Normal Distribution

Probability Distribution Plotter

See the shape of any distribution, adjust parameters in real time, and get the exact probability you need - all in your browser.

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Choose the question you want to answer. Each workflow opens with sensible defaults you can refine.

Find probability between two values

Compute P(a ≤ X ≤ b) with live bounds and shading.

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Find the cutoff for a percentile

Set p and read x_p where F(x_p) = p.

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Find probability above a threshold

Evaluate tail probability P(X > x) in survival view.

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Jump to:Normal Binomial Poisson Exponential Student's t Beta Chi-Squared

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Add multiple parameter sets and see how they differ. A dedicated difference chart highlights where one distribution dominates.

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From Normal and Binomial to Weibull, Cauchy, and Pareto - every distribution has the same controls, formulas, and tools.

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Draw thousands of random samples and watch the histogram converge to the theoretical PDF.

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Normal DistributionA bell-shaped, symmetric distribution for real‑valued variables. The mean sets the center and the standard deviation controls the spread.continuous Binomial DistributionDiscrete probability of k successes in n independent Bernoulli trials with probability p.discrete Poisson DistributionDiscrete probability of a given number of events occurring in a fixed interval.discrete Exponential DistributionModels the time between independent events that happen at a constant average rate.continuous Student's t DistributionSimilar to the normal distribution but with heavier tails; used for estimating means of small samples.continuous Chi-Squared DistributionUsed to test if data fits a model (goodness of fit) or if variables are independent.continuous Beta DistributionA flexible distribution plotter for probabilities, proportions, and rates bounded between 0 and 1.continuous Log-Normal DistributionA distribution of a random variable whose logarithm is normally distributed. Common in finance and biology.continuous Gamma DistributionA flexible distribution for positive continuous data, often used to model waiting times and rainfall.continuous Geometric DistributionThe number of failures before the first success in independent Bernoulli trials.discrete Weibull DistributionA versatile distribution for reliability engineering, modeling time-to-failure and survival analysis.continuous F DistributionUsed in ANOVA and regression analysis to compare variances between groups.continuous Uniform DistributionA continuous distribution where all intervals of the same length are equally probable.continuous Cauchy DistributionA heavy-tailed distribution where mean and variance are undefined. Educational for understanding pathological distributions.continuous Pareto DistributionA power-law distribution modeling wealth, city sizes, and the famous 80-20 rule.continuous Negative Binomial DistributionModels the number of failures before achieving a fixed number of successes. Common for overdispersed count data.discrete