Statistics Calculators
Free statistics calculators: confidence intervals, permutations, hypothesis testing, regression, Z-score, p-value, t-test, ANOVA, non-parametric tests, and more.
Statistics Calculators - From Basics to Advanced Inference
Statistics is the science of collecting, analysing, and interpreting data to make decisions under uncertainty. Whether you are running a clinical trial, analysing A/B test results, checking if two groups differ significantly, or fitting a curve to experimental data, the tools below give you precise, reproducible answers instantly.
Descriptive & Summary Statistics
Percentile Calculator - Find the percentile rank of any value in a dataset (midpoint formula), or find the value at any percentile using linear interpolation and nearest rank methods. Shows the five-number summary (min, Q1, median, Q3, max, IQR) and a sorted list with the target value highlighted. Two modes: Find Percentile Rank and Find Value at Percentile.
Sample Size Calculator - Find the minimum sample size for surveys (proportion mode: n = Z2 x p(1-p) / E2) or experiments (mean mode: n = (Z x sigma / E)2). Supports five confidence levels (80% to 99%), finite population correction (FPC), and shows the exact margin of error achieved with the computed n.
Correlation Coefficient Calculator - Compute Pearson r, R2, the regression equation (y = mx + b), t-statistic, and two-tailed p-value from raw X/Y data pairs or from summary statistics (n, SumX, SumY, SumX2, SumY2, SumXY). Interprets the correlation strength automatically and flags statistical significance.
Matthews Correlation Coefficient (MCC) Calculator - Compute MCC from a confusion matrix (TP, FP, FN, TN) or raw binary label arrays. Outputs 10 classification metrics: MCC, accuracy, balanced accuracy, precision, recall, specificity, NPV, F1, and Cohen’s kappa. Essential metric for evaluating binary classifiers on imbalanced datasets where accuracy is misleading.
Mean, Median & Mode Calculator - Central tendency for any dataset: mean, median, all modes, range, min, max.
Median Calculator - Find the median of any dataset (odd or even count). Enter numbers as a comma or space-separated list. Also shows mean, mode, count, min, max, and a sorted display with the median position highlighted. The preferred central value for skewed distributions like income and house prices.
Standard Deviation Calculator - Population and sample SD, variance, mean, and standard error.
Grouped Data Standard Deviation Calculator - Compute mean, population SD, sample SD, variance, and coefficient of variation from a grouped frequency distribution table. Enter up to 10 class midpoints and frequencies; shows the full working table with f times m, deviations, and weighted squared deviations for every class.
Variance Calculator - Compute sample variance (n-1), population variance (n), both standard deviations, mean, and a full deviation-squared table. Two modes: raw dataset (paste any numbers) and grouped frequency distribution (class midpoints and frequencies).
Descriptive Statistics Calculator - 25+ measures: mean, SD, quartiles, IQR, skewness, kurtosis, outliers, frequency table.
Probability Calculator - Single events, compound (AND/OR), conditional, binomial probability.
Coin Flip Probability Calculator - Two modes: (1) exact binomial probability of k heads in n flips (with at-least and at-most cumulative probabilities), (2) streak probability - P(at least s consecutive heads in n flips) using dynamic programming. Supports biased coins with custom head probability.
Conditional Probability Calculator - Calculate P(A|B) from two inputs: (1) direct input of joint probability P(A∩B) and marginal P(B), or (2) a 2×2 contingency table of raw counts giving both P(A|B) and P(B|A). Demonstrates Bayes’ theorem with real-world examples.
Dice Probability Calculator - Roll any number of dice (1–10) with any number of sides (2–20). Two modes: exact probability of a specific sum, and range probability (sum between min and max). Uses dynamic programming for accurate results. Shows probability as a percentage, reduced fraction, and number of favourable outcomes out of total.
Implied Probability Calculator - Convert betting odds to implied probability. Three modes: American (moneyline, e.g. +150 or −110), Decimal (e.g. 2.50), and Fractional (e.g. 5/2). Automatically converts to all three formats and shows the implied probability as a percentage - essential for evaluating fair value in sports betting and prediction markets.
Joint Probability Calculator - Calculate P(A∩B) for two events in two modes: (1) Independent events: P(A∩B) = P(A)×P(B), with union P(A∪B) and complement; (2) Dependent events via conditional probability: P(A∩B) = P(A)×P(B|A). Shows odds of the joint event and a plain-language interpretation.
Mean Absolute Deviation Calculator - Enter any comma-separated list of numbers to compute both MAD from the mean (Σ|xi−x̄|/n) and MAD from the median (Σ|xi−M|/n). Shows mean, median, each absolute deviation, and a full step-by-step breakdown. Useful for comparing spread when outliers make standard deviation misleading.
Median Absolute Deviation Calculator - Compute MAD = median(|xi − median(x)|) for any dataset. More robust to outliers than standard deviation (50% breakdown point). Also shows normalized MAD (×1.4826 as a consistent σ estimator), the MAD/SD ratio, and a per-value deviation table with automatic 3.5×MAD outlier flagging.
Relative Standard Deviation Calculator - Compute RSD (%) = (SD / |mean|) × 100, also called the Coefficient of Variation (CV). Supports both sample (n−1) and population (n) standard deviation. Handles near-zero mean with a warning. Used in analytical chemistry, quality control, and any field where spread must be compared across different scales.
Pooled Standard Deviation Calculator - Combine the standard deviations of two to five groups into a single estimate: Sp = √[Σ(ni−1)si² / Σ(ni−1)]. Two modes: Summary Stats (enter n and SD) or Raw Data (paste numbers). Shows pooled SD, pooled variance, total degrees of freedom, and a per-group breakdown table. Used in two-sample t-tests and ANOVA.
Probability of 3 Events Calculator - Calculate joint, union, and conditional probabilities for up to three events simultaneously. Two modes: (1) Independent - P(A∩B∩C) = P(A)×P(B)×P(C), with all unions and complements; (2) Dependent - use conditional probabilities P(B|A) and P(C|A∩B). Displays all 8 outcomes of the sample space and the probability tree.
Standardisation & Z-Scores
Z-Score Calculator - Convert raw scores to standard scores and find percentile rankings.
Raw Score Calculator - Convert between raw scores, Z-scores, T-scores (mean 50, SD 10), and percentiles.
Normal Approximation Calculator - Approximate binomial and Poisson probabilities using the normal distribution with continuity correction.
Normal Distribution Calculator - Find P(X less than x), P(X greater than x), P(a less than X less than b), and P(outside range) for any normal distribution. Two modes: Find Probability (left tail, right tail, between, outside) and Find X (inverse CDF for percentiles and critical values). Shows z-score and PDF value.
Hypothesis Testing
Hypothesis Testing Calculator - Full guided 6-step hypothesis test (Z, t, proportion) with conclusion and effect size.
p-Value Calculator - Find p-values from Z, t, F, or chi-square statistics. One-tailed and two-tailed.
Critical Value Calculator - Find critical values for Z, t, F, and chi-square distributions at any α level.
Z-Test Calculator - One-sample and two-sample Z-tests for means and proportions.
t-Test Calculator - One-sample, two-sample (Student’s and Welch’s), and paired t-tests with full output.
t-Statistic Calculator - Compute the t-value from sample data (one-sample, two-sample, paired).
F-Statistic Calculator - F-test for two variances, ANOVA F-test, and regression F-test.
Power Analysis Calculator - Calculate statistical power, required sample size, and Type I/II error rates.
Confidence Intervals & Estimation
Confidence Interval Calculator - CI for means and proportions at 90%, 95%, 99%, or any custom confidence level. Shows margin of error, critical z-value, and standard error.
Margin of Error Calculator - Survey MOE and required sample size for any confidence level.
Point Estimate Calculator - MLE, Wilson score, and Laplace estimates for proportions and means.
Sampling Error Calculator - Standard error of the mean, proportion SE, and finite population correction.
Degrees of Freedom Calculator - df for t-tests, chi-square, ANOVA, Welch’s, and regression.
Regression & Curve Fitting
Linear Regression Calculator - Least squares line (y = mx + b), slope, intercept, R², correlation, residuals.
Quadratic Regression Calculator - Fit y = ax² + bx + c to data using least squares.
Cubic Regression Calculator - Fit y = ax³ + bx² + cx + d to data.
Polynomial Regression Calculator - Fit polynomials up to degree 6 to your data.
Exponential Regression Calculator - Fit y = ae^(bx) to data (growth, decay, compound processes).
Coefficient of Determination (R²) Calculator - R², adjusted R², and SS decomposition from data, SS values, or correlation r.
Residual Calculator - Compute residuals, SSR, RMSE, and standardised residuals from regression output.
Error Analysis
Absolute Uncertainty Calculator - Propagate uncertainty through addition, multiplication, and power operations.
Relative Error Calculator - Absolute error, relative error, percentage error, MAE, and RMSE.
MSE Calculator (Mean Squared Error) - Enter actual and predicted value lists to compute MSE = (1/n)Σ(actual−predicted)², RMSE (root mean squared error), MAE (mean absolute error), and MAPE (mean absolute percentage error). Shows a residual table and handles zero-actual edge cases for MAPE. Used in regression model evaluation and forecasting.
Combinatorics
Combination Calculator - Calculate C(n,r) with step-by-step multiplicative expansion, side-by-side P(n,r) comparison, and a List All mode that enumerates every actual combination for n up to 10 and r up to 5.
Permutation Calculator - Calculate P(n,r) ordered arrangements with step-by-step multiplicative expansion, C(n,r) side-by-side comparison, and a List All mode that enumerates every actual arrangement for n up to 8 and r up to 4.
Permutation & Combination Calculator - Calculate nPr (ordered arrangements) and nCr (unordered selections) with full factorial step-by-step breakdown. Handles up to n = 170.
Specialised Tests
AB Test Calculator - Statistical significance for A/B experiments: conversion rates, lift, confidence intervals.
Bonferroni Correction Calculator - Adjust α for multiple comparisons (Bonferroni, Holm, Šidák methods).
Fisher’s Exact Test Calculator - Exact p-value for 2×2 contingency tables. Odds ratio and relative risk.
McNemar’s Test Calculator - Test for paired binary data (before/after, matched pairs).
Mann-Whitney U Test Calculator - Non-parametric test for two independent groups (alternative to t-test).
Wilcoxon Rank-Sum Test Calculator - Rank-sum test for two groups; also includes Wilcoxon signed-rank for paired data.
Youden Index Calculator - Diagnostic test performance: sensitivity, specificity, PPV, NPV, LR+, LR−, MCC.
Frequently Asked Questions
What is the difference between a Z-test and a t-test?
Use a Z-test when the population standard deviation σ is known, or when n > 30 (the Central Limit Theorem ensures normality of the sampling distribution). Use a t-test when σ is unknown and must be estimated from the sample - which is almost always the case in practice. For large samples, the two tests give virtually identical results.
How do I interpret a p-value?
A p-value is the probability of observing your test result (or something more extreme) if the null hypothesis were true. A small p-value (typically p < 0.05) means your result is unlikely under H₀, providing evidence to reject it. Crucially, p-value is NOT the probability that the null hypothesis is true - it is a conditional probability: P(data | H₀ true).
What is statistical power and why does it matter?
Statistical power (1−β) is the probability of correctly detecting a true effect. Low power means even real effects often go undetected (Type II errors). The Power Analysis Calculator helps you determine the sample size needed to achieve adequate power (typically 80% or 90%) before running your study - this is essential for clinical trials, psychology experiments, and quality control studies.
When should I use non-parametric tests?
Use non-parametric tests (Mann-Whitney U, Wilcoxon) when: your data is ordinal (e.g., ratings 1–5), the normality assumption is seriously violated, you have small samples with heavy-tailed distributions, or you are measuring something like pain scores or satisfaction ratings where the mean is not meaningful. They are based on ranks rather than raw values and are more robust to outliers.
What is R² and how do I interpret it?
R² measures the proportion of variance in Y explained by the regression model. R² = 0.85 means 85% of Y's variance is explained by X. Use adjusted R² when comparing models with different numbers of predictors - it penalises for adding variables that don't improve the model. R² alone does not tell you if the model is appropriate - always check residual plots too.
What is the Bonferroni correction and when is it needed?
When you run multiple hypothesis tests simultaneously, the probability of at least one false positive increases. The Bonferroni correction divides the significance threshold α by the number of comparisons k, requiring each test to meet α/k. For example, with 5 comparisons at α = 0.05, each test must reach p < 0.01. Use it for GWAS studies, pairwise ANOVA comparisons, or any analysis with multiple outcomes.