The Binomial Probability Calculator finds the probability of getting exactly a certain number of successes across a fixed number of independent trials. Simply fill in the fields above and click Calculate to get an instant result.
This calculator is part of Calculate Wiki’s Math Calculators collection.
What You’ll Need
- Number of Trials (n)
- Number of Successes (k)
- Probability of Success (per trial)
Formula Used
P(X = k) = C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ
Example Calculation
Using example inputs — n = 10; k = 3; p = 50% — the Binomial Probability Calculator returns:
| Value | Result |
|---|---|
| Combinations (n choose k) | 120 |
| Probability | 11.7188% |
11.7188% probability of exactly 3 successes in 10 trials.
Helpful Information
Results from the Binomial Probability Calculator are estimates based on standard formulas used in the math calculators field. This formula assumes each trial is independent with a fixed probability of success.
Frequently Asked Questions
Is the Binomial Probability Calculator free to use?
Yes — the Binomial Probability Calculator on Calculate Wiki is completely free, with no sign-up required.
How accurate is the Binomial Probability Calculator?
The Binomial Probability Calculator uses a standard, well-documented formula from the math calculators field. Results are for informational and educational purposes.
Can I use this on my phone?
Yes, this calculator is fully mobile-friendly and works on any modern browser.
What does the result mean?
For the example values shown above (n=10, k=3, p=50%), the probability of exactly 3 successes is 11.7188%.