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Binomial Distribution Calculator
Get exact and cumulative binomial probabilities for any number of independent trials.
Binomial probabilities
Probability: —
Mean: — · Standard deviation: —
Variance: — · Trials: —
How to use the Binomial Distribution Calculator
- Enter the number of trials and the chance of success as a percentage.
- Choose the probability you want and set the number of successes.
- Read the probability, mean, variance and standard deviation in the result panel.
Features
- Exact, at most, at least and range probabilities
- Mean, variance and standard deviation
- Handles large trial counts with logarithms
- Runs locally, no uploads
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Frequently Asked Questions
Common questions about the free online binomial distribution calculator.
Enter the number of trials, the chance of success and the number of successes, then pick
exact or cumulative results.
It describes the number of successes in a fixed number of independent trials, where each
trial has the same chance of success.
It is n choose k times p to the power k times one minus p to the power n minus k, summed over
the range you selected.
An exact result gives the chance of one specific count, while a cumulative result adds the
chances of a whole range of counts.
The mean is the number of trials times the success chance, and the variance is that mean
times one minus the chance.
Yes. Enter the chance as a percentage such as 50 or 12.5, and the tool converts it to a
probability before calculating.
You can enter up to 5000 trials. Large numbers are handled with logarithms so the results
stay accurate and fast.
It shows the number of trials actually used, after the tool caps very large entries and
rounds decimal input to a whole number.
No. Every calculation runs locally in your browser, so your numbers never leave your device.
Yes. It is completely free and unlimited, with no account, no sign-up and no usage limits of
any kind.
Last updated: October 10, 2026