Statistics Calculators: Data, Probability and Inference

Use these free statistics calculators to summarize data, estimate probabilities, test hypotheses, and explore relationships between variables. Students, researchers, and analysts can work through common statistical questions without doing every calculation by hand.Try Standard Deviation and Median & Mode to describe a dataset, or Normal Distribution and Binomial Distribution for probability questions. Confidence Interval, P-Value, T-Test, and Chi-Square Test help with statistical inference, while Linear Regression, Correlation Coefficient, and Sample Size support modeling and study planning.

Distributions 13

Poisson Distribution

Calculate Poisson probabilities from the average rate λ: the chance of exactly k events, a range, or cumulative at-most / at-least probabilities, plus mean and variance.

Z-Score

Convert any raw value into a z-score using the mean and standard deviation, or let the calculator derive them from your own data set. You also get the percentile and tail probabilities.

Uniform Distribution

Calculate probabilities, density, cumulative probability, mean, variance and standard deviation for a continuous uniform distribution X ~ U(a, b). Enter the bounds, a point x, and an interval [c, d].

Weibull Distribution

Enter the shape and scale parameters of a Weibull distribution to compute the density, failure and survival probabilities, hazard rate, mean and median time to failure, or the probability of failing within an interval.

Gamma Distribution

Compute the gamma distribution's density, cumulative and tail probabilities, interval probabilities, mean, variance and mode. Enter the shape k, scale θ and a value or interval.

Normal Distribution

Enter a mean, standard deviation and a value (or two bounds) to get the probability density, cumulative probabilities P(X < x), P(X > x), P(a < X < b) and the z-score for a normal distribution.

Beta Distribution

Enter the shape parameters α and β to compute the beta distribution's density, cumulative and tail probabilities, interval probabilities, mean, variance and mode for any proportion between 0 and 1.

Exponential Distribution

Calculate exponential distribution probabilities from a rate λ or a mean waiting time: density, P(X ≤ t), P(X > t), interval probability, mean and median. Enter the rate, a time, and an optional interval end.

Negative Binomial Distribution

Compute exact and cumulative probabilities for the negative binomial distribution: enter the success probability, the target number of successes, and whether you count total trials or failures. Get P(X = x), cumulative tails, mean and variance.

Binomial Distribution

Calculate binomial probabilities: P(X = k), cumulative P(X ≤ k), P(X ≥ k), or a range of successes. Enter the number of trials, the success probability, and k to get the mean, variance, and standard deviation too.

Geometric Distribution

Enter the success probability p and a trial number k to get P(X = k), the cumulative probability, the tail probability, mean and variance of the geometric distribution — the wait time until the first success.

Hypergeometric Distribution

Calculate exact and cumulative hypergeometric probabilities for sampling without replacement. Enter the population size, number of successes, draws, and desired successes.

Lognormal Distribution

Enter the mean and standard deviation of ln(X) to compute lognormal probabilities: density and CDF at a point, or the probability over an interval, plus the mean and median of X.

Hypothesis Testing 8

P-Value

Enter a z, t, chi-square, or F test statistic to find the p-value for two-tailed, left-tailed, or right-tailed tests. Choose the distribution, degrees of freedom, and significance level to see whether your result is statistically significant.

Chi-Square Test

Compute the chi-square statistic, degrees of freedom and p-value for a test of independence (contingency table) or a goodness-of-fit test (observed vs. expected counts).

Odds Ratio & Relative Risk

Enter the four cell counts of a 2×2 table (exposed and unexposed groups, outcome present or absent) to compute the odds ratio, relative risk, outcome rates, and 95% confidence intervals, with a plain-language interpretation.

T-Test

Compute a one-sample or two-sample t-test from raw data or summary statistics. Enter your values, choose the alternative hypothesis and significance level, and get the t-statistic, degrees of freedom, p-value and conclusion.

ANOVA

Compute a one-way ANOVA from 3 to 6 groups of numbers. Enter each group's data and get the F-statistic, degrees of freedom, p-value, effect size (eta squared) and a full ANOVA table.

Cohen's d

Compute Cohen's d and Hedges' g from two group means, standard deviations and sample sizes — or paste raw samples. You also get the pooled SD, a 95% confidence interval and an interpretation of the effect size.

Fisher's Exact Test

Enter the four counts of a 2×2 contingency table and get the exact p-value for Fisher's exact test (two-sided and one-sided), plus the sample odds ratio and an interpretation at the 0.05 level.

McNemar's Test

Enter the counts of matched pairs in a 2×2 table and this calculator runs McNemar's test — exact binomial or chi-square — comparing paired binary outcomes before and after an intervention.

Descriptive Statistics 7

Skewness & Kurtosis

Enter a dataset and instantly get skewness and excess kurtosis, using either sample (Excel/SPSS) or population formulas, plus an interpretation of the distribution's shape.

Kaplan–Meier Survival

Estimate the survival curve from time-to-event data with censoring. Enter each subject's follow-up time and event status, and the calculator returns the Kaplan–Meier survival probabilities, S(t) at a chosen time, and the median survival time.

Standard Deviation

Enter your numbers to instantly calculate the sample or population standard deviation, variance, mean and count. Supports comma, space or line-break separated data, decimals and negative values.

Median & Mode

Enter a data set separated by commas, spaces, semicolons or line breaks and instantly get the median, the mode (or modes), the count of values, the mean and the sorted data, with a full explanation of each result.

Percentile

Find the value at any percentile of your dataset, or find the percentile rank of a specific value. Supports linear interpolation (Excel PERCENTILE.INC) and the nearest-rank method. Just paste your numbers.

Variance

Enter a data set and choose sample or population variance to get the variance, standard deviation, mean and a full breakdown of the calculation steps.

Coefficient of Variation

Calculate the coefficient of variation (CV) from your own data set or from a known standard deviation and mean. Enter comma-, space- or line-separated numbers and get CV, SD, mean and an interpretation.

Correlation & Regression 4

Linear Regression

Fit a straight line to paired X–Y data using ordinary least squares. Enter both data sets, and get the slope, intercept, correlation coefficient, R², residuals and a predicted value of Y for any X.

Spearman Rank Correlation

Enter two paired sets of values and this calculator computes Spearman's rank correlation coefficient (ρ), ranks each variable, and tests the association with an approximate p-value.

Correlation Coefficient

Enter two paired data sets and instantly get Pearson's correlation coefficient r, the coefficient of determination r², covariance and a plain-English interpretation of the relationship's strength and direction.

Kendall's Tau

Enter two paired lists of values to compute Kendall's tau-b, the concordant and discordant pair counts, the z statistic and the p-value for the rank association between the variables.

Probability 3

Probability

Enter the probabilities of two events A and B, choose how they are related, and instantly get the union, intersection, complements, and the chance of exactly one or neither event occurring.

Permutations & Combinations

Calculate permutations (nPr), combinations (nCr) and factorials instantly, with or without repetition. Enter the total number of items n, how many you choose r, and read all results at once.

Bayes' Theorem

Enter the prior probability, the likelihood of the evidence, and either the total probability of the evidence or the false-alarm rate to compute the posterior probability P(H|E) using Bayes' theorem.

Sample Size 2

Confidence Interval

Compute a confidence interval for a population mean or proportion. Enter your sample statistics, pick a confidence level, and get the margin of error and the lower and upper limits.

Sample Size

Calculate how many respondents or observations your survey or study needs. Enter the confidence level, margin of error, expected proportion (or standard deviation) and population size to get the required sample size.