All Free Statistics Tools

Explore probability distributions interactively, adjust parameters, inspect PDF and CDF charts, and learn how shape and probability change.

Use the interactive probability distribution calculator when you already know the family you want to study and need to connect its parameters with probability. The workspace covers eight continuous and discrete models, including normal, binomial, Poisson, exponential, gamma, beta, Weibull, and log-normal distributions. Change valid parameters, compare PDF or PMF and CDF views, and inspect a selected point without sending data to a server. It is useful for probability coursework, checking tail direction, learning how spread or shape parameters affect a curve, and documenting a preliminary model calculation. Start from the data-generating process and support: counts, waiting times, bounded proportions, and positive skewed measurements require different candidates. The calculator visualizes a chosen model; it does not prove that the model fits observed data or replace a formal fitting workflow.

• Normal Distribution
• Binomial Distribution
• Poisson Distribution
• Exponential Distribution
• Gamma Distribution
• Beta Distribution
• Weibull Distribution
• Log-Normal Distribution
• Continuous Uniform Distribution
• Student’s t Distribution
• Chi-Square Distribution
• F Distribution
• Bernoulli Distribution
• Geometric Distribution
• Negative Binomial Distribution
• Hypergeometric Distribution
• Cauchy Distribution
• Pareto Distribution
• Laplace Distribution
• Logistic Distribution
• Rayleigh Distribution
• Triangular Distribution
• Discrete Uniform Distribution

Compare probability distribution families side by side, align parameters, and understand differences in support, shape, tails, and variability.

Use the distribution comparison tool when several probability families seem plausible or when you want to explain why matching centers does not make two models equivalent. Place supported distributions in a shared visual context, align meaningful parameter choices, and inspect support, symmetry, skewness, spread, modes, and tail behavior. Typical uses include comparing normal configurations with different spreads, contrasting Poisson rates, or showing how two Weibull settings assign different probability to extreme observations. Begin by ruling out candidates that permit impossible values, then compare shapes on common axes and examine tails separately from the center. The overlays are especially helpful for teaching and early model screening, but curve similarity is not statistical evidence of fit. When observed data are available, continue with the distribution fitting tool and evaluate diagnostics, sampling assumptions, and domain knowledge before selecting a model.

Visualize distribution approximations and relationships, including how parameter changes and repeated sampling illustrate the Law of Large Numbers and Central Limit Theorem.

Use the central limit theorem and distribution convergence tools to examine how finite probability models approach normal references as a governing parameter grows. Dedicated modules visualize binomial-to-normal, Poisson-to-normal, Student’s t-to-normal, and centered-and-scaled chi-square-to-normal relationships. Move through a sequence of trial counts, rates, or degrees of freedom and compare the center, boundaries, discreteness, skewness, and tails rather than judging only the peak. These views are useful for probability courses and for checking whether a proposed approximation is credible in the region that matters to a real calculation. A large parameter alone does not guarantee adequate tail accuracy, and discrete models remain discrete at every finite value. State the transformation, continuity correction when applicable, parameter value, and target probability; use an exact calculation when approximation error could change the conclusion.

• Binomial → Normal (Central Limit Theorem)
• Poisson → Normal (Large λ)
• t-Distribution → Standard Normal
• Chi-square → Normal (Large df)
• Binomial → Poisson (Rare Events)
• Poisson Process (Counts, Gaps, Arrivals)
• Sample Means: LLN & CLT

Free online distribution fitting tool: fit candidate probability distributions to sample data, compare diagnostics and inspect plots.

Use the online distribution fitting tool when you have observed numerical values and want to compare supported probability models rather than choosing a curve by appearance. Paste values, open an example dataset, or upload a CSV and select a numeric column; processing remains in the browser. The workspace estimates candidate parameters and places the histogram, best-ranked model’s Q-Q plot, AIC, BIC, and goodness-of-fit information in one review. Common exploratory uses include checking a normal model for roughly symmetric measurements, an exponential model for nonnegative waiting times under a constant-rate mechanism, or a uniform model for a genuinely bounded randomized process. Diagnostics rank or challenge candidates but do not certify assumptions. Investigate independence, outliers, censoring, truncation, mixtures, and measurement limits, then document the sample source, exclusions, fitted parameters, diagnostic evidence, and reason the selected family is scientifically credible.

Choose and calculate Z tests, T tests, chi-square tests, one-way or two-way ANOVA, then interpret statistics, p-values, assumptions, and limitations.

Use the free hypothesis test calculator when a population claim and study design match one of the supported procedures. Ten dedicated modules cover one- and two-sample Z tests, one-sample, independent, and paired T tests, one- and two-way ANOVA, chi-square independence and goodness of fit, and an F test for two variances. Each page opens the calculator already set to the named method and explains inputs, assumptions, result fields, worked examples, limitations, and validation steps. Choose from the outcome type, number of groups or factors, pairing, independence, and whether population variability is known—not from the p-value you hope to obtain. Report the observed effect, test statistic, degrees of freedom where relevant, p-value, alternative direction, and assumption checks. Statistical significance alone does not establish practical importance, equivalence, causation, or data quality.

• One Sample Z-Test
• One Sample T-Test
• Two Sample Z-Test
• Two Sample T-Test
• Paired Sample T-Test
• One-Way ANOVA
• Two-Way ANOVA with Replication
• Chi-Square Test of Independence
• Chi-Square Goodness-of-Fit Test
• F-Test for Equal Variances
• One-Proportion Z-Test
• Two-Proportion Z-Test
• Exact Binomial Test
• Fisher’s Exact Test
• McNemar Test
• Mann-Whitney U Test
• Wilcoxon Signed-Rank Test
• Sign Test
• Kruskal-Wallis Test
• Friedman Test
• Pearson Correlation Test
• Spearman Correlation Test
• Kendall Tau Test
• Levene Test
• Brown-Forsythe Test
• Welch ANOVA
• Repeated Measures ANOVA
• TOST Equivalence Test
• Power & Sample Size
• Confidence Interval Calculator
• Critical Value Lookup