPL instruction