Binomial Distribution Calculator
Calculate binomial probabilities, mean, variance, and visualize the distribution curve.
Input Parameters
Value between 0 and 1
Probability P(X = x)
Probability Distribution Graph
Calculation Steps
Formula: P(X=x) = nCx * p^x * q^(n-x)
Where:
- n (trials) = 0
- x (successes) = 0
- p (probability) = 0
- q (1-p) = 0
Calculation for P(X=x):
= C * p^x * q^(n-x)
= 0
Enter parameters on the left to calculate binomial distribution.
Binomial Probabilities, Solved Instantly
Enter the number of trials (n), the number of successes (k), and the probability of success (p) — this free calculator returns the exact binomial probability P(X = k), plus cumulative probabilities.
Ideal for statistics homework, quality-control sampling, and A/B test math. Everything computes instantly in your browser with a clear breakdown of the result.
Exact and cumulative probabilities
Get P(X = k) for an exact count, plus P(X ≤ k) and P(X ≥ k) for at-most and at-least questions.
Step-by-step clarity
Results show the inputs plugged into the binomial formula so you can follow the math, not just the answer.
Free and private
All statistics run locally in your browser — your numbers are never sent to a server.
How to use
- Enter the number of trials (n).
- Enter the number of successes (k) and the probability of success (p).
- Click Calculate to see the exact and cumulative probabilities.
Frequently Asked Questions
What is the binomial distribution?
It gives the probability of getting exactly k successes in n independent trials, each with success probability p — like flipping a coin n times.
What is the binomial formula?
P(X = k) = C(n,k) × p^k × (1−p)^(n−k), where C(n,k) is the number of ways to choose k successes from n trials.
What are cumulative probabilities?
P(X ≤ k) is the chance of at most k successes; P(X ≥ k) is the chance of at least k — useful for threshold questions.
When should I use it?
Use it for yes/no outcome experiments: coin flips, pass/fail tests, defective-item sampling, and conversion counts.
Is the calculator free?
Yes, free with no signup.
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