Statistical Distribution Calculators

Calculate probabilities, quantiles, and summary values for common probability distributions.

21 calculators in this category.

A probability distribution describes how the possible values of a random quantity are spread out. Choosing the right distribution depends on the kind of data: counts of events, waiting times, proportions, or continuous measurements each point to different families.

The calculators in this category cover discrete distributions, where outcomes are countable, and continuous distributions, where probabilities are areas under a curve. They also include approximation tools and checks such as the empirical rule and Benford's law.

Calculators in this category

21 calculators

Key concepts

Discrete and continuous
A discrete distribution assigns probability to individual values. A continuous distribution assigns probability to ranges, and any single exact value has probability zero.
Parameters
The numbers, such as a mean or a rate, that fix the exact shape of a distribution.
Central limit theorem
The distribution of a sample mean approaches a normal distribution as the sample size grows, under mild conditions.

Frequently asked questions

How do I choose between the binomial and Poisson distributions?

Use the binomial distribution when you count successes in a fixed number of independent trials. Use the Poisson distribution when you count events occurring over an interval of time or space at a steady average rate, with no fixed upper limit on the count.

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