Free Online Statistics Calculators

ANOVA Calculators cover analysis of variance for comparing means across multiple groups. Run a one-way ANOVA or two-way ANOVA to test for differences between groups, or use the three-way ANOVA and mixed model ANOVA calculators for more complex designs. The MANOVA calculator extends ANOVA to multiple dependent variables, while ANCOVA calculator adjusts for a covariate.

This section also includes post-hoc and effect size tools: the Tukey HSD post-hoc test, Bonferroni correction, eta squared, and omega squared calculators, plus a two-way repeated measures ANOVA calculator for within-subjects designs.

Bayesian Statistics Calculators apply Bayesian reasoning to update beliefs based on new evidence. Calculate posterior probability from a prior probability and observed data, or run a Bayesian A/B test calculator to compare two variants with Bayesian methods. The Bayesian credible interval calculator provides a Bayesian alternative to a confidence interval, and the naive Bayes classifier calculator applies Bayes' theorem to classification problems.

Betting & Odds Calculators cover the statistical side of sports betting and gambling odds. Convert odds between decimal, fractional, and moneyline formats with the betting odds converter, decimal odds calculator, fractional odds calculator, and moneyline odds calculator. The Kelly criterion calculator determines optimal bet sizing based on edge and odds, while the expected value (betting) calculator and parlay calculator evaluate the long-term profitability of a bet or combined wager.

Central Tendency Calculators measure the center of a data set. Calculate mean, median, and mode together with the mean median mode calculator, or use the descriptive statistics calculator and summary statistics calculator for a full overview of a data set. The weighted mean calculator accounts for different importance across data points, while trimmed mean and Winsorized mean calculators reduce the influence of outliers.

This section also includes a grouped data mean calculator and midrange calculator for other measures of central tendency.

Combinatorics Calculators count the number of ways to arrange or select items. Calculate combinations with the nCr calculator or permutations with the nPr calculator, or use combination without repetition and permutation without repetition calculators for more specific counting problems. The multinomial coefficient calculator extends combinations to multiple categories, while combinations with repetition and permutation with repetition calculators allow items to repeat.

This section also includes a possible combinations calculator and password combination calculator for estimating the number of possible passwords given a character set and length.

Confidence Interval Calculators estimate a range that likely contains a population parameter. Calculate a 90%, 95%, or 99% confidence interval directly, or use the confidence interval for mean calculator and confidence interval for proportion calculator for specific parameter types. The confidence interval for difference of means calculator compares two groups, while the confidence interval for variance calculator estimates a range for variability.

This section also includes a point estimate calculator, sampling error calculator, and Wilson score interval calculator for proportion confidence intervals with small samples.

Continuous Distributions Calculators model probability across a continuous range of values. Calculate probabilities from the normal distribution or standard normal distribution, or use the t-distribution, chi-square distribution, and F-distribution calculators for hypothesis testing distributions. The lognormal, Weibull, gamma, and beta distribution calculators model skewed and specialized data patterns, while the probability density function and cumulative distribution function calculators work with any continuous distribution directly.

This section also includes Cauchy, Gumbel, logistic, Pareto, Rayleigh, and triangular distribution calculators, plus an inverse normal distribution calculator for finding a value from a given probability.

Correlation Calculators measure the strength and direction of relationships between variables. Calculate the Pearson correlation coefficient for linear relationships, or use Spearman's correlation calculator for ranked, non-linear data. The covariance calculator measures how two variables change together, while Cramer's V calculator and phi coefficient calculator measure association between categorical variables.

This section also includes autocorrelation and cross-correlation calculators for time series data, plus partial correlation, point biserial correlation, tetrachoric correlation, and Matthews correlation coefficient calculators for specialized correlation types.

Data Visualization Calculators help you prepare data for charts and graphical analysis. Calculate class width for a histogram, or find the right angle and percentage for a pie chart with the pie chart angle calculator and pie chart percentage calculator. The QQ plot calculator and Bland-Altman plot calculator check statistical assumptions and measurement agreement, while the Pareto chart calculator and frequency polygon calculator visualize frequency data.

There's also a dot plot calculator for a simple visual summary of small data sets.

Diagnostic Statistics Calculators evaluate how well a test or classifier distinguishes between conditions. Calculate sensitivity and specificity together, or use the positive predictive value and negative predictive value calculators to interpret test results in context. The ROC curve calculator and AUC calculator (area under curve) measure overall classifier performance, while the confusion matrix calculator and accuracy calculator summarize classification results directly.

This section also includes a likelihood ratio calculator, Youden index calculator, number needed to treat calculator, relative risk reduction calculator, and false positive paradox calculator for interpreting diagnostic test results correctly even with rare conditions.

Discrete Distributions Calculators model probability for countable outcomes. Calculate probabilities from the Bernoulli distribution for single trials, or use the hypergeometric distribution calculator and negative binomial distribution calculator for sampling without replacement and trials until a fixed number of successes. The multinomial distribution calculator extends binomial probability to more than two outcomes, while the discrete uniform distribution calculator handles equally likely outcomes and the probability mass function calculator works with any discrete distribution directly.

Dispersion & Variability Calculators measure how spread out a data set is. Calculate the interquartile range (IQR) or population variance, or use MSE (mean squared error) and RMSE (root mean square error) calculators to evaluate prediction accuracy. The relative standard deviation and RSE (relative standard error) calculators express variability as a percentage, while the pooled standard deviation calculator combines variability across multiple groups.

This section also includes a sum of squares calculator, standard deviation of sample mean calculator, and general dispersion calculator for other spread measures.

Diversity & Information Calculators measure inequality and diversity within a data set. Calculate the Gini coefficient to measure income or wealth inequality, or use the Shannon entropy calculator to quantify information content or diversity. The Herfindahl-Hirschman index calculator measures market concentration, while the evenness index calculator and index of qualitative variation calculator assess diversity in categorical data.

Error & Uncertainty Calculators quantify how much a measurement or estimate might be off. Calculate absolute error and relative error to compare a measured value against a true value, or use the absolute uncertainty calculator and measurement uncertainty calculator for lab and scientific measurements. The error propagation calculator combines uncertainty from multiple measurements into a final result, while the standard deviation index calculator standardizes error for quality control comparisons.

Hypothesis Testing Calculators run the statistical tests used to evaluate a claim against data. Calculate a Z-test or t-statistic for comparing means, or use the chi-square goodness of fit and chi-square test of independence calculators for categorical data. The Fisher's exact test calculator and McNemar's test calculator handle small samples and paired categorical data, while the critical value calculator and F-statistic calculator support broader hypothesis testing decisions.

This section also includes normality tests like the Kolmogorov-Smirnov test, Anderson-Darling test, and Lilliefors test calculators, plus a binomial test, sign test, runs test, and Type I and Type II error calculator for evaluating test reliability.

Multivariate & Advanced Calculators cover statistical methods for complex, multi-variable data. Run a principal component analysis or factor analysis to reduce dimensionality, or use cluster analysis calculator and discriminant analysis calculator to group and classify observations. Survival analysis is covered by the Cox proportional hazards calculator, log-rank test calculator, and survival analysis calculator, while Cronbach's alpha calculator and Cohen's kappa calculator assess reliability and inter-rater agreement.

This section also includes a Monte Carlo simulation calculator, bootstrap calculator, jackknife calculator, meta-analysis calculator, structural equation modeling calculator, canonical correlation calculator, Hotelling's T² test calculator, and funnel plot calculator for advanced research methods.

Non-Parametric Tests Calculators run hypothesis tests that don't assume a normal distribution. Use the Wilcoxon rank-sum test calculator or Wilcoxon signed-rank test calculator for comparing two groups, or the Kruskal-Wallis test calculator for comparing three or more groups. The Friedman test calculator and Cochran's Q test calculator handle repeated measures data, while Kendall's tau calculator measures rank correlation and Mood's median test calculator compares medians across groups.

Probability Games & Paradoxes Calculators explore famous and counterintuitive probability problems. Work through the Monty Hall problem calculator or Boy or Girl paradox calculator to see how intuition can mislead in probability, or use Bertrand's paradox calculator and Bertrand's box paradox calculator for classic probability puzzles. The two envelopes paradox calculator and Parrondo's paradox calculator explore other surprising probability results.

This section also includes practical gambling tools like the roulette payout calculator, lottery calculator, coin toss streak calculator, dice average calculator, two dice probability calculator, and a false positive paradox (medical) calculator for understanding misleading test results.

Quality Control Calculators support statistical process control in manufacturing and operations. Build a control chart or calculate upper control limit to monitor a process over time, or use the process capability index calculator to see if a process meets specifications. The Six Sigma calculator and Gage R&R calculator assess measurement system reliability, while the Pareto analysis calculator identifies the most significant causes of defects.

There's also an exponential growth prediction calculator for forecasting trends in quality metrics.

Regression Calculators fit models to data and measure how well they predict outcomes. Run a linear regression or multiple linear regression, or use logistic regression calculator for binary outcomes. Curve-fitting options include quadratic regression, cubic regression, quartic regression, exponential regression, logarithmic regression, and power regression calculators, while ridge regression and lasso regression calculators handle regularized models.

This section also includes R-squared (coefficient of determination) and adjusted R-squared calculators for model fit, a residual calculator and prediction interval calculator for evaluating predictions, and mediation analysis and moderation analysis calculators for testing more complex relationships between variables.

Sample Size & Power Calculators determine how much data you need before running a study. Calculate power analysis or minimum detectable effect to plan a study with enough statistical power, or use the AB test calculator to size an A/B test correctly. The effect size calculator and Cohen's h calculator quantify the magnitude of a difference, while the P-hat calculator estimates a sample proportion for planning purposes.

Sampling Calculators cover the methods used to select a representative sample from a population. Calculate stratified sampling or cluster sampling allocations, or use the systematic sampling calculator for evenly spaced sample selection. The finite population correction calculator adjusts standard error when sampling a large fraction of a population, while sampling distribution and sampling distribution of proportion calculators describe how sample statistics vary.

This section also includes a continuity correction calculator and normal approximation calculator for approximating discrete distributions with the normal distribution.

Shape & Position Calculators locate specific values within an ordered data set. Calculate a Z-score to see how many standard deviations a value is from the mean, or find the first quartile and third quartile to summarize data spread. The decile calculator divides data into ten equal parts, while the upper and lower fence calculator identifies outlier boundaries using the IQR method.

This section also includes minimum and maximum, greatest to least, least to greatest, and raw score calculators for organizing and interpreting individual data points.

Statistical Tables Calculators generate the reference values traditionally looked up in the back of a textbook. Find critical values with the Z-table, t-table, chi-square table, and F-table calculators, or calculate degrees of freedom for a given test. The contingency table calculator and frequency table calculator organize categorical data, while Benford's law calculator checks whether a data set follows expected digit frequency patterns.

This section also includes an average rating calculator and constant of proportionality calculator for other common table-based lookups.

Time Series & Forecasting Calculators analyze and predict data that changes over time. Calculate a moving average or run exponential smoothing to smooth out short-term fluctuations, or use the Holt-Winters calculator and ARIMA model calculator for more advanced forecasting models. The decomposition calculator separates a time series into trend, seasonal, and residual components, while seasonal index and trend analysis calculators isolate specific patterns.

This section also includes a growth rate calculator (statistical), CAGR calculator (statistical), and forecasting calculator for general trend projection.