Binomial Probability Calculator
P(X = k) = C(n,k) × p^k × (1 − p)^(n − k)
Find the probability of exactly k successes in independent equal-probability trials.
Formula
P(X = k) = C(n,k) × p^k × (1 − p)^(n − k)
Worked example
Independent trials: 10
Exact successes: 3
Success probability: 0.5
With these inputs, the result is 11.71875 %.
How to use this calculator
- Identify the quantity you want to calculate.
- Enter your measurements in the units shown on each field.
- Read the result, which updates as you change the inputs.
- Check the assumptions below before applying the result.
Assumptions and limits
Assumes independent trials and a constant success probability. Limited to 170 trials.
Precision and checking
Results are rounded for display. Use the most accurate measurements available, and avoid rounding your inputs unnecessarily. Extra decimal places in a result do not make an estimate more reliable.
To check a result, substitute the same input values into the formula shown above. Change one value at a time to understand how the quantity responds.
Frequently asked questions
What assumptions does this calculation use?
Assumes independent trials and a constant success probability. Limited to 170 trials.
Are my inputs sent to a server?
No. The calculation runs locally in your browser. The result updates as you edit the inputs.
