Math Calculators
Probability Distribution Calculator - Normal, Binomial & Poisson
Calculate PDF, PMF, and CDF values for the Normal, Binomial, and Poisson probability distributions. Visualize the distribution curve instantly in your browser.
PDF f(x): 0.398942
CDF P(X ≤ x): 50.00%
Common probability distributions
| Distribution | Use case | Key parameters |
|---|---|---|
| Normal (Gaussian) | Heights, test scores, measurement errors | Mean (μ), standard deviation (σ) |
| Binomial | Coin flips, pass/fail outcomes in n trials | n (trials), p (probability of success) |
| Poisson | Rare events in fixed time/space (calls per hour) | λ (average rate) |
| Uniform | Equal probability outcomes (dice roll) | a (min), b (max) |
| Exponential | Time between events (wait time) | λ (rate) |
The 68-95-99.7 rule
For a normal distribution: 68% of values fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ. This is also called the empirical rule.