Statistics

Standard deviation calculator for sample and population data. Find standard deviation, variance, mean, sum, and range from a list of numbers instantly.

Standard deviation calculator: compute sample SD, population SD, mean, variance, and CV from any dataset. Enter numbers and get results instantly.

Variance calculator for sample and population data. Computes variance, standard deviation, mean, median, mode, and IQR from any list of numbers instantly.

Calculate the pooled standard deviation for two samples using sizes, means, and standard deviations. Accurate results for t-tests and statistical analysis.

Standard deviation of sample mean (SEM) calculator: compute SEM, mean, variance, and SD from raw data. Enter comma-separated numbers to get results instantly.

Standard error calculator: compute SE from raw data or summary statistics. Includes confidence intervals at 90%, 95%, and 99% — free and accurate.

RSD = (standard deviation ÷ mean) × 100%: paste your data set and get RSD/CV instantly with steps shown — under 5% is usually considered precise in lab work. Free, no signup.

Relative Standard Error (RSE) calculator — divide standard error by the estimate to get a unit-free precision percentage and a qualitative reliability rating.

Weighted mean calculator for grades, finance, and surveys. Enter values and weights to compute the weighted average — supports any number of data points.

IQR calculator: compute interquartile range, Q1, Q3, and identify outliers from any dataset. Enter comma-separated numbers and get instant quartile analysis.

Outlier calculator using the IQR method: enter a data set to find mild outliers (1.5×IQR) or extreme outliers (3×IQR) with Q1, Q3, and fence values instantly.

Calculate upper and lower fences using the IQR method to identify outliers in your dataset. Instantly find Q1, Q3, IQR, and all data points outside the fences.

Coefficient of variation calculator: enter comma-separated numbers to get mean, sample standard deviation, and CV% for instant relative variability comparison.

Dispersion calculator: enter comma-separated numbers to get range, variance, standard deviation, IQR, coefficient of variation, and MAD in one click.

Calculate population variance, standard deviation, and mean for any data set. Free online statistical dispersion tool — paste numbers and get results instantly.

Find k in y = kx with this proportionality calculator. Enter one or more (x, y) pairs to compute the constant and verify direct proportion.

Calculate Cohen's d effect size from two group means, standard deviations, and sample sizes. Ideal for psychology, education, and medical research analysis.

Paired samples t-test calculator: enter two matched data groups to get the t-statistic, degrees of freedom, p-value, and 95% confidence interval.

One-sample and two-sample Z-test calculator for hypothesis testing. Enter sample mean, population SD, and sample size to get the Z-statistic and p-value.

P-value calculator for Z, T, F, and Chi-square tests: enter a test statistic and degrees of freedom to get the exact p-value and significance verdict.

Perform an F-test for equality of two variances. Enter sample variances and sizes to get the F-statistic, p-value, and reject/fail-to-reject decision.

Calculate the F-statistic and p-value for comparing two sample variances. Enter group variances and sizes to run an ANOVA or F-ratio test instantly.

Wilcoxon signed-rank test calculator for paired samples. Compare before-and-after measurements with W statistic, Z-score, and p-value — no normality assumption.

Perform a Wilcoxon Rank Sum Test (Mann-Whitney U) for two independent samples. Get the U statistic, Z-score, and p-value instantly — no normality required.

Run Fisher's Exact Test on a 2×2 contingency table. Get one-tailed and two-tailed p-values plus the odds ratio — ideal for small sample sizes in research.

Wald test calculator for statistical significance. Enter parameter estimate, standard error, and alpha level to get the Wald statistic, z-score, and p-value.

Sample size calculator using Cochran's formula. Enter confidence level, margin of error, and proportion to get the minimum sample size for reliable surveys.

Confidence interval calculator for sample means. Enter summary stats or raw data to get CI bounds, margin of error, and SE at 90%, 95%, or 99%.

Hypothesis testing calculator for Z-tests and T-tests. Compute test statistic, p-value, and critical value to determine statistical significance.

Z-score calculator: find how many standard deviations a value is from the mean. Enter raw score, mean, and standard deviation to get z-score and interpretation.

Perform one-way repeated measures ANOVA analysis. Enter subject data to get F-statistic, effect size (eta squared), and complete ANOVA table instantly.

Perform Tukey's HSD post-hoc test after ANOVA. Compare all group mean pairs to find statistically significant differences with one free online tool.

Spearman's rank correlation calculator: compute ρ for two datasets. Measures monotonic relationships without normality requirements — ideal for ordinal data.

Fit data to a polynomial equation with this free curve fitting tool. Get the best-fit polynomial equation, R-squared value, and predict new values instantly.

Fit an exponential regression model y = ab^x to your data. Get coefficients a and b, R-squared, correlation, and predicted values from paired data points.

Calculate linear regression residuals instantly. Enter X and Y values to get the regression line, predicted values, residuals, and R-squared for any dataset.

Find P(A|B), joint P(A∩B), or marginal P(B) with this conditional probability calculator. Covers Bayes' theorem and real-world probability problems.

Calculate expected value, variance, and standard deviation for discrete probability distributions. Enter outcomes and probabilities to get E[X] instantly.

Free nCr nPr calculator: enter n and r to compute combinations and permutations instantly for probability, lottery, and combinatorics.

Implied probability calculator: convert American, Decimal, or Fractional betting odds to a winning probability percentage for sports betting value analysis.

Online coin flipper: simulate one or thousands of random coin tosses, choose fair or biased coins, and track real-time heads/tails counts and percentages.

Binomial coin flip probability calculator: find the chance of N heads in any number of flips — compute exactly, at least, or at most outcomes instantly.

Coin streak probability: find the chance of consecutive heads or tails in N tosses, or compute the expected tosses needed to achieve any streak length.

Dice roller calculator: simulate rolling multiple dice and get instant statistics — mean, median, mode, standard deviation, and full frequency distribution.

Dice probability calculator: find exact, at-least, or at-most probabilities for any combination of dice with up to 10 dice and 20 sides per die.

Roulette payout calculator for American and European wheels. Enter bet type and wager to get net winnings, total payout, payout odds, and win probability.

Explore the Two Envelopes Paradox interactively. Calculate expected values for switching or keeping, and understand the probability math behind this puzzle.

Calculate the probability of truly having a condition after a positive test. Enter prevalence, sensitivity, and specificity to see the false positive paradox.

Inverse normal distribution calculator: find the x-value for a given probability. Supports left-tailed, right-tailed, and two-tailed modes with custom μ and σ.

Calculate exact and cumulative Poisson probabilities instantly. Find P(X=x), P(X≤x), P(X≥x) for any lambda and event count — free online statistics tool.

Compute exponential distribution PDF, CDF, mean, variance, and survival probability. Enter rate parameter λ and value x for instant statistical results.

Calculate PDF, CDF, mean, variance, and interval probability for any uniform distribution. Enter the range parameters a and b to get instant results.

Weibull distribution calculator for reliability analysis. Compute PDF, CDF, hazard rate, mean, median, and variance from shape and scale parameters instantly.

Rayleigh distribution calculator: compute PDF, CDF, complementary CDF, mean, median, mode, and variance from scale parameter σ and value x instantly.

Sampling distribution of the sample mean calculator: find SE, z-score, and probability (less than, greater than, between) using the Central Limit Theorem.

Sampling distribution of the sample proportion calculator. Find mean, standard error, normality check, Z-score, and cumulative probabilities instantly.

Create a frequency distribution table from any data set. Calculate frequency, relative frequency, cumulative frequency, mean, median, and standard deviation.

Dot plot calculator: enter a data set to generate a visual dot plot with mean, median, mode, and range — perfect for classrooms and quick data exploration.

Relative frequency calculator: enter a comma-separated data set and instantly get frequency counts, relative frequency, and cumulative frequency for each value.

Venn diagram calculator for 2 and 3 sets. Find union, intersection, and exclusive regions instantly — ideal for set theory, probability, and survey analysis.

Calculate AUC and plot ROC curves for binary classifiers. Input prediction scores and true labels to get sensitivity, specificity, and optimal threshold.

Calculate the Upper Control Limit (UCL) for statistical process control charts. Enter raw data or summary stats to monitor process variation and quality.

Index of Qualitative Variation calculator: measure categorical data diversity from frequency counts. Compute IQV, observed and possible pairs instantly.

Predict future values with exponential growth. Use initial value and rate, or two data points to forecast population, investment, or bacterial growth.

Odds ratio calculator for 2×2 contingency tables: compute OR, confidence interval, Z-score, and p-value for case-control and epidemiological research studies.

Relative risk calculator for 2×2 contingency tables: compute risk ratio, 95% confidence interval, and attributable risk for exposed vs. unexposed cohort data.

Relative risk reduction calculator: compute RRR, ARR, NNT, and relative risk from treatment and control group data to evaluate any intervention's effectiveness.

Calculate relative risk (RR), absolute risk reduction (ARR), and number needed to treat (NNT). Free online risk calculator for clinical trials and epidemiology.

Calculate post-test probability using Bayes' theorem. Enter prior probability, sensitivity, and specificity to find PPV, NPV, and likelihood ratios.

P-hat calculator: enter sample size (n) and successes (x) to compute the sample proportion p̂ and its complement q̂ as decimals and percentages in one click.

Confusion matrix calculator: enter TP, FP, TN, FN to compute accuracy, precision, recall, F1-score, specificity, and MCC for binary classification models.

Calculate error propagation and measurement uncertainty for sum/difference and product/power formulas. Get absolute and relative uncertainty instantly.

Relative error calculator: find absolute error, relative error, and percentage error by comparing an observed value to the true value in any measurement.

Sampling error calculator for proportions and means. Enter sample data and confidence level to get the standard error and margin of error with FPC support.

Empirical rule calculator: enter mean and standard deviation to get the 68%, 95%, and 99.7% ranges for any normal distribution instantly.

Calculate a Yates-corrected chi-square statistic for 2×2 contingency tables. Enter a, b, c, d cell counts and get the adjusted χ² value and p-value instantly.

Lognormal distribution calculator finds PDF, CDF, mean, median, mode, and variance from mu, sigma, and any positive x value instantly.

Log-rank test calculator compares two survival distributions with censored data, observed and expected events, chi-square statistic, and p value.

Linear regression calculator finds the line of best fit, slope, intercept, correlation, R-squared, and predictions from paired data instantly.

Least to greatest calculator sorts number sets in ascending order and finds mean, median, mode, count, and range for instant data analysis.

Kruskal-Wallis H test calculator compares three independent groups with ranked data, tie correction, chi-square statistic, and p value instantly.

Critical value calculator finds Z, t, chi-square, and F cutoffs from alpha, tails, and degrees of freedom for accurate hypothesis tests.

Covariance calculator finds sample and population covariance, means, and paired-data relationships from two numeric data sets instantly.

Matthews correlation coefficient calculator evaluates binary classifiers from TP, TN, FP, and FN counts with MCC and key performance metrics.

Pearson correlation coefficient calculator finds r, R-squared, and the t-statistic from paired X and Y data for fast relationship analysis.

Continuity correction calculator approximates binomial probabilities with a normal distribution, corrected bounds, and z-scores for accurate results.

Coefficient of determination calculator finds R-squared, adjusted R-squared, correlation, and the linear regression equation from paired data.

Class width calculator finds frequency distribution and histogram intervals from minimum, maximum, raw data, and a chosen class count instantly.

Chi-square goodness of fit calculator compares observed and expected frequencies, returning the test statistic, degrees of freedom, and p-value.

Chi-square test calculator finds the statistic, degrees of freedom, and p-value for a contingency table to assess categorical association instantly.

Chebyshev's theorem calculator finds probability bounds and intervals from a mean, standard deviation, and k value for any distribution instantly.

Frequency polygon calculator to group raw data into class intervals, count frequencies, and find midpoint coordinates for a clear distribution graph.

Geometric distribution calculator for exact and cumulative first-success probability, mean, and variance from any Bernoulli success rate.

Grouped data standard deviation calculator using class midpoints and frequencies. Find weighted mean, sample or population variance instantly.

Histogram calculator to organize raw values into customizable bins, summarize frequencies, and reveal the shape of your data distribution instantly.

Hypergeometric distribution calculator for sampling without replacement. Find exact probability, expected successes, and variance instantly.

Sensitivity and specificity calculator for diagnostic tests. Find PPV, NPV, and accuracy from confusion matrix counts with instant results.

Shannon entropy calculator for probabilities or text. Measure information uncertainty, randomness, and entropy in bits with instant results.

Sign test calculator for paired data and median differences. Get sign counts, an exact two-sided p-value, and a clear significance result.

Simpson's Diversity Index calculator for species counts. Find D, Index of Diversity, and Reciprocal Index to measure biodiversity instantly.

Skewness calculator with excess kurtosis, mean, and sample standard deviation. Analyze data distribution asymmetry and tail shape instantly.

Quadratic regression calculator for curve fitting, R-squared analysis, and y predictions. Enter paired data to get an accurate best-fit equation instantly.

Quartile calculator for Q1, median, Q3, IQR, and five-number summaries. Enter any data set to measure center and spread with clear results instantly.

Random number generator for custom integer or decimal sets. Choose a range, quantity, and duplicate rules to create results instantly for any task.

Range calculator for mean, median, mode, variance, and standard deviation. Enter a number set to get a complete descriptive statistics summary instantly.

Raw score calculator to convert values into Z-scores, T-scores, and normal percentiles. Enter the mean and standard deviation for instant context.

Stem and leaf plot calculator for ordered whole-number data. Build a clear plot, preserve frequencies, and inspect distributions instantly for free.

Sum of squares calculator for raw and corrected data totals. Find mean, total variation, and sample variance with clear instant results.

Survival analysis calculator for Kaplan-Meier estimates. Enter event times and censoring data to get risk sets, survival rates, and median survival.

T statistic calculator for a one-sample mean. Enter summary statistics to find the t value, standard error, and degrees of freedom instantly.

T test calculator for two independent means using Welch's method. Find the t statistic, degrees of freedom, and two-tailed p-value instantly.

Parrondo's paradox calculator compares capital-dependent games and mixed strategies to reveal long-run expected returns with exact results.

Partial correlation calculator controls for a third variable using three Pearson coefficients, revealing the adjusted relationship instantly.

Password combination calculator finds possible passwords and theoretical entropy from length and character-set size for instant security insight.

Pearson correlation calculator finds Pearson's r, r squared, and linear relationship strength from paired data with clear instant results.

Percentile calculator finds any data percentile using sorted values and linear interpolation, with quartile presets and clear instant results.

Mean absolute deviation calculator finds MAD, arithmetic mean, sum, and count for any numeric data set with clear, instant statistical results.

Mean, median, mode calculator finds central tendency, range, variance, and standard deviation from any numeric data set with instant results.

Median absolute deviation calculator finds raw MAD, the median, and sorted absolute deviations for robust statistical analysis with outliers.

Median calculator finds the middle value, mean, mode, range, minimum, and maximum from any number set with sorted, easy-to-check results.

Midrange calculator finds the midpoint, range, minimum, and maximum of any numeric data set, with a sorted list and transparent formula.

Percentile rank calculator finds a score's relative standing in any data set with tie-adjusted ranking and transparent counts for instant insight.

Permutation calculator for nPr arrangements with or without repetition. Enter n and r to count ordered selections with clear formulas instantly.

Pie chart calculator converts category values into a proportional circle graph with exact percentages and a readable data summary instantly.

Point-biserial correlation calculator measures binary and continuous variable association with group means and a clear coefficient instantly.

Point estimate calculator finds a population mean or proportion from sample data, success counts, and sample size with instant clear results.

Birthday paradox calculator finds shared birthday probability for any group size using the classic birthday problem formula with instant results.

Bonferroni correction calculator adjusts alpha for multiple hypothesis tests, controlling family-wise error with an instant significance threshold.

Box plot calculator finds the five-number summary, quartiles, median, IQR, and outliers from your data for fast box-and-whisker analysis.

Boy or girl paradox calculator compares conditional gender probability scenarios and explains Bayesian sample spaces with clear instant results.

Central limit theorem calculator finds sample mean probability, standard error, and z-scores from population parameters with instant results.

5 number summary calculator finds minimum, Q1, median, Q3, maximum, and IQR from any data set for quick box plot and descriptive analysis.

A/B test calculator compares conversion rates with a two-proportion z-test, p-value, and relative uplift so you can evaluate experiments confidently.

Absolute uncertainty calculator finds mean, range, half-range error, and standard uncertainty from repeated measurements for clear lab reporting.

Power analysis calculator estimates sample size from effect size, significance level, and statistical power for clear, evidence-based study planning.

Probability calculator finds complements, intersections, unions, and neither outcomes for two independent events with clear percentage results.

Probability of 3 events calculator finds all, at least one, none, and exactly one outcome for three independent events with instant results.

Process capability index calculator finds Cp, Cpk, Cpu, and Cpl from specification limits, process mean, and standard deviation instantly.

Propensity score matching calculator pairs treated and control observations by nearest score and estimates ATT for transparent causal analysis.

Lottery odds calculator finds jackpot probability for main and bonus ball games, including Powerball-style draws and multiple tickets, instantly.

Mann-Whitney U test calculator compares two independent samples with ranked data, returning U, Z score, and a tie-corrected p value instantly.

Margin of error calculator estimates survey confidence interval precision and standard error with an optional finite population correction.

McNemar chi-squared test calculator analyzes paired binary data in a 2 by 2 table, returning the uncorrected statistic and p value instantly.

McNemar's test calculator compares paired proportions in a 2 by 2 table with continuity-corrected chi-squared and p value results.

Negative binomial distribution calculator for exact and cumulative probabilities, expected failures, and variance with clear instant results.

Normal approximation calculator for binomial probability with continuity correction, mean, standard deviation, and z-score in seconds.

Normal distribution calculator for PDF, CDF, z-scores, upper tails, and interval probabilities from any mean and standard deviation.

Normal probability calculator for sampling distributions of means and proportions. Find standard errors, z-scores, and interval probabilities.

Odds calculator to convert favorable and unfavorable outcomes into odds for, odds against, probability, percentage chance, and decimal odds.

Minimum and maximum calculator to find the smallest value, largest value, range, count, and sorted data from any number set instantly.

Mode calculator to find the most frequent number, frequency, and multiple modes in any data set. Get accurate unimodal or multimodal results instantly.

Monty Hall problem simulator comparing stay and switch strategies. Explore conditional probability and expected win rates with any number of trials.

MSE calculator for actual and predicted values. Calculate mean squared error, RMSE, and mean absolute error instantly to evaluate model accuracy.

Multiple linear regression calculator for ordinary least squares. Enter dependent and independent variables to get coefficients, R-squared, and an equation.

Classification accuracy calculator finds precision, recall, specificity, and F1 score from confusion matrix counts with instant clear results.

One-way ANOVA calculator compares independent group means and returns the F-statistic, degrees of freedom, and sums of squares instantly.

Two-way ANOVA calculator tests two main effects and their interaction in a balanced 2 x 2 design with clear F-statistics and error degrees.

Average rating calculator finds the weighted mean of one- to five-star vote counts and reports the total reviews for a clear result.

Bayes theorem calculator finds posterior and evidence probabilities from a prior, likelihood, and alternative likelihood with clear results.

Benford's Law calculator compares first-digit distribution, mean absolute deviation, and chi-square statistics to reveal data anomalies instantly.

Bertrand's Box Paradox calculator explains conditional probability and Bayes' theorem for classic or custom gold and silver coin boxes instantly.

Bertrand's Paradox calculator solves the classic box problem with conditional probability and expected trial outcomes for instant insight.

Beta distribution calculator finds PDF, CDF, mean, variance, and mode from alpha, beta, and x values for fast probability analysis.

Binomial distribution calculator finds exact and cumulative probabilities, mean, and variance for Bernoulli trials with instant results.

Dice average calculator for expected value, variance, and standard deviation. Analyze any fair dice pool and its possible total range instantly.

Descriptive statistics calculator for mean, median, mode, variance, and standard deviation. Summarize any numeric data set instantly and accurately.

Degrees of freedom calculator for t-tests, chi-square, ANOVA, and regression. Enter sample dimensions to get the correct DF and formula instantly.

Decile calculator for any numeric data set. Calculate D1 through D9 with interpolated ranks and explore distribution cut points instantly.

Cubic regression calculator for fitting paired data to a third-degree polynomial. Find the curve equation, coefficients, and R-squared instantly.

Flip a virtual water bottle with true randomness, tune the fill level, and see on a live probability curve why one-third full lands best.