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
ShowHide the working
- 1P(X = k) = C(10,3) × 0.5^3 × 0.5^7
- 2= 120 × 0.125 × 0.007813 = 0.117188
Formula
P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏHow 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.
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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.