Free Statistics & Probability Calculators

Standard Deviation Calculator

Calculate standard deviation, variance, and other statistics for a dataset.

Z-Score Calculator | Standard Score & Percentile

Calculate z-score, percentile rank, and p-values from any data point, mean, and standard deviation. Includes reverse calculation and step-by-step solutions.

Probability Calculator | Events

Calculate single event, multiple event, conditional, and complementary probabilities.

Correlation Coefficient Calculator

Calculate Pearson r and Spearman ρ between two datasets with p-value, R², regression line, and scatter plot.

Linear Regression Calculator

Find the best-fit line (y = mx + b) using least squares regression.

Binomial Distribution Calculator

Calculate binomial probability P(X=k), CDF, mean, variance, and distribution statistics for any n and p. Includes bar chart and full probability table.

Poisson Distribution Calculator

Calculate Poisson probabilities for rare event modeling.

Chi-Square Calculator

Perform chi-square goodness-of-fit and independence tests with p-value, critical value, effect size (Cramér's V, Cohen's w), Yates' correction, standardised residuals, and chi-square distribution curve. Supports 2–5×2–5 contingency tables with real-world presets.

Confidence Interval Calculator | Mean & Proportion

Calculate confidence intervals for means (z and t-test) and proportions (Wald and Wilson). Shows margin of error, critical value, SE, step-by-step working, and a visual bell curve diagram.

Sample Size Calculator

Calculate the required sample size for surveys and experiments.

Percentile Calculator | Rank & Value

Find percentile ranks and values from a dataset.

ANOVA Calculator | One-Way with p-value & Effect Size

Perform one-way ANOVA with up to 6 groups. Shows the full ANOVA table, exact p-value, effect size η², group statistics, and a significance verdict, no F-table look-up needed.

Bayes' Theorem Calculator

Calculate posterior probability P(A|B) from prior, sensitivity, and false positive rate. Includes natural frequencies, Bayes factor, and step-by-step derivation.

T-Test Calculator | One-Sample

Perform a one-sample t-test to determine if a sample mean differs significantly from a known value.

Variance Calculator | Population & Sample

Calculate population variance and sample variance from a dataset with step-by-step workings.

Quartile Calculator | Q1, Q2, Q3 & IQR

Calculate Q1, Q2 (median), Q3, interquartile range (IQR), and detect outliers from data.

Frequency Distribution Calculator | Tables & Charts

Build grouped or ungrouped frequency distribution tables from raw data. Shows relative and cumulative frequencies, modal class, estimated mean and standard deviation, and a bar chart.

Geometric Mean Calculator | How to Calculate Geometric Mean

Calculate geometric mean for growth rates, investment CAGR, and multiplicative data. Compare AM, GM, and HM with warnings for zeros and negatives.

Moving Average Calculator | SMA & EMA

Calculate simple moving average (SMA) and exponential moving average (EMA) for time series data.

Effect Size Calculator | Cohen's d, η² & r

Calculate Cohen's d, Hedges' g, Glass's Δ, r, and η² effect sizes from means, t-statistics, F-statistics, or correlation r. Includes 95% CI, power, and required sample size.

P-Value Calculator | Z, T, Chi-Square & F

Calculate the exact p-value from a z-score, t-statistic, chi-square statistic, or F-statistic. Supports one-tailed and two-tailed tests with significance interpretation.

Mean, Median & Mode Calculator

Calculate the mean, median, mode, range, variance, standard deviation, quartiles, and IQR for any dataset. Detects outliers, shows sorted data, and supports both population and sample statistics.

Normal Distribution Calculator | PDF, CDF & Inverse

Compute exact probabilities for any normal distribution: P(X < a), P(X > a), P(a ≤ X ≤ b), inverse CDF (quantile), and PDF at a point. Works with standard normal (μ=0, σ=1) and custom parameters. Bell curve visualization included.

Process Capability Calculator | Cp, Cpk, Ppk & Six Sigma Level

Calculate process capability indices Cp, Cpk, Pp, and Ppk from specification limits and process statistics. Computes the Six Sigma level, DPMO (defects per million opportunities), control chart limits (UCL, LCL), and the probability of a defect. Classifies the process as world-class, capable, marginal, or inadequate.

Box Plot Calculator | Five-Number Summary, IQR & Outlier Detection

Compute the five-number summary (minimum, Q1, median, Q3, maximum) from raw data. Calculates the interquartile range (IQR), inner and outer Tukey fences, and identifies mild and extreme outliers. Shows sorted data, mean, and standard deviation alongside the box plot statistics.

Power Analysis Calculator | Sample Size, Effect Size & Statistical Power

Determine the required sample size for a study given desired statistical power (1 − β), significance level α, and effect size. Supports Cohen's d for t-tests and z-tests, Cohen's h for proportion tests, and Cohen's w for chi-square tests. Also computes achieved power for a given sample size.

Beta Distribution Calculator | PDF, CDF, Mean & Bayesian Inference

Compute the probability density function (PDF), cumulative distribution function (CDF), mean, variance, mode, and skewness of the Beta(α, β) distribution. Evaluates P(X ≤ x) and P(a ≤ X ≤ b) numerically, with applications in Bayesian inference, proportion modeling, and project completion time estimation.

Weibull Distribution Calculator | Reliability, Failure Rate & MTTF

Compute the PDF, CDF, reliability function, failure (hazard) rate, and mean time to failure (MTTF) for the Weibull distribution with shape parameter k and scale parameter λ. Evaluates survival probability at any time t, computes B10 life, and classifies the failure mode: infant mortality, random, or wear-out.

Two-Way ANOVA Calculator | Factorial Design with Interaction Term

Perform a two-way analysis of variance for a factorial design with up to 4 levels per factor. Computes sum of squares, degrees of freedom, mean squares, F-statistics, and p-values for factor A, factor B, their interaction A×B, and error. Reports eta-squared effect sizes and overall model fit.

Multiple Regression Calculator | Coefficients, R², F-Test & Residuals

Fit a multiple linear regression model with 2–5 predictor variables. Computes regression coefficients, standard errors, t-statistics, p-values, R², adjusted R², and F-statistic. Includes variance inflation factor (VIF) to diagnose multicollinearity and residual analysis.

Logistic Regression Calculator | Log-Odds, Odds Ratios & ROC AUC

Fit a binary logistic regression model using iterative gradient descent. Computes log-likelihood, coefficients, standard errors, odds ratios, predicted probabilities, and ROC AUC. Includes confusion matrix with accuracy, precision, recall, and F1 score.

Mann-Whitney U Test Calculator | Non-Parametric Two-Sample Test

Perform the Mann-Whitney U test (Wilcoxon rank-sum test) on two independent samples. Computes U statistic, z-score approximation with continuity correction, exact p-value for small samples, and effect size r = z/√n.

Spearman Rank Correlation Calculator | ρ, t-Statistic & p-Value

Compute the Spearman rank correlation coefficient ρ for two paired data sets with up to 50 observations. Handles tied ranks with the correction factor, computes the t-statistic for significance testing, and produces a confidence interval.

Kruskal-Wallis H Test Calculator | Non-Parametric One-Way ANOVA

Perform the Kruskal-Wallis H test across 2–6 independent groups as a non-parametric alternative to one-way ANOVA. Computes the H statistic, degrees of freedom, chi-square p-value, and pairwise Dunn post-hoc comparisons with Bonferroni correction.

Birthday Problem Calculator | Shared Birthday Probability & Group Size

Compute the probability that at least two people in a group share a birthday using the exact combinatorial formula and Poisson approximation. Find the minimum group size for any target probability, and visualize how probability grows from n = 1 to 100.

Bayes Factor Calculator | BF₁₀, Prior/Posterior Odds & Jeffreys Scale

Compute the Bayes factor BF₁₀ from a likelihood ratio, t-statistic, or chi-square statistic. Updates prior odds to posterior odds, interprets evidence strength on the Jeffreys scale (decisive, strong, moderate, anecdotal), and computes posterior probability of H₁.