Probability Calculator
Counting (nPr, nCr, n!), binomial distribution, and normal distribution probabilities — with z-scores, updated as you type.
How it works
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Pick a tab: Counting, Binomial, or Normal distribution.
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Enter your values — n and r for counting, n, p, and k for binomial, or mean, standard deviation, and x for normal.
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Read the results instantly: exact, cumulative, and tail probabilities, plus mean, standard deviation, and z-score.
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Adjust any input and the answers update live — no calculate button needed.
Frequently asked questions
What is the difference between nPr and nCr?
nPr counts ordered arrangements (permutations) of r items chosen from n, while nCr counts unordered selections (combinations). For example, picking a president and a vice-president from 10 people is 10P2 = 90, but picking a 2-person committee is 10C2 = 45.
Why is n capped at 170 on the Counting tab?
171! is larger than the biggest number JavaScript can represent (about 1.8×10³⁰⁸), so factorials beyond 170 overflow to infinity. Up to that cap, very large results are shown in scientific notation.
How are the normal probabilities computed?
From the exact cumulative distribution function via the error function: P(X < x) = ½(1 + erf((x − μ)/(σ√2))). That is the same method statistical software uses — no lookup-table rounding.
Are my numbers sent to a server?
No. All calculations run entirely in your browser — nothing is uploaded or stored anywhere. The math library loads once and everything happens on your device.
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