Binomial Distribution Calculator

Exact and cumulative binomial probabilities.

P(X = 3)
0.117188

exactly 3 of 10

P(X ≤ 3)
0.171875
P(X ≥ 3)
0.945313
Mean (np)
5
Std dev
1.5811
Ways (10C3)
120
Show the working
  1. 1P(X = k) = C(10,3) × 0.5^3 × 0.5^7
  2. 2= 120 × 0.125 × 0.007813 = 0.117188
Formula
P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ

How it works

The probability of a given number of successes in a fixed number of independent yes/no trials.

Example

10 coin flips landing exactly 3 heads has probability 0.117.

About the Binomial Distribution Calculator

Exact and cumulative binomial probabilities. It sits in the Statistics section of NWS Calc, a free collection of calculators that run entirely in your browser. There is no signup, no paywall and no tracking — open the page, enter your numbers, get an answer.

Frequently asked questions

Is the Binomial Distribution Calculator free to use?
Yes. Every calculator on NWS Calc is completely free, with no signup, no usage limits and no ads.
Does my data leave my device?
No. The Binomial Distribution Calculator runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
Can I use the Binomial Distribution Calculator on my phone?
Yes. The page is fully responsive and works in any modern mobile or desktop browser — there is nothing to install.
What else is in Statistics?
Mean, deviation, regression, probability and distributions. You can browse the full Statistics category for related calculators.

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