Binomial distribution calculator

Distribution visualization
Probability mass function for n = 12, p = 0.3

Calculate binomial distribution probabilities online

Our binomial distribution calculator helps you analyze probability distributions for experiments with fixed number of independent trials and two possible outcomes (success/failure). Calculate exact probabilities, cumulative probabilities, and distribution parameters instantly.

Calculate probability mass function (PMF)

Compute cumulative distribution function (CDF)

Get mean and variance of the distribution

Visualize probability distributions

Perfect for statistics students and professionals

Free to use with no registration required

How to use the binomial distribution calculator

  1. Enter number of trials (n)
    Input the total number of independent trials in your experiment
  2. Specify probability of success (p)
    Enter the probability of success for each individual trial (between 0 and 1)
  3. Set number of successes (k)
    Input the number of successes you want to calculate the probability for
  4. View results
    Get instant probability calculations, distribution statistics, and visualization

Binomial distribution examples with calculations

Fair coin flips

Calculating the probability of getting exactly 6 heads when flipping a fair coin 10 times. Each flip has a 50% chance of success (heads).

Parameters:

  • Number of trials (n) = 10
  • Probability of success (p) = 0.5
  • Number of successes (k) = 6

Results:

  • P(X = 6) = 0.2051 (exactly 6 successes)
  • P(X ≤ 6) = 0.8281 (at most 6 successes)
  • Mean = 5.00 successes
  • Variance = 2.50

Quality control inspection

In manufacturing quality control, finding the probability of discovering 2 or fewer defective items in a sample of 20, with a 5% defect rate per item.

Parameters:

  • Number of trials (n) = 20
  • Probability of success (p) = 0.05
  • Number of successes (k) = 2

Results:

  • P(X = 2) = 0.1887 (exactly 2 successes)
  • P(X ≤ 2) = 0.9245 (at most 2 successes)
  • Mean = 1.00 successes
  • Variance = 0.95

Basketball free throws

For a basketball player with a 75% free throw success rate, calculating the probability of making at least 8 out of 10 free throws.

Parameters:

  • Number of trials (n) = 10
  • Probability of success (p) = 0.75
  • Number of successes (k) = 8

Results:

  • P(X = 8) = 0.2816 (exactly 8 successes)
  • P(X ≤ 8) = 0.7560 (at most 8 successes)
  • Mean = 7.50 successes
  • Variance = 1.88