Statistics Calculators

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).

Frequency Distribution Calculator - Build a complete frequency distribution table for any dataset. Ungrouped mode lists exact counts for each value; Grouped mode creates class intervals with midpoints. Outputs frequency, relative frequency, cumulative frequency, and cumulative relative frequency columns for up to 500 data points.

Percentile Rank Calculator - Find the percentile rank of any score using two methods: Normal Distribution mode (enter population mean, SD, and score; outputs z-score and PR via normal CDF for standardized tests like IQ, SAT, GRE) and From Count mode (enter values below, values equal, and total N; outputs PR using the midpoint formula PR = (L + 0.5E)/N x 100 for empirical data). - Build a complete frequency distribution table for any dataset. Ungrouped mode lists exact counts for each value; Grouped mode creates class intervals with midpoints. Outputs frequency, relative frequency, cumulative frequency, and cumulative relative frequency columns for up to 500 data points.

Descriptive Statistics Calculator - 25+ measures: mean, SD, quartiles, IQR, skewness, kurtosis, outliers, frequency table.

Probability Calculator - Single events, compound (AND/OR), conditional, binomial probability.

Binomial Distribution Calculator - Exact probability P(X=k), cumulative P(X≤k), upper tail P(X≥k), mean, variance, and standard deviation for any Binomial(n, p). Distribution Table mode generates the full PMF and CDF for all k from 0 to n.

Poisson Distribution Calculator - Exact probability P(X=k), cumulative P(X≤k), upper tail P(X≥k), mean, and standard deviation for any Poisson(lambda). Distribution Table mode generates the full PMF and CDF table. Supports lambda up to 500 using log-space computation.

Geometric Distribution Calculator - Exact probability P(X=k), cumulative P(X≤k), upper tail P(X≥k), mean (1/p), variance ((1-p)/p²), and standard deviation for the geometric distribution. Distribution Table mode generates a full PMF and CDF table from k=1 to your chosen maximum. Models the number of trials until the first success.

Negative Binomial Distribution Calculator - Exact probability P(X=k), cumulative P(X≤k), upper tail P(X≥k), mean (r/p), variance (r(1-p)/p²), and standard deviation for the negative binomial distribution. Distribution Table mode generates the full PMF and CDF. Models the number of trials needed to achieve r successes.

Exponential Distribution Calculator - CDF P(X≤x), survival P(X>x), PDF f(x), mean (1/λ), variance (1/λ²), standard deviation, and median (ln2/λ) for any Exp(λ). Between Values mode computes P(a≤X≤b) with above and below tail probabilities. Models waiting times in Poisson processes.

Rayleigh Distribution Calculator - PDF f(x), CDF P(X≤x), survival P(X>x), mean (σ√(π/2)), variance, SD, median, and mode for any Rayleigh(σ). Distribution Stats mode adds Q1, Q3, IQR, skewness (0.6311), and excess kurtosis (0.2451). Models signal amplitudes in Rayleigh fading channels, wind speeds, and ocean wave heights.

Sampling Distribution of the Sample Proportion Calculator - Find P(p̂≤query), P(p̂>query), z-score, SE = √(p(1−p)/n), mean, and variance for the sampling distribution of p̂. Between Values mode computes P(lower≤p̂≤upper). Displays normal-approximation validity note (np≥10 and n(1−p)≥10). Used for polling, quality control, A/B testing, and proportion hypothesis tests.

Weibull Distribution Calculator - PDF f(x), CDF P(X≤x), reliability S(x), mean (λΓ(1+1/k)), median, mode, variance, and SD for any Weibull(k, λ). Distribution Stats mode adds skewness and excess kurtosis. Models bearing lifetimes, wind speeds, material fatigue, and failure-time data in reliability engineering.

Uniform Distribution Calculator - Calculate P(x1 to x2), CDF, mean, variance, SD, IQR, skewness, and kurtosis for any continuous uniform distribution U(a, b). Two modes: Probability (enter query limits to get exact probabilities) and Distribution Stats (full parameter table).

Hypergeometric Distribution Calculator - Exact probability P(X=k), cumulative P(X≤k), upper tail P(X≥k), mean (nK/N), variance with finite population correction, and standard deviation for the hypergeometric distribution. Distribution Table mode generates the full PMF and CDF for all valid k values. Models sampling without replacement from a finite population.

Beta Distribution Calculator - PDF f(x), CDF P(X≤x), survival P(X>x), mean (α/(α+β)), variance, SD, and mode for any Beta(α, β) distribution on [0, 1]. Distribution Stats mode adds median, skewness, and excess kurtosis. Used for Bayesian conjugate priors, PERT estimates, and A/B test conversion rate modeling.

Frequency Polygon Calculator - Draw a frequency polygon chart from class midpoints and frequencies, or from raw comma-separated data. Computes grouped mean (sum f_i*m_i / N), population SD, modal class midpoint, and median class midpoint. Two modes: From Frequency Table and From Raw Data (auto-builds equal-width classes).

Lognormal Distribution Calculator - Compute PDF f(x), CDF P(X≤x), survival function, mean (exp(μ+σ²/2)), median (exp(μ)), mode (exp(μ−σ²)), variance, standard deviation, skewness, and excess kurtosis for any lognormal distribution. Probability mode queries a specific x; Stats mode gives full distributional moments.

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.

Post-Test Probability Calculator - Apply Bayes theorem to diagnostic testing. Sensitivity and Specificity mode: enter pre-test probability, sensitivity, and specificity to get post-test probability for both positive and negative test results, plus LR+ and LR-. Likelihood Ratio mode: enter pre-test probability and LR directly. Shows pre-test odds, post-test odds, and PPV. Covers the base-rate fallacy, Fagan nomogram method, and clinical interpretation of LR values.

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.

Dice Average Calculator - Compute the expected value (mean), variance, standard deviation, minimum, maximum, and range for any die (d2–d100) or for rolling multiple identical dice (up to 20 dice). Uses exact closed-form formulas: E[X] = (n+1)/2 and Var(X) = (n²−1)/12 for a single n-sided die.

Quiz: Dice Average Calculator - Practice expected value, expected sum for multiple dice, and variance calculations with randomly generated problems. Enter your answer, click Check Answer for instant feedback, and see the full worked solution.

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.

Standard Deviation Index Calculator - Calculate the Standard Deviation Index (SDI) for laboratory proficiency testing and external quality assurance. Formula: SDI = (Lab Result minus Survey Mean) divided by Survey SD. Returns SDI, absolute SDI, absolute bias, percentage bias, and a performance rating (Excellent, Acceptable, Warning, or Unacceptable) using standard CAP/RCPA thresholds. Essential tool for clinical laboratory scientists evaluating analytical bias against a peer group consensus mean.

Standard Deviation of Sample Mean Calculator - Compute the standard error of the mean (SE = sigma divided by sqrt(n)) from any population standard deviation and sample size. Two modes: Compute SE (returns SE, SE as a percentage of sigma, and margins of error at 90%, 95%, and 99% confidence) and Find Sample Size (find the minimum n required for a target margin of error at any confidence level, with actual SE and MOE after rounding). Essential for survey planning, clinical study design, and quality control.

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.

Inverse Normal Distribution Calculator - Find the x value or critical z-score for any normal distribution given a cumulative probability. Find X Value mode: enter mean, SD, and probability (left or right tail) to get the exact quantile and z-score. Critical Values mode: enter significance level and tail type to get rejection-region z-values for z-tests and confidence intervals.

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.

Normal Probability Calculator for Sampling Distributions - Find P(X-bar less than x), P(X-bar greater than x), or P(a less than X-bar less than b) for any sampling distribution using the Central Limit Theorem. Automatically computes standard error SE = sigma / sqrt(n) and the corresponding Z-score. Two modes: Single Tail and Between Two Values. Essential for hypothesis tests about sample means and quality control probability calculations.

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.