Binomial Distribution Calculator
Probability of k successes in n trials.
Enter your values
Enter the number of trials you are working with.
Enter the successes you are working with.
Enter the probability of success you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- P(X = k)
- 0.161351
- P(X ≤ k)
- 0.762378
- P(X ≥ k)
- 0.398973
- Mean
- 7
- Standard deviation
- 2.1331
Quick answer
The binomial distribution gives the chance of exactly k successes in n independent trials each with probability p.
P(X=k) = C(n,k) p^k (1−p)^(n−k)
At a glance
| What it does | Probability of k successes in n trials. |
|---|---|
| Category | Statistics |
| Inputs needed | Number of trials, Successes, Probability of success |
| Main output | P(X = k) |
| Formula | P(X=k) = C(n,k) p^k (1−p)^(n−k) |
| Cost | Free — no sign-up, no download |
How to use the Binomial Distribution Calculator
- 1Enter the number of independent trials.
- 2Enter the number of successes you are testing.
- 3Enter the success probability as a decimal.
Inputs explained
- Number of trials
- Enter the number of trials you are working with.
- Successes
- Enter the successes you are working with.
- Probability of success
- Enter the probability of success you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Number of trials20
- Successes8
- Probability of success0.35
Results
- P(X = k)0.161351
- P(X ≤ k)0.762378
- P(X ≥ k)0.398973
- Mean7
- Standard deviation2.1331
Frequently asked questions
When is binomial appropriate?
Fixed trials, two outcomes, constant probability and independence.
What if n is huge?
Use the normal approximation when np and n(1−p) both exceed 5.
What do I need to enter into the Binomial Distribution Calculator?
Just 3 values: number of trials, successes, probability of success. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Binomial Distribution Calculator work out the answer?
The binomial distribution gives the chance of exactly k successes in n independent trials each with probability p. It applies the formula P(X=k) = C(n,k) p^k (1−p)^(n−k) and shows the working so you can check each step by hand.
Is the Binomial Distribution Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.