On Line RPN Calculator
Contents
Intro
Screen Display Control
Basic Math
Transendental Functions
Statistical Functions
Repeat Commands
Unit Conversions
Loan Finance and Date Functions
Stack Control
Variables
User Defined Functions
RPN Calculator Examples
Intro
The RPN calculator is a powerful tool for doing things you might normally
do with a calculator, and more. It uses Reverse Polish Nomenclature (RPN)
in its expressions, numbers first, followed by operators, similar in concept
to my trusty HP HP48GX RPN Expandable Graphic Calculator
The RPN calculator gives users the ability to create their own functions, and with a single function they could make calculations that fill all 26 variables. This minimal programming ability is what amplifies the calculator's usability above most all traditional calculators. It's handily available for anyone with an internet connection, ready for any college or university student, or anyone else needing math, financial, statistical or other general calculater functions.
All operators work with the stack. Math operators work with the top
value(s) on the stack and leave results on the stack. Memory operators
move values either from the stack to the variables a
thru z
, or
from the variables to the stack.
The program is different from most calculators in that one can either enter commands into the command window, or click on function buttons. It's also different in that with a typical calculator, clicking on a button performs the indicated operation. With this calculator, clicking on a button other than Enter places the command in the command window. Multiple calculations can be entered, then pressing the keyboard enter key or clicking on the Enter button executes the command(s).
Because some of the more powerful aspects are best implemented with a keyboard, the calculator works very well with Desktops, Laptops, and Chromebooks. However, the keypad utilty does make it work pretty well with Tablets as well. The RPN calculator has been successfully tested with Google Chrome, Firefox, Seamonkey, Opera, and an Android tablet and Android phone.
The command box concept may seem awkward at first, but offers some real
power as you learn the calculator. For example, one can enter the command:
10 20 30 40 50 60 all nput a to put the values 10 thru 60 into variables
a
thru f
, all as one statement. Commands are saved in a history
and can be recalled for editing and re-use by clicking on the History
button. More power is available when you learn how to define your own
operations
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Display Control Operators
Screen control operators select the keypad mode to display, and the numeric display format The keypad selections are only available through button clicks. The numeric display functions can be keyboard or keypad selected.
| Example | Result |
|---|---|
| ee | Switch numeric display to/from exponential format |
| 3 nd | Switch numeric display to 3 decimal places |
| cls | Clear all values from stack |
| clm | Clear all variables |
| Math Ops | Sets keypad to basic math operators |
| Stats Ops | Sets keypad to statistical operators |
| Units Ops | Sets keypad to unit conversion operators |
| User Keys | Sets keypad to user defined operators |
| User Defs | Sets keypad to user definition display |
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Basic Commands
The basic math operators, like +, -, *, / (for add, subtract, multiply, and divide), all work with pairs of numbers on the stack.
| Example | Result |
|---|---|
| 30 neg | Negate 30, leaves -30 |
| 30 +/- | Keypad negate 30, leaves -30 |
| 10 20 + | Puts 10 and 20 on the stack and adds them, leaving the sum. |
| 30 14 - | Subtracts 14 from 30 (top is subtracted from next level). |
| 3 8 * | Multiplies 3 times 8, leaving result on stack. |
| 33 12 / | Divides 33 by 12, leaving result on stack. |
| 10 sqr | Square the number 10 |
| 13 sqrt | Compute square root of 13 |
| 2 1/x | Compute reciprocal of 2, result is 0.5 |
| int | Leave integer portion of top stack value |
| frac | Leave fractional portion of top stack value |
| min | Leave mininum of top two stack on stack |
| max | Leave maximum of top two stack on stack |
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Transcendental Operators
Note, all of the trig functions work with radians. Use the rad operator to turn the top stack value into radians, and deg operator to go back to degrees. For example, to get sine of 30 degrees: 30 rad sin. To get arc-sine of .5 as degrees: .5 asin deg.
| Example | Result |
|---|---|
| pi | Put value of PI on the stack |
| 30 rad sin | Returns sine of 30 degrees (converts to radians first) |
| 25 rad cos | Returns cosine of 25 degrees. |
| 45 rad tan | Returns tangent of 45 degrees. |
| .5 asin deg | Returns arc-sine of .5 as degrees. |
| .5 acos deg | Returns arc-cosine of .5 as degrees. |
| .5 atan | Returns arc-tangent of .5 as radians. |
| 300 log | Returns the base 10 log of 300. |
| 300 ln | Returns the base e log of 300. |
| 3 exp10 | Raises 10 to the power of 3. |
| 3 exp | Raises e to the power of 3. |
| 12 3 ^ | Raises 12 to the 3rd power. |
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Statistical Functions
The RPN calculator has a number of statistical and probability functions. These often work on several values at once, either on the stack or in a consecutive range of variables. For example, the fit function will compute the slope and offset of a range of values assuming that the X values of a Y=mX+b equation is a simple count, 1, 2, 3, ... . This will work for any data that's obtained at equal increments in time for example, like daily, or monthly.
The res function, given the same range used in the fit
function, will compare the range variable values against the computed
line and leave a corresponding list of fit errors on the stack. For
example: fit a g computes a slope and offset from values in
a
thru z
, and res a g will compare the computed line
values with the values in a thru g, leaving the errors on the stack. The
computed slope and offset are left on the stack, and saved internally for
options that need them.
The x2y function uses the most recent fit results to compute
corresponding Y values for any given range of X values on the stack, again
assuming Xs of the fit interval were 1 thru number_of_points. This can be used
to compute Y values for any X values, within or outside of the original fit
range. For example, for fit a e, variables a
thru e
amount
to 5 points, which assume X values from 1 to 5. To extrapolate the next few Y
values from the fit, put the desired X values on the stack and use the
x2y operator. 6 13 x2y will extrapolate the 5 point line to
give Y values for X values 6 thru 13.
The do operator iterates an operation, placing each value of a variable range on the stack prior to calling the desired function. The operator looped upon must be a single operator, but using a user defined operation, this can lead to significant power.
As a simple example, do a f log computes the log of each value from variables a thru f, leaving the results on the stack. 5 nput n would place the log values in the display's second column beside the original values in the expected order.
But suppose you wanted the log of each number in base 2? Since do can only repeatedly execute a single operation, just define your own operator as follows: def log2 log 2 log /, which takes the log of a passed in (on the stack) value, and divides by the log of two, which leaves the log in base 2. Then do a f log2 would execute your definition, which has been reduced to a single name using def.
| Example | Result |
|---|---|
| 6 ! | Computes 6 factorial, or 720 |
| 13 3 nCr | Computes the number of combinations of 3 in 13 |
| 13 3 nPr | Computes the number of permutations of 3 in 13 |
| 0 12 2 seq | Generates sequence from 0 to 12 with increment 2 |
| sum a f | Computes the sum of variables a thru f |
| avg a f | Computes the average of variables a thru f |
| var a f | Computes the variance of variables a thru f |
| std a f | Computes the std deviation of variables a thru f |
| ssum | Computes the sum of all stack values |
| savg | Computes the average of all stack values |
| svar | Computes the variance of all stack values |
| sstd | computes the std deviation of all stack values |
| rnd | Returns a uniform (0 to 1) random number |
| fit a f | Fits a line thru variables a to f and leaves offset and slope on stack |
| res a f | Computes the residuals of the last line fit |
| 7 10 x2y | Extrapolates the line fit at X values 7 to 10 |
| do a c sqrt | Computes sqrt of values in a thru c, leaving 3 values on stack |
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Unit Conversion Operators
The calculator has a number of built in unit conversions. These can be used in sequence to get conversions not already defined. For example, to get a conversion from kilometers to inches: 3 km2mi mi2yd yd2ft ft2in. Of course, if you needed such a conversion often, you could define it as a new operation thus: def km2in km2mi mi2yd yd2ft ft2in. Then you could use the new operation as follows: 10 km2in.
| Example | Result |
|---|---|
| 30.5 d2hms | converts degrees to hms format: 303000 |
| 304500 hms2d | converts hms format to degrees: 30.75 |
| 3 ft2in | Converts 3 feet to 36 inches |
| 42 in2ft | Converts 42 inches to 3.5 feet |
| 4 yd2ft | Converts 4 yards to 12 feet |
| 30 ft2yd | Converts 30 ft to 10 yards |
| 2640 yd2mi | Converts 2640 yards to 1.5 miles |
| 1.5 mi2yd | Converts 1.5 miles to 2640 yards |
| 3 in2cm | Converts 3 inches to 7.62 cm |
| 7.62 cm2in | Converts 7.62 cm to 3 inches |
| 6 ft2m | Converts 6 feet to 1.8288 meters |
| 1.8288 m2ft | Converts 1.8288 meters to 6 feet |
| 3 yd2m | Converts 3 yards to 2.7432 meters |
| 2.7432 m2yd | Converts 2.7432 meters to 3 yards |
| 3 mi2km | Converts 3 miles to 4.82... km |
| 10 km2mi | Converts 10 km to 6.2... miles |
| 300 ci2cc | Converts 300 cubic inches to 4916... cc |
| 5200 cc2ci | Converts 5200 cc to 317... cubic inches |
| 6 qt2lt | Converts 6 quarts to 5.6... liters |
| 10 lt2qt | Converts 10 liters to 10.5... quarts |
| 10 gal2lt | Converts 10 gallons to 37.8... liters |
| 10 lt2gal | Converts 10 liters to 2.6... gallons |
| 6 gal2cf | Converts 6 gallons to 0.8... cubic feet |
| 3 cf2gal | Converts 3 cubic feet to 22.4... gallons |
| 30 lb2kg | Converts 30 pounds to 13.6... kilograms |
| 30 kg2lb | Converts 30 kilograms to 66.1... pounds |
| 95 f2c | Converts 95 deg Fahrenheit to 35 deg Celsius |
| 40 c2f | Converts 40 deg Celsius to 104 deg Fahrenheit |
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Loan, Finance , and Date Functions
The calculator can calculate loan values for given payment, interest, and number of period values, or calculate payment values for given loan, interest, and number of period values. Each operation expects the values on the stack in a specific order: loan interest n-periods or payment interest n-periods. Interest is percent per year, and periods are months.
| Example | Result |
|---|---|
| 5000 .5 36 pmt | Calculates payment for a $5000 loan at .5 pct per month for 36 months |
| 200 .5 36 loan | Calculates loan value for a $200 payment at .5 pct per month for 36 months |
| 5000 36 200 irate | Calculates Int Rate per month on $5000 loan for 36 months with $200 pmt |
| 5000 .5 200 nper | Calculates n-periods on $5000 loan at .5 pct per period with $200 pmt |
| 5000 .5 36 12 ppaid | Calculates principal paid on $5000 loan, .5 pct per month, 36 months, after month 12 |
| 5000 .5 36 12 pleft | Calculates principal left on $5000 loan, .5 pct per month, 36 months, after month 12 |
| 200 .5 36 fv | Calculates Future Value of $200 pmt, .5 pct per month, 36 month annuity |
| 200 .5 36 pv | Calculates Present Value of $200 pmt, .5 pct per month, 36 months annuity |
| 200 250 225 6 npv | Calculates Net Present Value of list of cashflows followed by discount rate per period |
| 200 250 225 560 irr | Calculates internal rate return of list of cashflows followed desired NPV |
| 39.95 15 tip | Calcuates tip on 39.95 bill and 15 pct tip |
| date | Places month, day, and year on stack |
| 3 1 2016 11 15 2018 ndays | m1 d1 yy1 m2 d2 yy2 returns ndays between dates |
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Stack Control
Don't be confused by the stack. It's easy to view it as an array, but it's actually just a history and temporary repository for values used by operations. The newest entry is on top, and the older ones below. Operators that work on stack numbers use the newest ones (top values). One can use the stack in more of a permanent way for some project, in that the save command saves not only variables and definitions, but also saves the stack. The stack has a depth of 50, so in addition to the 26 variables (a thru z), the stack adds the capacity to save another 50 values. You can easily put values on the stack and pop off the top value for use, and to a limited degree use the pick command to access a value that's not on the top of the stack.
If you enter 10, 20, and 30, for example, the stack shows:
3020
10
The 10 was entered first, and is thus on the bottom of the stack. However, if you use 3 nput a to put the 3 numbers into a, b, and c, you'll see:
a 10b 20
c 30
The oldest entry is in a, and so on. Why? Because you'll often want to
preset variables for computations, and the natural inclination is to put the
values in consecutive variable order, like a series of interest values in
a
thru e
. For example: 2 4 5 8 10 all nput a would show
a
with 2, b
with 4, and so on. It seems right. So the variables
can be thought of as an array, but remember that the stack is just a history.
That can make it appear upside down for the bulk memory operations.
It's often handy to be able to manipulate values on the stack, especially when making user definitions. Most of these move values from the stack to variables, or vice versa. Some manipulate the top few values, and are simple but often indispensable operators.
| Example | Result |
|---|---|
| dup | Duplicate the top value on the stack |
| swap | Swap the top two values on the stack |
| drop | Drop the top value from the stack |
| 3 pick | Pick 3rd stack value and place on top |
| cls | Clear all stack values |
| > z | Store top stack value into z |
| a | Place value in variable a on top of stack |
| put x z | Put top 3 stack values into z, y, and x |
| 3 nput a | Put top 3 stack values into c, b, and a |
| get a d | Copy variabls a thru d onto stack (a oldest) |
| 3 nget a | Copy 3 variables starting with a onto stack |
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How To Use Variables
The calculator has 26 variables, labeled a
thru z
. You can
store the top value to a variable or place the contents of a variable on the
stack. You can also store a number of stack values (or all) to a contiguous
range of variables with a single command, and likewise place a range of
variable values back onto the stack.
| Example | Result |
|---|---|
| all | Put stack depth on top of stack |
| > x | Store top stack to variable x |
| = x | Store top stack to variable x |
| a | Put value in variable a onto stack |
| put a c | Put top 3 stack values into a thru c |
| 4 nput w | Put 4 stack values in w thru z |
| all nput a | Put all stack values starting at a |
| get c e | Get values in c thru e and put onto stack |
| 3 nget x | Get 3 values starting at x and put onto stack |
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User Defined Functions
One of the most powerful features of the calculator is the ability of a user to create his/her own function definitions. Each definition can use any constants, variable references, and existing functions. User definitions can also refer to other user definitions.
The User Keys button on the keypads brings up a keypad that lists user defined functions as click-able functions. The User Defs keypad shows the actual definitions of each user defined function. Note that any functions that used the do operator have been expanded with the do replaced with the respective variable references and repeated function reference.
A simple example might be to define a word to aid in the calculation of payment values for long term loans, where months is cumbersome. You could do: def years 12 * as a new function, which multiplies a year value on the stack by 12, converting it into months. Using it with the pmt function would be: 75000 6 30 years pmt. You see that prior to the execution of the pmt operator, loan value, interest, and months would be on the stack.
If you've allowed cookies, the save command will save the calculator state (variables, numeric display format, and user defs) in year long cookies. If you want to get rid of all browser cookies, you can load the RPN calculator web page first, clear cookies, then save, to allow clearing of all other cookies, but still keeping your user defs.
The ed function, such as: ed years to edit definition years, will put the definition of an operation in the command window. After editing, the keyboard enter or Enter button will re-save the new definition. clearing the command window before Enter will simply remove the definition.
As new and more useful definitions of your own occur to you, you may find that you wish you could re-arrange your user-defined buttons. With the move command, you can do that. The move function is available on the User Keys and User Defs keypads. To use it, just click on move, then the user definition you'd like to move, then the user definition that you wish to have preceding the moved definition. move places the first definition after the second one.
It's possible to have 75 or more user defs in a cookie. The User Keys keypad displays up to 25 at a time. The Next and Prev buttons allow you to move through your user defs if you have more than 25 defined. If you are at the first row, the Prev button doesn't show. Likewise, if your are at the end of your defs, the Next button doesn't show.
For example, assume you have a sum1 command, and some time later you create a sum2 command. But they are just in the user definition list in the order you created them, and may not be together. So you could in order clickmove sum2 sum1 to have button sum2 placed just after sum1. Use the move function to arrange your user buttons in the most comfortable order.
| Example | Result |
|---|---|
| def years 12 * | Defines an op that would convert years to months |
| def mypmt 5000 swap 36 pmt | Defines an op that would assume a 5000 loan for 36 months, but take interest from the stack. Like 12 mypmt. See how swap puts arguments in proper order? |
| undef | Removes most recent def, but puts the def command in history |
| sdefs | List defs to screen so user can copy and save them locally. Pasting the saved text in command window and Enter will restore them. |
| cldefs | Remove all user definitions, but place in history |
| ed years | Places definition of user def years in command window for editing |
| move user1 user2 | Moves the user command user1 just after user command user2 |
| Next | If shown, moves forward one row of user defs |
| Prev | If shown, moves back one row of user defs |
| save | Save current calculator state in year long cookies. Saves variables, numeric display mode, and user definitions |
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