๐Binomial Distribution Calculator
Find exact, at-most, at-least, and between-range probabilities from n and p.
Runs entirely in your browser. No data is sent to a server.
Free Binomial Distribution Calculator
Need to find the probability of a specific number of successes in repeated trials? Our free binomial distribution calculator computes exact, at-most, at-least, and between-range probabilities instantly from your number of trials and success probability.
Enter n and p, choose your query type, and get the probability along with the mean, variance, and standard deviation of the distribution. A full bar chart plots every possible outcome, with the region matching your query highlighted, so you can see where your result sits in the overall distribution โ not just a single number in isolation.
Built for probability and statistics coursework, quality-control problems, and anyone modeling repeated yes/no trials. Every formula is shown with your values substituted in. Free, no sign-up, no limits. See the About page or the FAQ for more.
About the Binomial Distribution Calculator
Features
Four query types
Exactly, at most, at least, and between k1/k2.
Full PMF chart
Bar chart of every outcome, with the queried region highlighted.
Mean/variance/SD
Computed alongside every probability.
Exact combinatorics
Log-space computation avoids precision loss for larger n.
Frequently Asked Questions
What is a binomial distribution?
It models the number of successes in a fixed number of independent trials, each with the same probability of success.
What do n and p represent?
n is the number of trials, and p is the probability of success on each individual trial.
What's the difference between "exactly," "at most," and "at least"?
"Exactly k" is a single outcome's probability; "at most k" sums probabilities from 0 to k; "at least k" sums from k to n.
How is the mean of a binomial distribution calculated?
As n ร p, the expected number of successes.
Can I find a probability for a range of successes?
Yes, the "between" mode sums probabilities across a range k1 to k2.
Does it show the formula?
Yes, the binomial PMF formula is shown with your n, k, and p values substituted in.
Does it show a chart?
Yes, a bar chart plots the probability of every possible outcome, with your queried region highlighted.
What if n is large?
The calculator uses exact combinatorics to avoid precision loss even for moderately large n.
Is my data stored?
No, everything runs client-side in your browser.
Is it free?
Yes, completely free with no sign-up or limits.