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Statistics Calculators
Explore 160 working tools for describing data, modeling probability, planning samples, estimating uncertainty, and testing clearly stated hypotheses. Each calculator explains its convention, assumptions, interpretation, and decision limits.
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Statistics topics
Select a topic to reveal its calculators. Multiple topics can remain open at the same time.Descriptive statisticsInspect center, spread, quartiles, frequencies, shape, and potential outliers from raw or grouped observations.31 available
- Descriptive Statistics CalculatorAnalyze a numeric dataset with central tendency, spread, shape, quartiles, and outlier fences in one result.Open calculator
- Mean, Median and Mode CalculatorCompare three measures of center and identify every mode in a numeric dataset.Open calculator
- Standard Deviation and Variance CalculatorCalculate sample and population variance and standard deviation from raw observations.Open calculator
- Five-Number Summary CalculatorFind the minimum, first quartile, median, third quartile, and maximum using interpolated quantiles.Open calculator
- Quartile and Percentile CalculatorLocate any requested percentile and report its position within an ordered dataset.Open calculator
- Interquartile Range CalculatorMeasure the spread of the middle half of a dataset and calculate standard outlier fences.Open calculator
- Range and Midrange CalculatorCalculate the total span and midpoint between the smallest and largest observations.Open calculator
- Coefficient of Variation CalculatorExpress standard deviation relative to the magnitude of the mean for ratio-scale measurements.Open calculator
- Z-Score CalculatorStandardize a value by its distance from a supplied mean in standard-deviation units.Open calculator
- Outlier CalculatorScreen observations using 1.5×IQR fences and list values outside those limits.Open calculator
- Frequency and Relative Frequency CalculatorCount repeated values and express each count as a proportion and percentage of the dataset.Open calculator
- Grouped Data Statistics CalculatorEstimate a mean and standard deviation from class midpoints and corresponding frequencies.Open calculator
- Box Plot CalculatorGenerate the values needed for a box-and-whisker plot, including fences, whiskers, and flagged observations.Open calculator
- Histogram and Frequency Table GeneratorGroup numeric observations into equal-width bins using an automatic or visitor-selected bin count.Open calculator
- Stem-and-Leaf Plot GeneratorArrange nonnegative whole-number observations into stems and sorted leaves while retaining individual values.Open calculator
- Skewness and Kurtosis CalculatorMeasure distribution asymmetry and tail weight with adjusted sample coefficients and clearly identified population moments.Open calculator
- Median Absolute Deviation CalculatorCalculate the median absolute deviation from the median and its normal-consistency scaling as robust measures of spread.Open calculator
- Mean Absolute Deviation CalculatorAverage absolute distances from the mean, median, or a visitor-supplied reference without squaring the deviations.Open calculator
- Percentile Rank CalculatorLocate a value within an empirical dataset using lower, equal, and midrank percentile counts with tied values handled explicitly.Open calculator
- Weighted Descriptive Statistics CalculatorSummarize values with positive frequencies or importance weights, including weighted center, spread, quantiles, and effective sample size.Open calculator
- Combined Mean and Variance CalculatorReconstruct the combined mean and sample variance from each group’s size, mean, and sample standard deviation without raw observations.Open calculator
- Pooled Standard Deviation CalculatorPool within-group sample standard deviations by their degrees of freedom without adding variation caused by different group means.Open calculator
- Compare Two Datasets CalculatorCompare two datasets side by side across center, spread, quartiles, range, and relative variability without implying significance or causation.Open calculator
- Trimmed and Winsorized Mean CalculatorCompare the ordinary mean with symmetric trimmed and Winsorized means while showing exactly how many observations change at each tail.Open calculator
- Modified Z-Score CalculatorStandardize every observation by the dataset median and median absolute deviation for a robust potential-outlier screen.Open calculator
- Empirical CDF and Cumulative Frequency CalculatorCalculate counts and proportions at or below a query value and build a cumulative empirical distribution from raw observations.Open calculator
- Grouped Frequency Distribution CalculatorBuild a controlled equal-width frequency distribution with class counts, proportions, densities, and cumulative percentages from raw data.Open calculator
- Data Standardization CalculatorTransform an entire dataset by population z-scores, mean centering, or robust median-and-MAD scaling and return copyable values.Open calculator
- Min–Max Normalization CalculatorRescale a numeric dataset into zero-to-one or any visitor-selected increasing interval while preserving order and relative spacing.Open calculator
- Sum of Squares CalculatorCalculate corrected and uncorrected sums of squares, individual deviations, and their exact relationship to sample and population variance.Open calculator
- Categorical Data Summary CalculatorCount text categories, proportions, percentages, and tied modes without forcing nominal observations into artificial numeric codes.Open calculator
ProbabilityWork with event relationships, conditional probability, Bayesian updating, expected values, and familiar random experiments.28 available
- Probability CalculatorCombine two event probabilities using union and intersection rules with a supplied overlap.Open calculator
- Conditional Probability CalculatorCalculate the probability of event A given that event B has occurred.Open calculator
- Bayes’ Theorem CalculatorUpdate a prior probability using evidence sensitivity and its false-positive probability.Open calculator
- Independent Events CalculatorCalculate joint and union probabilities under an explicit independence assumption.Open calculator
- Mutually Exclusive Events CalculatorAdd event probabilities when the events cannot occur together and check whether their total is valid.Open calculator
- Expected Value CalculatorCalculate the probability-weighted average outcome of a discrete random variable.Open calculator
- Odds and Probability ConverterConvert a probability to odds in favor and against, or derive probability from odds in favor.Open calculator
- Complement Probability CalculatorFind the probability that a defined event does not occur within the same complete sample space.Open calculator
- Joint and Marginal Probability CalculatorAnalyze a 2×2 count table with joint, marginal, and conditional probabilities.Open calculator
- Dice Probability CalculatorCalculate the probability of a target sum for identical fair dice using exact outcome counting.Open calculator
- Coin Toss Probability CalculatorFind exact, cumulative, and upper-tail probabilities for heads in repeated independent tosses.Open calculator
- Birthday Probability CalculatorEstimate the chance that at least two people share a birthday in a group.Open calculator
- Probability from Outcomes CalculatorConvert favourable and total equally likely outcome counts into probability, complement, odds, percentage, and one-in-N context.Open calculator
- Experimental Probability CalculatorEstimate event probability from observed occurrences and trials, then compare observed and expected counts against an optional theoretical value.Open calculator
- Repeated Event Probability CalculatorAnalyze an independent event across repeated trials and reverse-solve how many trials reach a selected at-least-once probability.Open calculator
- Probability Tree CalculatorBuild a complete two-stage binary probability tree with four path probabilities, marginals, and reverse conditionals.Open calculator
- Law of Total Probability CalculatorCombine an exhaustive list of case probabilities and case-specific conditional probabilities into an auditable total event probability.Open calculator
- General Bayes’ Theorem CalculatorUpdate several mutually exclusive hypotheses from their priors and the likelihood of the same observed evidence under each hypothesis.Open calculator
- Three-Event Probability CalculatorAnalyze three overlapping events from individual, pairwise, and triple-intersection probabilities with full feasibility validation.Open calculator
- Venn Diagram Probability CalculatorValidate seven disjoint regions of a three-set Venn diagram and reconstruct event totals, overlaps, union, exactly-one, and outside probabilities.Open calculator
- Dependent Events CalculatorAnalyze two-stage dependent events using a first-stage probability and different second-stage probabilities under that event and its complement.Open calculator
- Independence Checker CalculatorCompare an entered joint probability with the product of its marginals and show conditional differences where denominators exist.Open calculator
- Drawing Without Replacement CalculatorCompare exact, cumulative, and expected target counts for finite draws without replacement or repeated draws with replacement.Open calculator
- Discrete Probability Distribution CalculatorValidate an arbitrary finite probability distribution and calculate moments, cumulative thresholds, interval probability, and loss probability.Open calculator
- Random Variable Variance CalculatorCalculate first and second moments, variance, standard deviation, and each outcome’s contribution for a finite discrete random variable.Open calculator
- Expected Value Decision CalculatorCompare two uncertain choices by net expected value, loss probability, outcome range, and the probability needed for a binary option to break even.Open calculator
- Probability Bounds CalculatorFind sharp possible ranges for intersection, union, exactly-one, neither, and selected conditional probabilities when dependence is unknown.Open calculator
- Reverse Probability CalculatorSolve one unknown in common complement, union, conditional, independent-joint, repeated-event, or expected-value relationships.Open calculator
DistributionsEvaluate point, cumulative, tail, and interval probabilities under explicitly parameterized probability models.40 available
- Normal Distribution CalculatorCalculate density, left-tail, right-tail, and interval probability for a normal model.Open calculator
- Standard Normal Distribution CalculatorTranslate a z-score into density and cumulative tail probabilities.Open calculator
- Binomial Distribution CalculatorFind exact and cumulative success probabilities for repeated Bernoulli trials.Open calculator
- Poisson Distribution CalculatorCalculate event-count probabilities for a supplied mean count over a fixed exposure.Open calculator
- Uniform Distribution CalculatorCalculate density and interval probabilities when every value in a bounded interval has equal density.Open calculator
- Exponential Distribution CalculatorModel waiting time between Poisson-process events using a constant positive rate.Open calculator
- Geometric Distribution CalculatorFind the probability that the first success occurs on a specified independent trial.Open calculator
- Negative Binomial Distribution CalculatorFind the probability that a selected trial produces the r-th success.Open calculator
- Hypergeometric Distribution CalculatorCalculate success counts when sampling without replacement from a finite population.Open calculator
- Student’s t-Distribution CalculatorCalculate density and tail probabilities for a t variable with chosen degrees of freedom.Open calculator
- Chi-Square Distribution CalculatorCalculate density and upper- and lower-tail probabilities for a chi-square statistic.Open calculator
- F-Distribution CalculatorCalculate tail probabilities for an F statistic with numerator and denominator degrees of freedom.Open calculator
- Lognormal Distribution CalculatorCalculate density and probabilities for positive values whose natural logarithm is normally distributed.Open calculator
- Weibull Distribution CalculatorCalculate density, reliability, and cumulative probability for a Weibull lifetime model.Open calculator
- Beta Distribution CalculatorCalculate density and cumulative probability on zero to one for positive shape parameters.Open calculator
- Gamma Distribution CalculatorEvaluate density, cumulative and survival probability, a requested quantile, and moments for a shape-and-rate gamma model.Open calculator
- Cauchy Distribution CalculatorCalculate density, two tails, central interval probability, and quantiles for a location-scale Cauchy model with heavy tails.Open calculator
- Laplace Distribution CalculatorEvaluate density, tails, interval probability, quantiles, and moments for a symmetric double-exponential location-scale model.Open calculator
- Logistic Distribution CalculatorCalculate density, cumulative and survival probability, interval probability, quantiles, and moments for a logistic model.Open calculator
- Pareto Distribution CalculatorEvaluate density, tails, quantiles, and moment-existence boundaries for a Type I Pareto model above a positive minimum.Open calculator
- Triangular Distribution CalculatorCalculate density, tails, interval probability, quantiles, and moments from a minimum, most-likely value, and maximum.Open calculator
- Rayleigh Distribution CalculatorEvaluate density, cumulative and survival probability, quantiles, and moments for a nonnegative Rayleigh magnitude model.Open calculator
- Gumbel Distribution CalculatorCalculate maximum- or minimum-convention Gumbel density, tails, quantiles, and moments with explicit orientation.Open calculator
- Generalized Extreme Value Distribution CalculatorEvaluate a block-maximum GEV model with explicit support checks, density, tails, return level, quantile, and moment boundaries.Open calculator
- Generalized Pareto Distribution CalculatorCalculate density, exceedance probability, quantiles, and moment boundaries for threshold excesses under a GPD model.Open calculator
- Discrete Uniform Distribution CalculatorCalculate exact, cumulative, interval, and quantile probabilities when every integer from a through b is equally likely.Open calculator
- Multinomial Distribution CalculatorEvaluate the exact probability and category moments for a complete vector of counts from repeated categorical trials.Open calculator
- Poisson Binomial Distribution CalculatorCalculate exact and cumulative success-count probabilities when independent Bernoulli trials have different success probabilities.Open calculator
- Beta-Binomial Distribution CalculatorEvaluate exact and cumulative counts under a beta-binomial model with extra-binomial variation in the trial probability.Open calculator
- Multivariate Hypergeometric Distribution CalculatorCalculate the exact probability of a complete category composition drawn without replacement from a finite population.Open calculator
- Zero-Inflated Poisson Distribution CalculatorEvaluate count probabilities and moments for a Poisson process mixed with an additional structural-zero state.Open calculator
- Skellam Distribution CalculatorCalculate the exact probability and moments for the integer difference between two independent Poisson event counts.Open calculator
- Erlang Distribution CalculatorCalculate density, cumulative and survival probability, quantiles, and moments for waiting time until an integer-numbered Poisson event.Open calculator
- Chi Distribution CalculatorEvaluate density, tails, quantiles, and moments for the Euclidean magnitude of independent standard-normal components.Open calculator
- Half-Normal Distribution CalculatorCalculate density, cumulative and survival probability, quantiles, and moments for the absolute value of a zero-mean normal variable.Open calculator
- Inverse Gaussian Distribution CalculatorEvaluate density, tails, quantiles, and moments for a positive inverse Gaussian first-passage model using mean and shape.Open calculator
- Log-Logistic Distribution CalculatorCalculate density, cumulative and survival probability, quantiles, hazard, and moment boundaries for a positive log-logistic model.Open calculator
- Birnbaum–Saunders Distribution CalculatorEvaluate fatigue-life density, tails, quantiles, and moments under the Birnbaum–Saunders shape-and-scale model.Open calculator
- Kumaraswamy Distribution CalculatorEvaluate density, cumulative and survival probability, quantiles, and moments for a flexible two-shape distribution on zero to one.Open calculator
- Probability Distribution Finder CalculatorNarrow candidate distribution families from outcome type, support, generating process, sampling structure, and observed shape clues.Open calculator
Sampling & confidencePlan precision and power, quantify uncertainty, and account explicitly for paired, clustered, weighted, and stratified designs.28 available
- Margin of Error CalculatorCalculate a normal-approximation margin of error for a mean or proportion.Open calculator
- Sample Size CalculatorEstimate a minimum simple-random-sample size for a proportion with optional finite-population correction.Open calculator
- Confidence Interval for a Mean CalculatorEstimate a population mean with a t interval from sample mean, sample standard deviation, and sample size.Open calculator
- Confidence Interval for a Proportion CalculatorCalculate a Wilson score interval for a binomial proportion from successes and trials.Open calculator
- Confidence Interval for Two Means CalculatorEstimate the difference between two independent population means using Welch’s t interval.Open calculator
- Confidence Interval for Two Proportions CalculatorEstimate the difference between two independent proportions with an unpooled standard error.Open calculator
- Confidence Interval for a Variance CalculatorEstimate population variance and standard deviation using chi-square critical values.Open calculator
- Standard Error CalculatorCalculate the estimated standard error of a sample mean from sample standard deviation and size.Open calculator
- Sampling Distribution CalculatorCalculate the mean and standard error of a sample-mean distribution from population parameters.Open calculator
- Central Limit Theorem CalculatorExplore the normal approximation for a sample mean using population mean, spread, and sample size.Open calculator
- Sample Size for a Mean CalculatorPlan a simple-random-sample size for estimating a mean to a chosen margin of error.Open calculator
- Sample Size for Two Means CalculatorPlan two independent group sizes for detecting a specified mean difference with normal-approximation power.Open calculator
- Sample Size for Two Proportions CalculatorPlan independent group sizes for detecting a difference between two anticipated proportions.Open calculator
- Paired-Sample Size CalculatorPlan the number of complete pairs needed to detect a mean within-pair change.Open calculator
- Sample Size for Correlation CalculatorPlan observations for testing a Pearson correlation against a null correlation using Fisher’s transformation.Open calculator
- Confidence Interval for Paired Means CalculatorEstimate the mean within-pair difference from two aligned datasets with a t interval.Open calculator
- Confidence Interval for a Correlation CalculatorCalculate a Fisher-z confidence interval for a Pearson correlation from paired data.Open calculator
- Confidence Interval for a Regression Slope CalculatorFit a simple linear regression and estimate its slope with a t confidence interval.Open calculator
- Confidence Interval for a Poisson Rate CalculatorEstimate an event rate per unit exposure with an exact Garwood interval.Open calculator
- Confidence Interval for an Odds Ratio CalculatorEstimate a 2×2-table odds ratio and its log-scale confidence interval.Open calculator
- Confidence Interval for a Relative Risk CalculatorEstimate a 2×2-table risk ratio with a logarithmic confidence interval.Open calculator
- Statistical Power Analysis CalculatorSolve achieved power, required sample size, or minimum detectable standardized effect for common z-approximation designs.Open calculator
- Minimum Detectable Effect CalculatorFind the smallest raw and standardized mean effect detectable at a target power.Open calculator
- A/B Test Sample Size and Power CalculatorPlan or evaluate a two-group conversion experiment from baseline and alternative rates.Open calculator
- Cluster Sampling Design Effect CalculatorEstimate variance inflation and effective sample size for equal-sized clustered observations.Open calculator
- Effective Sample Size CalculatorCalculate Kish effective sample size from positive sampling or importance weights.Open calculator
- Stratified Sampling Estimator CalculatorCombine stratum means into a population mean and standard error under independent stratified random sampling.Open calculator
- Optimal Sample Allocation CalculatorAllocate a fixed stratified sample using proportional or Neyman allocation.Open calculator
Hypothesis testingRun exact, parametric, rank-based, categorical, variance, association, normality, and randomness procedures with visible assumptions.33 available
- Statistical Test SelectorNarrow candidate statistical methods from outcome type, group count, and sample relationship.Open calculator
- P-Value CalculatorConvert a z, t, or chi-square test statistic into a one- or two-sided tail probability.Open calculator
- Critical Value CalculatorFind normal, t, chi-square, or F cutoffs for a selected significance level and tail convention.Open calculator
- One-Sample t-Test CalculatorTest a population-mean claim from a sample mean, sample standard deviation, and sample size.Open calculator
- Two-Sample t-Test CalculatorCompare two independent means using Welch’s unequal-variance t procedure.Open calculator
- Paired t-Test CalculatorTest the mean of within-pair differences from two aligned numeric datasets.Open calculator
- One-Proportion z-Test CalculatorTest a binomial proportion against a hypothesized value with a null-based normal approximation.Open calculator
- Two-Proportion z-Test CalculatorTest equality of two independent binomial proportions using a pooled null standard error.Open calculator
- Exact Binomial Test CalculatorTest a binomial success probability with exact one- or two-sided tail probabilities.Open calculator
- Fisher’s Exact Test CalculatorTest association in a 2×2 count table conditional on its observed margins.Open calculator
- Chi-Square Goodness-of-Fit Test CalculatorCompare observed category counts with a fully specified expected probability distribution.Open calculator
- Chi-Square Test of Independence CalculatorTest association in an r×c contingency table and report Cramér’s V.Open calculator
- McNemar’s Test CalculatorCompare paired binary outcomes using the discordant cells of a 2×2 matched table.Open calculator
- Cochran’s Q Test CalculatorCompare three or more related binary conditions across the same subjects.Open calculator
- One-Way ANOVA CalculatorCompare means across three or more independent groups with a classical one-factor ANOVA.Open calculator
- Two-Way ANOVA CalculatorAnalyze two crossed fixed factors and their interaction in a balanced design with replication.Open calculator
- Repeated-Measures ANOVA CalculatorCompare three or more numeric conditions measured on the same complete subjects.Open calculator
- F-Test for Two Variances CalculatorCompare two independent normal-population variances with an F ratio.Open calculator
- Levene’s Test CalculatorTest equality of group variances using absolute deviations from group means.Open calculator
- Brown–Forsythe Test CalculatorTest equality of group variances using absolute deviations from group medians.Open calculator
- Bartlett’s Test CalculatorTest equality of several normal-population variances from independent groups.Open calculator
- Mann–Whitney U Test CalculatorCompare two independent samples using pooled ranks, with tie-corrected normal inference.Open calculator
- Wilcoxon Signed-Rank Test CalculatorTest the symmetry-centered location of paired differences using signed absolute ranks.Open calculator
- Kruskal–Wallis Test CalculatorCompare three or more independent groups using pooled ranks and a tie-corrected chi-square approximation.Open calculator
- Friedman Test CalculatorCompare three or more related conditions using within-subject ranks.Open calculator
- Pearson Correlation Significance Test CalculatorTest a Pearson linear correlation against a specified null correlation.Open calculator
- Spearman Rank Correlation Test CalculatorMeasure monotonic association using average ranks and test it with a large-sample t approximation.Open calculator
- Kendall Tau Significance CalculatorCalculate Kendall’s tau-b from concordant and discordant pairs with tie-adjusted asymptotic inference.Open calculator
- Linear Regression Significance Test CalculatorFit a simple least-squares line and test whether its population slope differs from zero.Open calculator
- Jarque–Bera Normality Test CalculatorScreen normality through sample skewness and kurtosis with the Jarque–Bera statistic.Open calculator
- Anderson–Darling Normality Test CalculatorAssess normal-model fit with a tail-sensitive Anderson–Darling statistic and Stephens approximation.Open calculator
- Kolmogorov–Smirnov Test CalculatorCompare an empirical sample with a fully specified normal distribution using the one-sample KS statistic.Open calculator
- Runs Test for Randomness CalculatorTest whether a binary sequence has too few or too many runs for independent ordering.Open calculator