Statistics & probability calculators
Descriptive statistics, distributions and inference, with the estimator named (sample or population, one- or two-sided) so the result can be reported correctly.
A/B testing
- A/B Test Significance CalculatorCheck whether variant B’s conversion rate differs from A’s with a pooled two-proportion z-test: p-value, lift and a confidence interval for the difference.
- A/B Test Sample Size CalculatorFind how many visitors each variant needs to detect a chosen lift in conversion rate at your significance level and power, one- or two-sided.
Bayesian inference
- Bayesian Posterior Probability CalculatorUpdate a prior probability with new evidence using Bayes’ theorem: enter P(H), P(E | H) and P(E | not H) to get P(H | E), P(E) and the likelihood ratio.
- Bayes Factor CalculatorCompute the Bayes factor BF₁₀ for a binomial proportion against a point null with a beta prior, or from two marginal likelihoods, with evidence labels.
Cohort & data metrics
- Churn Cohort Retention CalculatorTrack one sign-up cohort over time: retention against the starting size, churn in each period, cumulative churn and the average churn rate per period.
- Data Missingness Percentage CalculatorWork out the percentage of missing cells in a data set and how many complete rows are left for a complete-case (listwise deletion) analysis.
Correlation & regression
- Pearson Correlation CalculatorPaste paired x and y data to get Pearson’s r, r², the t test of zero correlation (two- or one-sided p) and a Fisher z confidence interval for r.
- Spearman Correlation CalculatorCompute Spearman’s rank correlation ρ from paired data, with average ranks for ties, Σd² and a two- or one-sided p-value from the t approximation.
- Linear Regression Slope CalculatorFit a least-squares line to x and y data and get the slope with its standard error, t statistic, two-sided p-value and confidence interval.
- Linear Regression Intercept CalculatorFind the y-intercept of the least-squares line with its standard error, t test of b₀ = 0, two-sided p-value and confidence interval.
- R-Squared CalculatorGet R² and adjusted R² for a straight-line fit with its F test, or for any model’s predictions against actual values, with SSres and SStot shown.
Counting
Descriptive statistics
- Statistics CalculatorPaste a list of numbers to get a full summary: mean, median, mode, quartiles and IQR, sample and population standard deviation, standard error and skewness.
- Weighted Average CalculatorFind the weighted mean of a list of values with their weights, plus the sum of weights, the unweighted mean for comparison and the weighted standard deviation.
- Geometric Mean CalculatorFind the geometric mean of positive numbers, or the compound average of percentage changes, with the geometric standard deviation and arithmetic mean.
- Harmonic Mean CalculatorCalculate the harmonic mean of positive numbers, optionally weighted, to average rates such as speeds or price-to-earnings ratios correctly.
- Median Absolute Deviation CalculatorCompute the median absolute deviation, its normal-consistent scaled version (×1.4826) and modified z-score outliers from a list of numbers.
- Interquartile Range CalculatorFind Q1, Q3 and the interquartile range using the inclusive (Excel QUARTILE.INC), exclusive (QUARTILE.EXC) or Tukey hinge method, compared side by side.
- Tukey Fence Outlier CalculatorFind outliers with Tukey’s fences: Q1 − k×IQR and Q3 + k×IQR, with k = 1.5 for outliers and 3 for far-out values, and the quartile method stated.
- Percentile Rank CalculatorFind the percentile rank of a score within a list of values, with ties counted half, plus the share of values strictly below and at or below it.
Forecast & model error
- RMSE CalculatorPaste actual and predicted values to get the root mean square error, MSE, MAE, mean bias and RMSE normalised by the mean and by the range.
- Mean Absolute Error CalculatorCompute the mean absolute error between actual and predicted values, with the mean bias, median and maximum absolute error and RMSE for comparison.
- MAPE CalculatorMeasure forecast accuracy as a percentage: MAPE, symmetric MAPE and weighted WAPE from actual and forecast values, with zero actuals handled explicitly.
Hypothesis tests
Inference
- Sample Size CalculatorFind how many responses a survey needs to estimate a proportion within a chosen margin of error and confidence level, with a finite population correction.
- Confidence Interval CalculatorFind the confidence interval for a population mean from the sample mean, standard deviation and size, using the t-distribution or a known σ.
- P-value CalculatorGet the exact p-value for a z, t, chi-square or F test statistic, one- or two-tailed, and see whether it is significant at your chosen α.
- Cohen’s d Effect Size CalculatorCompute Cohen’s d from two group means, SDs and sizes using the pooled sample SD, plus bias-corrected Hedges’ g and an approximate confidence interval.
- Statistical Power CalculatorApproximate the power of a test of means from effect size d, sample size and α, and the sample size needed for a target power, one- or two-sided.
- Confidence Interval for a Proportion CalculatorGet a confidence interval for a proportion from successes and trials by the Wilson, Clopper–Pearson exact, Agresti–Coull or Wald method, compared in a table.
- Wilson Score Interval CalculatorCompute the Wilson score interval for a proportion, with or without continuity correction, plus the one-sided lower bound used to rank ratings.
- Bootstrap Mean Interval CalculatorResample your data thousands of times to get a percentile bootstrap confidence interval and standard error for the mean, with a seed for repeatable runs.
Information theory
- Shannon Entropy CalculatorCalculate the Shannon entropy of a probability distribution or set of counts in bits, nats or hartleys, with maximum entropy, evenness and perplexity.
- Gini Impurity CalculatorCalculate the Gini impurity of a node from its class counts, with the maximum possible impurity, a normalised score and the entropy for comparison.
- Information Gain CalculatorEnter the class counts in each child node of a split to get information gain (entropy or Gini), split information and the gain ratio used by C4.5.
- KL Divergence CalculatorCalculate the Kullback–Leibler divergence D(P‖Q) and D(Q‖P) between two discrete distributions, plus cross-entropy and Jensen–Shannon divergence.
Machine learning metrics
- Class Imbalance Ratio CalculatorEnter class counts to get the imbalance ratio (majority ÷ minority), each class’s share, entropy-based balance and balanced class weights.
- Precision Recall F1 CalculatorCalculate precision, recall, the F1 score and any F-beta score from true positives, false positives and false negatives, with the error rates shown too.
- Confusion Matrix Accuracy CalculatorFrom TP, FP, FN and TN, calculate accuracy, error rate, balanced accuracy, the Matthews correlation coefficient and Cohen’s kappa for a binary classifier.
- Sensitivity and Specificity CalculatorCalculate sensitivity, specificity, false-positive rate, Youden’s J, likelihood ratios and predictive values at any prevalence from a 2 × 2 table.
Normal distribution
Probability
- Probability CalculatorFind the probability of A and B, A or B, exactly one, neither, and of A happening at least once in several tries, for independent events.
- Expected Value CalculatorFind the expected value, variance and standard deviation of a discrete random variable from its outcomes and probabilities, percentages or weights.
- Conditional Probability CalculatorFind P(A given B), P(B given A), P(A or B) and whether two events are independent from P(A), P(B) and P(A and B), as decimals, fractions or percentages.
- Hypergeometric Probability CalculatorProbability of exactly, at most or at least k successes when drawing n items without replacement from N containing K successes, with mean and SD.
Probability distributions
- Binomial Probability CalculatorFind binomial probabilities for k successes in n trials: P(X = k), P(X ≤ k), P(X < k), P(X ≥ k) and P(X > k), with the mean and standard deviation.
- Poisson Probability CalculatorFind Poisson probabilities for k events when the average count is λ: exactly k, at most k, fewer than, at least and more than k, with mean and SD.
- Normal Distribution CDF CalculatorFind the area under any normal curve: P(X ≤ x), P(X ≥ x), between two values or outside them, for your mean and standard deviation.
- Normal Distribution Quantile CalculatorFind the value that cuts off a given probability of a normal distribution: the left-tail percentile, the right-tail cut-off or a central interval.
- Exponential Distribution CalculatorFind the probability that a waiting time or lifetime is below, above or between given values for an exponential distribution, from the rate or the mean.
Simulation
Time series
- Moving Average CalculatorCalculate simple (SMA), exponential (EMA) and linearly weighted (WMA) moving averages for any window, with the full series in a table and chart.
- Exponential Smoothing CalculatorForecast a series with simple exponential smoothing or Holt’s linear trend method, and see one-step errors (SSE, MAE, RMSE) for your chosen alpha and beta.
- Time Series Growth CalculatorPaste a series of values to get each period’s growth rate, the compound average growth rate across the series, the arithmetic average and an annualised rate.