*Extreme precision*

**References & credits:** ↑

1. Hover your mouse cursor over the parameters & options in the input form, for “tool-tip” help.

2. If you download binomcalc.pl and run it with no parameters, it displays a brief help message.

3. Pierce, Rod (2020). “The Binomial Distribution,” Math Is Fun.

4. OnlineMathLearning Binomial Distribution lesson.

5. There are many other on-line binomial probability calculators,
but most fail for large values of **n**. Here are the best ones I've found. I tested them with a difficult binomial
probability calculation (n=35,750), here are the results. *(Hover your
mouse over the links below for my comments about each tool.)*:

~~Keisan online binomial probability calculator. This one is~~__very__good. In fact, if I'd been aware of it when I wrote mine, I probably wouldn't have bothered to write mine.

*Unfortunately, the Casio Keisan website was closed on Sept. 30, 2023.*

**2/29/2024:**Good news! The Japanese language version of the Casio Keisan website is still available, and their excellent binomial probability calculator can used via an English translation tool.

- WolframAlpha binomial probability calculator.

- Dr. Harvey Berman's online binomial probability calculator.

- VassarStats online binomial probability calculator.

- iCalcu online binomial probability calculator.

- Richard Lowrey's online binomial probability calculator.

*(please let me know if you find another good one)*

6. This tool is written in Perl 5, and it uses the Perl BigRat module.

7. This tool uses GMP, the GNU Multiple Precision arithmetic library.

8. Q: What's with that odd “.sphp” file extension, anyhow?

A: This webpage is unusually designed,
using HTML, PHP, CGI Perl, GMP, and a smidgen of JavaScript. Just as **.**shtml is HTML with Server-Side Includes, **.**sphp is PHP with Server-Side Includes (CGI Perl).

**Download:** ↑

To download this binomial probability calculator, as a standalone program, right-click here (preview), and
“save link as,” or “save target as,” or similar. It is written in Perl, so you'll need to have Perl installed to use it.
On Windows I use 64-bit Strawberry Perl (currently v5.38.2.2), but most other recent version 5 Perls should
also work. 32-bit Strawberry Perl works, but it's nearly twice as slow.

(There are no warranties, express nor implied, but you can contact me if you have difficulty.)

**Footnotes:** ↑

^{1} Large values of **n** make the calculation slower. For example, if
` perl binomcalc.pl m=cu a=s n=50000 k=10 p=1/10000 `

^{2} Calculating cumulative probablities, rather than a simple binomial probability, makes the calculation slower,
especially for large values of **k**. For example, calculating cumulative probabilities for k=100 requires calculating binomial
probabilities for 101 different values of k, and summing them.

^{3} Long decimal or repeating decimal values of **p** (or their
rational
equivalents) can make the calculation slower. This mainly affects the “Experimental” precision settings. For example, if
` perl binomcalc.pl m=acu a=x n=35750 k=3 p=1/10000 b=1 `

Last modified: * 29-Feb-2024 (version 39)*

By David A. Burton.

The “last modified” date & version number on this web page are
maintained automatically by TLIB Version Control.