Binomial Probability Calculator
Calculate binomial probability with explicit inputs and a worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent trials with constant success probability. Very small probabilities can underflow to zero.
Example Calculation
- Trials n: 10
- Successes k: 3
- Success probability: 0.5
Exactly 3 successes in 10 fair independent trials has probability 0.1171875.
Method references
Frequently asked questions
How do I use this calculator?
Enter trials n, successes k, success probability. The result updates automatically. Use Reset to restore the example values.
What method does it use?
P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ. Independent trials with constant success probability. Very small probabilities can underflow to zero.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.