Statistics & probability
Descriptive measures, probability distributions and significance tests, with the intermediate steps shown. 67 tools, including ANOVA Calculator (One-Way), Average (mean) calculator, Average Deviation Calculator (mean absolute deviation) and Bayes Theorem Calculator. All free, with no account and nothing to install.
ANOVA Calculator (One-Way)Full one-way ANOVA table — SS, df, MS, F and p — plus η², ω² and Cohen's f, because a significant F on its own tells you nothing about how large the difference is. The equal-variance assumption is stated, not buried.Average (mean) calculatorCompute the mean, sum and count of a list of numbers.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Bayes Theorem CalculatorCompute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.Binomial Theorem Expansion CalculatorExpand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign.Central Limit Theorem CalculatorProbabilities for a sample mean from the population mean, standard deviation and sample size, with the standard error and the z-scores shown.Chi-Square Test Calculatorχ² test of independence on any contingency table, showing observed, expected, the contribution and the standardised residual of every cell, plus Cramér's V. Cells with an expected count below 5 are flagged, because that is when the test stops being valid.Coefficient of variation calculatorCompute the coefficient of variation (CV) of a dataset — its relative variability.Cohen's d CalculatorEffect size from raw data or from summary statistics, with pooled SD (Cohen's d) or control SD (Glass's delta). Hedges' g is shown alongside, because d is biased upward on small samples and the correction is not optional there.Confidence interval calculatorCompute a confidence interval for a mean from its standard deviation and sample size.Confidence interval for a proportionFrom x successes in n trials, the confidence interval for the true proportion — computed both the simple Wald way and the Wilson score way, which stays sensible for small samples or proportions near 0 or 1.Contingency Table CalculatorRun the chi-square test of independence on any table up to 10×10: expected counts, per-cell contributions, degrees of freedom, p-value, Cramér’s V, and Fisher’s exact test when the counts are too small.Correlation coefficient calculatorCompute Pearson's correlation coefficient between two lists of numbers.Dice Roll Probability CalculatorExact odds that a roll of nd s (+ modifier) meets a target — built by convolution, not simulated.Effect Size CalculatorFour ways in — two groups, a t, an F, or a correlation r — and conversions between d, r, η² and the odds ratio. A p-value says whether an effect is there; these say how big it is, which is the number a reader actually needs.Expected value calculatorCompute the expected value from a list of outcomes and their probabilities.Exponential Distribution CalculatorCompute exponential-distribution probabilities for waiting times from the rate λ, including P(X≤x), P(X>x) and a range.F-Test CalculatorThree ways in: a one-way ANOVA from raw groups, a two-sample variance ratio, or a bare F with its two degrees of freedom. Each gives the p-value, the critical value at your α and the decision, from the same exact F distribution.Fisher's Exact Test CalculatorThe exact hypergeometric p for a 2×2 table — the right test when χ² fails on small counts. The two-tailed p sums every table at most as probable as the observed one, which is not the same as doubling the one-tailed p, and the odds ratio comes with its confidence interval.Five Number Summary CalculatorGet the minimum, quartiles and maximum of a dataset with the IQR, the outlier fences and a box plot, in three quartile conventions.Gaussian Distribution GeneratorNormally-distributed numbers via Box–Muller, with an optional seed and the sample mean and SD.Geometric Distribution CalculatorCompute the probability of the first success on trial k (or after k failures) from the per-trial success probability p.Geometric mean calculatorCompute the geometric mean of a list of positive numbers.Gini coefficient calculatorThe Gini coefficient of a distribution — the standard measure of inequality, from 0 (everyone equal) to 1 (one person has everything). Paste any set of non-negative values — incomes, wealth, market shares — and it computes the Gini and expresses it as a percentage, the way income inequality is usually reported.Harmonic mean calculatorCompute the harmonic mean of a list of positive numbers.Hypergeometric Distribution CalculatorCompute hypergeometric probabilities of drawing k successes in n draws without replacement from a population of N with K successes.Interquartile range (IQR) calculatorCompute the first quartile, third quartile and interquartile range of a dataset.Jordan Normal Form Calculator (J, P and block structure)Exact Jordan form of a 1×1 to 6×6 matrix: the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing.Kruskal-Wallis Test CalculatorThe rank-based alternative to ANOVA when the data are not normal. Shows the ranks assigned, each group's rank sum, H, df and p — with the tie correction applied, which matters as soon as two values are equal.Linear Regression CalculatorFit an ordinary least-squares line to your X/Y data: get the equation, slope, intercept, Pearson r, R² and predictions.Loot drop probability calculatorThe chance of getting a rare drop over many tries — the maths behind grinding for a mount, a shiny, or a knife skin. From the per-attempt drop rate and the number of attempts, it works out the probability of at least one (or several) drops, and how many runs you need for a 50%, 90% and 99% chance.Mean absolute deviation (MAD) calculatorCompute the mean absolute deviation of a data set around its mean.Mann-Whitney U Test CalculatorCompares two independent samples without assuming normality. Gives U₁, U₂, the rank sums, and a z corrected for both continuity and ties — with the exact distribution used instead of the normal approximation while the samples are small enough for it to matter.Mean, median & mode calculatorThe three averages of a data set at once — the mean (arithmetic average), the median (middle value) and the mode (most frequent) — plus the range. When several values tie for most frequent, they are all shown.Median absolute deviation calculatorA robust measure of spread: the median of the absolute distances from the median. It shrugs off outliers where the standard deviation would blow up. Multiply by 1.4826 to estimate the standard deviation of clean data.Median calculatorFind the median, min and max of a list of numbers.Midrange calculatorCompute the midrange (the average of the smallest and largest value) of a list.Mode calculatorFind the mode — the most frequent value(s) in a list of numbers.Negative Binomial Distribution CalculatorProbability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.Normal Distribution CalculatorCompute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation.Odds to probability converterConvert fractional odds into an implied probability and decimal odds.Outlier detector (IQR method)Flag outliers in a data set using the 1.5×IQR rule with quartile bounds.p-Value CalculatorTurns a z, t, χ² or F statistic into a p-value, one- or two-tailed, with the density curve and the rejected area drawn. The reading in words is included, because a p-value is the most misread number in statistics.Percentile calculatorFind the value at a given percentile in a list of numbers.Poisson distribution calculatorThe probability of exactly k events when they happen at an average rate λ per interval, independently — P(X=k) = e^(−λ)·λ^k / k!. It returns the exact probability, the cumulative P(X≤k), the tail P(X≥k), and reminds you that the mean and variance both equal λ.Population standard deviation calculatorThe population standard deviation σ of a data set — how far the values spread from their mean when your data covers the whole group, dividing by N (not n−1). Enter the numbers and it returns σ, the variance σ², the mean and the count.Probability calculatorCompute the probability of an event from favorable and total outcomes.Probability distribution calculatorOne calculator for the seven distributions you actually use — normal, binomial, Poisson, exponential, uniform, chi-square and Student's t. Pick the distribution and whether you want the density (PDF/PMF), the cumulative probability P(X ≤ x), or the quantile (the inverse, for a critical value), enter the parameters, and read the answer with the mean and variance.Quartile CalculatorCompute Q1, the median and Q3 with the position-by-position working, in the exclusive, inclusive and linear-interpolation methods.Quartile Deviation CalculatorCompute the semi-interquartile range and its coefficient, a spread measure that the extreme values cannot distort.Range calculatorFind the range, minimum and maximum of a list of numbers.Relative Risk CalculatorCompute relative risk, odds ratio, confidence interval, absolute risk reduction and NNT from a 2×2 table of exposed and unexposed groups.Root Mean Square CalculatorRMS shown next to the plain mean, because on signed data the mean collapses to nearly zero while the RMS holds the magnitude that actually matters. Also gives the crest factor, the sum of squares and each value's share of it.Sample Mean CalculatorCompute the sample mean, sum, count and range of a set of numbers.Sample size calculatorFind the survey sample size needed for a population, confidence level and margin of error.Sample Standard Deviation CalculatorCompute the sample standard deviation (n−1), variance, mean and detect outliers.Spearman Rank Correlation CalculatorCompute Spearman's ρ with proper tie handling (average ranks), plus a two-tailed t-test to judge statistical significance.Standard deviation calculatorCompute the standard deviation, variance and mean of a list.Standard error calculatorCompute the standard error of the mean from a list of numbers.Statistics calculatorA full descriptive summary of a data set in one pass: count, sum, mean, median, mode, minimum, maximum, range, the quartiles and interquartile range, plus the sample variance and standard deviation. Paste your numbers and read the whole picture.T-Test Calculator (Welch and Student)Paste two independent samples and get t, the degrees of freedom, the p-value, the critical value and the decision — computed BOTH ways, Welch and Student's pooled variance, with Welch as the default because it does not assume the two variances are equal. The Welch–Satterthwaite degrees of freedom are computed exactly, not rounded down. Sample means, standard deviations, the confidence interval of the difference and Cohen's d come with it.Variance calculatorCompute the sample variance and mean of a list of numbers.Weibull Distribution CalculatorCompute Weibull reliability probabilities F(x) and R(x) for failure analysis from the shape β and scale η.Weighted average calculatorCompute a weighted average from a list of values and their weights.Z-score calculatorCompute the z-score of a value given the mean and standard deviation.