Trouble? If you don't see the calculator above this line within a few seconds after all of the files are loaded, make sure your browser supports Java and that Java is enabled (e.g., in Explorer, make sure Tools | Internet Options | Advanced | Enable Java is checked). If you are using CoCalc from files on your computer, make sure CoCalc.class is in the same directory as CoCalc.html.

If you don't have Java installed on your computer, you can download it for free from http://www.java.com. It is a reasonably big download, but a simple installation.

After reading this documentation, you can shrink the window so that only the calculator is visible.

CoCalc RPN Scientific Calculator

Table of Contents:

• What is CoCalc?
  • What is CoCalc2?
  • CoCalc Is Free
  • Other Software from CoHort Software
  • Source Code
  • Support
  • History
• Introduction
  • Entering Numbers
  • The Stack
  • Operations
  • Degrees vs. Radians
  • Display Options
  • Storage Registers
  • Statistics
  • Precision and Errors
• Alphabetic List of Buttons

What is CoCalc?

What is CoCalc2?

CoCalc Is Free

"Can I install CoCalc on my computer?" Yes, in fact, we prefer that you install it on your computer instead of using it from the cohort web site.

For regular CoCalc:

1. Download (right click or Apple click) http://www.cohort.com/CoCalc.html and choose to save the file somewhere on your hard drive.
2. Download (right click or Apple click) http://www.cohort.com/CoCalc.class and choose to save the file in the same directory as CoCalc.html.
3. Use your browser to view your copy of the calculator (CoCalc.html) even when you aren't connected to the internet. Consider adding a bookmark to your copy of CoCalc.html.

For CoCalc2 (the large text version):

1. Download (right click) http://www.cohort.com/CoCalc2.html and choose to save the file somewhere on your hard drive.
2. Download (right click) http://www.cohort.com/CoCalc2.class and choose to save the file in the same directory as CoCalc2.html.
3. Use your browser to view your copy of the calculator (CoCalc2.html) even when you aren't connected to the internet. Consider adding a bookmark to your copy of CoCalc2.html.

"Can I put CoCalc on my web page?" Yes, if you:

1. Credit CoHort Software and include a link to the CoHort Software home page. For example, you might include a paragraph like:

   Here is a free RPN scientific calculator available as a Java applet. CoCalc is free for personal use (but please do not alter or resell it). Try CoCalc now. Or, download these files ( http://www.cohort.com/CoCalc.html and http://www.cohort.com/CoCalc.class ) and use your browser to view your copy of the calculator (CoCalc.html) even when you aren't connected to the internet.

   There is also a large text version of CoCalc, called CoCalc2. Try CoCalc2 now. Or, download these files ( http://www.cohort.com/CoCalc2.html and http://www.cohort.com/CoCalc2.class ) and use your browser to view your copy of the calculator (CoCalc2.html) even when you aren't connected to the internet.

   Please change the http references to the CoCalc files on your server.
2. Distribute the files for free and without making any changes to them.
3. Send us an email message with your web site address (so we can see the reference) and your email address (so we can notify you of updates). We won't use this information for any other purpose.

Disclaimer: THIS CODE IS PROVIDED "AS IS", AND COMES WITHOUT ANY WARRANTY, EXPRESSED OR IMPLIED; WITHOUT EVEN THE IMPLIED WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE. COHORT SOFTWARE SHALL NOT BE LIABLE FOR ANY DAMAGES, WHETHER DIRECT, INDIRECT, SPECIAL, INCIDENTAL OR CONSEQUENTIAL ARISING FROM THE USE OF THE SOFTWARE OR FROM THE INABILITY TO USE THE SOFTWARE OR FROM A FAILURE OF THE SOFTWARE TO OPERATE IN A MANNER DESIRED BY THE USER.

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Other Software:

• CoPlot - for making publication-quality 2D and 3D graphs, maps, and technical drawings.
• CoStat - for statistical analysis.

Our web site will always have the latest version of CoCalc.

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Source Code

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Support

Upgrades: If you want to be put on an email mailing list to be notified when there is a new version of CoCalc, send email to info at cohort.com with the words "subscribe CoCalc" plus your email address on one line in the body of the message.

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History

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Introduction to Using CoCalc

On ordinary, non-RPN calculators, you do calculations by pressing buttons in the order that you would write an equation on paper (e.g., 5 - 2 = ). On RPN calculators, you enter the numbers and and then do something to them (e.g., 5 Enter 2 - ). You will note that RPN calculators don't have an = button or parentheses buttons, but they do have an Enter button.

If you aren't used to it, RPN seems odd at first. But when you get used to it and use it for non-trivial calculations, you will see that it is a wonderful system.

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Entering Numbers

To enter a number with an exponent: after entering the mantissa of the number, press eex, and then enter the exponent. For example, to enter 4.56*10^5, press 4 . 5 6 eex 5. The display will show 4.56e5, which is the program's notation the numbers with exponents.

To make a number negative, type the number and then press chs (change sign). For example, to enter -4.56, press 4 . 5 6 chs. You can press chs repeatedly to add/remove the minus sign.

To make an exponent negative, press chs (change sign) after you have entered the exponent. For example, to enter 4.56*10^-5, press 4 . 5 6 eex 5 chs. The display will show 4.56e-5, which is the program's notation the numbers with exponents.

For many of the buttons, you can also type the similarly named keys. This works for the following keys: 0 1 2 3 4 5 6 7 8 9 a A b B c C d D e E f F ^ ! % . / x - + Enter backspace. The buttons that they correspond to should be obvious. Also supported are ',' (an alias for '.') and '*' (an alias for 'x'). Warning: note that '-' corresponds to the subtraction button ('-'); to change the sign of a number, you must use the 'chs' button.

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The Stack

When you have finished entering a number, you can do something to the number (e.g., press a button that does something to the value in the x register, like 10^x), or you can enter another number (press Enter and then start entering the next number.

Many buttons are commands that use the values in the x and y registers, e.g., +. When you use these, the result is placed in x, and the values in the z and t registers are move down: y= previous z, z= previous t. The t register is not changed.

There are 3 important keys for manipulating the numbers in the stack:

• Enter - this button pushes all of the values upwards. The x value stays in x and is also pushed into y; y goes into z; z goes into t; and t goes into oblivion. For example, press 1 Enter 2 Enter Enter.
• rollDn - this rolls down all of the registers. The t value moves to z; z moves to y; y moves to x; x moves to t. For example, press 3 Enter 4 rollDn rollDn rollDn rollDn.
• x<->y - this button swaps the values in the x and y registers. For example, press 5 Enter 6 x<->y.

Automatic stack lift: After you use a command (e.g., ln or +), you can immediately enter another number; you don't need to press Enter to lift all of the values in the stack. After a command, if you press a digit, CoCalc will automatically lift the stack (as if you had pressed Enter).

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Operations

Here are some simple equations and the buttons you need to press to do the calculation in CoCalc:

Problem: square root(9)=
Solution: press 9 x^0.5

Problem: 8/5=
Solution: press 8 Enter 5 /

Problem: 4 + (5*6) =
Solution 1) Press: 4 Enter 5 Enter 6 * +.
Solution 2) Press: 5 Enter 6 * 4 +. Note that you don't have to press Enter before typing 4; the stack is automatically lifted when you start typing a number after doing an operation.

Problem: 3*sin(1.5degrees)=
Solution 0) For either method, press Deg so the calculations will be done in degree mode.
Solution 1) Press: 3 Enter 1.5 sin *.
Solution 2) Press: 1.5 sin 3 *.

Problem: (16/5.6 + .5) / (pi*.8^2 + 4)
Solution: press 16 Enter 5.6 / .5 + pi Enter .8 x^2 * 4 + /

For more complicated equations or if you repeatedly use a constant, you may want to store values in a storage register.
Problem: Convert several length measurements (in inches) into centimeters.
Solution: Press 2.54 Store 0, then repeatedly press (a number) Recall 0 *

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Degrees vs. Radians

The Deg and Rad radio buttons let you choose which mode will be used for subsequent trigonometric operations (sin, cos, tan, asin, acos, atan, ->Rec, ->Pol).

The ->Deg and ->Rad buttons let you convert an angle value in the x register from radians to degrees, or from degrees to radians, respectively.

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Display Options

For all of these options, the numbers stored in the registers are not changed; the numbers are just displayed in different ways.

Fix - This format always shows a fixed number of digits to the right of the decimal place. To select the Fix display mode and specify the number of digits to the right of the decimal point, press Fix and then the desired number of digits, 0 - F. For example, 98765.12345 appears as 98765.123 if you use Fix 3. The last digit is rounded. If the number is too big or too small, scientific notation will be used.

Sci - Scientific notation always displays the number with one digit to the left of the decimal place, some specified number of digits to the right, and an exponent. To select the Sci display mode and specify the number of digits to the right of the decimal point, press Sci and then the desired number of digits, 0 - F. For example, 98765.12345 appears as 9.877e+004 if you use Sci 3. The last digit is rounded.

Eng - Engineering notation is similar to scientific notation, except that the exponent is constrained to be a multiple of 3. To select the Eng display mode and specify the number of digits to the right of the decimal point, press Eng and then the desired number of digits, 0 - F. For example, 98765.12345 appears as 98.765e+003 if you use Sci 3. The last digit is rounded. [HP calculator purists: no, this is not exactly the way HP does it. But this way makes the decimal points line up nicely.]

Hex - The Hex option displays the numbers in the registers by displaying rounded values in base 16. Hexadecimal, as base 16 is called, is widely used by computer programmers. When you are typing in numbers in this mode, you can use digits 0 - 9 and additional hex digits (A, B, C, D, E, and F) which stand for the base 10 numbers: 10, 11, 12, 13, 14, and 15, respectively. Because the calculator only works with integer hexadecimal numbers, you can't use the . or eex keys in Hex mode. Negative numbers are displayed with a '-' sign, which avoids a problem: there are two common ways to store negative numbers in Hex notation (two's complement and one's complement) and the number of digits is different for 16, 32, and 64 bit numbers. To select the Hex display mode, press Hex.

Bin - The Bin option displays the numbers in the registers by displaying rounded values in base 2. Binary, as base 2 is called, is widely used by computer programmers. When you are typing in numbers in this mode, you can only use digits 0 and 1. Because the calculator only works with integer binary numbers, you can't use the . or eex keys in Bin mode. Negative numbers are displayed with a '-' sign, which avoids a problem: there are two common ways to store negative numbers in Bin notation (two's complement and one's complement) and the number of digits is different for 16, 32, and 64 bit numbers. Since binary notation is not very dense, you will get an error message if a number is too long to display. To select the Bin display mode, press Bin.

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Storage Registers

To store the current x value, press store and the number of the register into which you want to store it (0 - F), e.g., store 4.

To recall a stored number and put it in x (as if you typed it in), press recall and the number of the register from which you are getting it (0 - F), e.g., recall 4.

You can set all of the storage registers to 0 by pressing clrReg.

Registers 0 - 5 are used by the statistics procedures to hold various sums. So, before using the statistics procedures, use clrReg. Until you are done with statistics don't store anything in registers 0 - 5.

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Statistics

1. Initialize the statistics system by pressing clrReg. Storage registers 0 - 5 are used by the statistics procedures to hold various sums. So, while using the statistics procedures, don't store anything new in registers 0 - 5.
2. For each x,y pair of numbers, type the y value, press Enter, type the x value, and press Sig+. When you press Sig+, the program increments the storage registers (s0=s0+1, s1=s1+x, s2=s2+x^2, s3=s3+y, s4=s4+y^2, s5=s5+xy,) and displays the s0 value in x. These values will be used to calculate various statistics.
3. When you are done entering the data, press any of the statistics keys:
   • mean - Sets x=the mean of the x values, y=the mean of the y values, z=z, t=t.
   • S.D. - Sets x=the standard deviation of the x values, y=the standard deviation of the y values, z=z t=t.
   • L.R. - Linear Regression: x=intercept, y=slope, z=z, t=t.
   • x^,r - Given a y value in the x register, this sets x=expected x, y=correlation coefficient (r), z=z, t=t.
   • y^,r - Given an x value in the x register, this sets x=expected y, y=correlation coefficient (r), z=z, t=t.

All of the discussion above presumes you have x,y pairs. However, most of the statistics procedures (Sig+, Sig-, mean, S.D.) can be used if you just have x values.

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Precision and Errors

• Precision: All registers (x,y,z,t and storage) are 64 bit doubles that have roughly 17-18 significant decimal digits and a range of +/-1e300. The +/-1e300 limit is slightly smaller than the true range of doubles; CoCalc restricts it to help avoid numeric errors.
• Integer precision: Calculations that are done on rounded values (e.g., div, mod, <<, >>, and, or, xor, not) are done on 64 bit integers (called "long's"). Unfortunately, since the precision of doubles is slightly less than the precision of long's, the full range of long's is not available. This should only be a problem in truly extreme cases (e.g., numbers greater than 1e17).
• Errors: CoCalc tries to catch and prevent numeric overflows, division by 0, sqrt, log or ln of a negative number, and other errors. Any calculation that leads to a value greater than +/-1e300 (and some that lead to +/-1e295) lead to an error message. Any calculation done with a error value leads to an error (e.g., 1+error=error).
• Clearing Errors: You can clear an error value in the x register by pressing clx
• Round-off errors: Computers are not good at exactly storing decimal values. After a series of calculations this often leads to the situation where the internal value of a number is not exactly what you expect (e.g., what appears as 100.0000 may be 99.9999999999 internally). Usually, this doesn't matter, because the numbers are rounded when they are displayed (e.g., Fix 4 will show you 100.0000). But if you subsequently use int the result will be 99 and the result of frac will appear as 1 (although it is 0.9999999999 internally)! There isn't much you can do about this; just be aware of it.

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Alphabetic List of Buttons:

.

While you are typing in a number, this appends '.' to the number.

%

Set x=x*y/100, y=y, z=z, t=t. Note that the y, z, and t registers are unchanged. For example, to calculate 15% of $30, press 30 Enter 15 %.

->Deg

Change x from Radians to Degrees: Sets x= x / 2pi * 360. This assumes that the original x value is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

->Pol

Converts from rectangular coordinates(x,y) to Polar coordinates (x=radius, y=theta): Set x=sqrt(x^2+y^2), y=arcTan2(y,x), z=z, t=t. The y result is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

->Rad

Change x from Degrees to Radians: Sets x= x * 360 / 2pi. See Degrees vs. Radians.

->Rec

Converts from polar coordinates (x=radius, y=theta) to Rectangular coordinates: set x=x*cos(y), y=x*sin(y), z=z, t=t. This assumes that the original y value is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

/

Set x=x/y, y=z, z=t, t=t.

x

(Multiply) Set x=x*y, y=z, z=t, t=t.

-

Set x=x-y, y=z, z=t, t=t.

+

Set x=x+y, y=z, z=t, t=t.

<-

When you are typing in a number, this backspaces. It removes the rightmost character in the number (which is usually the last digit entered).

>>

Set x=round(y) shiftRight round(x), y=z, z=t, t=t. Shifting right is like doing an integer division by 2, x times. For example, 16 Enter 2 >> returns 4.

<<

Set x=round(y) shiftLeft round(x), y=z, z=t, t=t. Shifting left is like doing an integer multiplication by 2, x times. For example, 4 Enter 2 << returns 16.

0

While you are typing in a number, this appends '0' to the number.

1

While you are typing in a number, this appends '1' to the number.

1/x

Set x=1/x, y=y, z=z, t=t.

10^x

Set x=10 to the x. Also called common antilog.

2

While you are typing in a number, this appends '2' to the number.

3

While you are typing in a number, this appends '3' to the number.

4

While you are typing in a number, this appends '4' to the number.

5

While you are typing in a number, this appends '5' to the number.

6

While you are typing in a number, this appends '6' to the number.

7

While you are typing in a number, this appends '7' to the number.

8

While you are typing in a number, this appends '8' to the number.

9

While you are typing in a number, this appends '9' to the number.

A

While you are typing in a number in Hex mode, this appends 'A' to the number.

acos

Set x=arccos(x), y=y, z=z, t=t. The result is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

and

Set x=round(y) and round(x), y=z, z=t, t=t. and compares the two numbers bit by bit. If the both bits are 1's, the resulting number has a 1 for that bit.

asin

Set x=arcsin(x), y=y, z=z, t=t. The result is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

atan

Set x=arctan(x), y=y, z=z, t=t. The result is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

B

While you are typing in a number in Hex mode, this appends 'B' to the number.

Bin

Display rounded numbers in binary format. See Display Options.

C

While you are typing in a number in Hex mode, this append 'C' to the number.

chs

Change the sign of x (or its exponent). See Entering Numbers.

clrReg

Clears the storage registers (0-F). Do it before doing Statistics. See Statistics.

clx

clear x: Set x=0, y=y, z=z, t=t.

CoCalc

Refresh the screen, and show some information about CoCalc, including the version number.

cos

Set x=cos(x), y=y, z=z, t=t. This assumes that the original x value is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

D

While you are typing in a number in Hex mode, this appends 'D' to the number.

Deg

Trigonometric functions will be done in degrees. See Degrees vs. Radians.

div

Set x=round(y) integerDivide round(x), y=z, z=t, t=t. Div is the result of an integer division. See Mod. For example, 7 Enter 3 div returns 2.

E

While you are typing in a number in Hex mode, this appends 'E' to the number.

e^x

Set x=e to the x. Also called natural antilog. e is a constant approximately equal to 2.71828183.

eex

If in Fix/Sci/Eng modes, enter an exponent for x. See Entering Numbers.

Eng

Display numbers in engineering notation (with 0 - F digits). See Display Options.

Enter

Set x=x. y=x, z=y, t=z. See The Stack.

F

While you are typing in a number in Hex mode, this appends 'E' to the number in x.

Fix

Display a fixed number of decimal digits (0 - F). See Display Options.

frac

Set x=the fractional part of x, y=y, z=z, t=t.

Help

For a description of a button, press Help then press another button.

Hex

Display rounded numbers in hexadecimal format. See Display Options.

int

Set x=the integer part of x, y=y, z=z, t=t.

L.R.

Linear Regression: Sets x=intercept, y=slope, z=z, t=t. See Statistics.

last x

Set x=last x, y=x, z=y, t=z. The 'last x' is saved when you do an operation (e.g., ln, +) so you can recover the x value that existed before the operation.

ln

Set x=the natural log (base e) of x.

log

Set x=the natural log (base 10) of x.

mean

Sets x=mean of x's, y=mean of y's, z=z, t=t. See Statistics.

mod

Set x=round(y) modulus round(x), y=z, z=t, t=t. Modulus is the remainder of an integer division. See Div. For example, 7 Enter 3 mod returns 1.

n!

Set x=factorial(round(x)), e.g., 4!=1*2*3*4.

not

Set x=64bit 2's complement of round(x), y=y, z=z, t=t.

or

Set x=round(y) or round(x), y=z, z=t, t=t. or compares the two numbers bit by bit. If either of the bits is a 1, the resulting number has a 1 for that bit.

pi

Set x=3.14159265359, y=x, z=y, t=z.

Rad

Trigonometric functions will be done in radians. See Degrees vs. Radians.

recall

Recall x from a stored value (slots 0 - F). For example, to recall the value in slot 5 and put it in x, press recall 5. See Storage Registers.

roll Dn

roll down: Sets x=y, y=z, z=t, t=x. See The Stack.

S.D.

Sets x=standard deviation of the x's, y=standard deviation of the y's, z=z, t=t. See Statistics.

Sci

Display numbers in scientific notation (with 0 - F digits). See Display Options.

Sig-

Set storage registers: s0=s0-1, s1=s1-x, s2=s2-x^2, s3=s3-y, s4=s4-y^2, s5=s5-xy; x=s0. See Statistics.

Sig+

Set storage registers: s0=s0+1, s1=s1+x, s2=s2+x^2, s3=s3+y, s4=s4+y^2, s5=s5+xy; x=s0. See Statistics.

sin

Set x=sin(x), y=y, z=z, t=t. This assumes that the original x value is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

store

Store x in a slot (0 - F). For example, to store the x value in slot 5, press store 5. See Storage Registers.

tan

Set x=tan(x), y=y, z=z, t=t. This assumes that the original x value is an angle in Radians or Degrees, depending on the current Rad or Deg setting. See Degrees vs. Radians.

x^0.5

Set x=square root of x, y=y, z=z, t=t.

x<->y

Swap the x and y register values, z=z, t=t. See The Stack.

x^2

Set x=x^2, y=y, z=z, t=t.

x^,r

Given a y value in the x register, this sets x=expected x, y=correlation coefficient (r), z=z, t=t. See Statistics.

xor

Set x=round(y) xor round(x), y=z, z=t, t=t. xor compares the two numbers bit by bit. If one bit is 0 and the other is 1, the resulting number has a 1 for that bit.

y^x

Set x=y^x, y=z, z=t, t=t.

y^,r

Given a x value in the x register, this sets x=expected y, y=correlation coefficient (r), z=z, t=t. See Statistics.

Return to the calculator.

This is the end of the CoCalc documentation.