# Statistics & probability calculators

> Statistics and probability calculators for averages, spread, z-scores, confidence intervals, sample size, p-values and combinations.

Page: https://calculators.geekmidst.com/categories/statistics

- [Sample Size Calculator](https://calculators.geekmidst.com/calculators/sample-size-calculator.md): Find how many responses a survey needs to estimate a proportion within a chosen margin of error and confidence level, with a finite population correction.
- [Probability Calculator](https://calculators.geekmidst.com/calculators/probability-calculator.md): Find 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.
- [Statistics Calculator](https://calculators.geekmidst.com/calculators/statistics-calculator.md): Paste a list of numbers to get a full summary: mean, median, mode, quartiles and IQR, sample and population standard deviation, standard error and skewness.
- [Permutation and Combination Calculator](https://calculators.geekmidst.com/calculators/permutation-and-combination-calculator.md): Count the ways to choose r items from n: permutations (order matters) and combinations (order does not), with and without repetition, exactly.
- [Z-score Calculator](https://calculators.geekmidst.com/calculators/z-score-calculator.md): Convert a value to a z-score (or a z-score back to a value) and see the share of a normal distribution below, above and beyond it.
- [Confidence Interval Calculator](https://calculators.geekmidst.com/calculators/confidence-interval-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/p-value-calculator.md): Get 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.
- [Bayesian Posterior Probability Calculator](https://calculators.geekmidst.com/calculators/bayesian-posterior-probability-calculator.md): Update 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 Calculator](https://calculators.geekmidst.com/calculators/bayes-factor-calculator.md): Compute the Bayes factor BF₁₀ for a binomial proportion against a point null with a beta prior, or from two marginal likelihoods, with evidence labels.
- [Binomial Probability Calculator](https://calculators.geekmidst.com/calculators/binomial-probability-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/poisson-probability-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/normal-distribution-cdf-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/normal-distribution-quantile-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/exponential-distribution-probability-calculator.md): Find 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.
- [Chi-Square Goodness of Fit Calculator](https://calculators.geekmidst.com/calculators/chi-square-goodness-of-fit-calculator.md): Test whether observed counts match expected proportions: Pearson’s χ² statistic, degrees of freedom, right-tailed p-value, critical value and each category’s share.
- [Pearson Correlation Calculator](https://calculators.geekmidst.com/calculators/pearson-correlation-calculator.md): Paste 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 Calculator](https://calculators.geekmidst.com/calculators/spearman-correlation-calculator.md): Compute 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 Calculator](https://calculators.geekmidst.com/calculators/linear-regression-slope-calculator.md): Fit 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 Calculator](https://calculators.geekmidst.com/calculators/linear-regression-intercept-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/regression-r-squared-calculator.md): Get 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.
- [RMSE Calculator](https://calculators.geekmidst.com/calculators/root-mean-square-error-calculator.md): Paste 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 Calculator](https://calculators.geekmidst.com/calculators/mean-absolute-error-calculator.md): Compute the mean absolute error between actual and predicted values, with the mean bias, median and maximum absolute error and RMSE for comparison.
- [MAPE Calculator](https://calculators.geekmidst.com/calculators/mean-absolute-percentage-error-calculator.md): Measure forecast accuracy as a percentage: MAPE, symmetric MAPE and weighted WAPE from actual and forecast values, with zero actuals handled explicitly.
- [Weighted Average Calculator](https://calculators.geekmidst.com/calculators/weighted-average-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/geometric-mean-calculator.md): Find the geometric mean of positive numbers, or the compound average of percentage changes, with the geometric standard deviation and arithmetic mean.
- [Harmonic Mean Calculator](https://calculators.geekmidst.com/calculators/harmonic-mean-calculator.md): Calculate the harmonic mean of positive numbers, optionally weighted, to average rates such as speeds or price-to-earnings ratios correctly.
- [Median Absolute Deviation Calculator](https://calculators.geekmidst.com/calculators/median-absolute-deviation-calculator.md): Compute the median absolute deviation, its normal-consistent scaled version (×1.4826) and modified z-score outliers from a list of numbers.
- [Interquartile Range Calculator](https://calculators.geekmidst.com/calculators/interquartile-range-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/outlier-tukey-fence-calculator.md): Find 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.
- [Cohen’s d Effect Size Calculator](https://calculators.geekmidst.com/calculators/cohen-d-effect-size-calculator.md): Compute 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 Calculator](https://calculators.geekmidst.com/calculators/statistical-power-approximation-calculator.md): Approximate 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.
- [A/B Test Significance Calculator](https://calculators.geekmidst.com/calculators/ab-test-conversion-significance-calculator.md): Check 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 Calculator](https://calculators.geekmidst.com/calculators/ab-test-sample-size-calculator.md): Find how many visitors each variant needs to detect a chosen lift in conversion rate at your significance level and power, one- or two-sided.
- [Confidence Interval for a Proportion Calculator](https://calculators.geekmidst.com/calculators/confidence-interval-proportion-calculator.md): Get 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 Calculator](https://calculators.geekmidst.com/calculators/wilson-score-interval-calculator.md): Compute the Wilson score interval for a proportion, with or without continuity correction, plus the one-sided lower bound used to rank ratings.
- [Expected Value Calculator](https://calculators.geekmidst.com/calculators/expected-value-calculator.md): Find the expected value, variance and standard deviation of a discrete random variable from its outcomes and probabilities, percentages or weights.
- [Conditional Probability Calculator](https://calculators.geekmidst.com/calculators/conditional-probability-calculator.md): Find 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 Calculator](https://calculators.geekmidst.com/calculators/hypergeometric-probability-calculator.md): Probability of exactly, at most or at least k successes when drawing n items without replacement from N containing K successes, with mean and SD.
- [Monte Carlo Pi Estimator](https://calculators.geekmidst.com/calculators/monte-carlo-pi-estimator-calculator.md): Estimate π by scattering random points in a unit square and counting those inside the quarter circle, with the standard error and a 95% interval.
- [Bootstrap Mean Interval Calculator](https://calculators.geekmidst.com/calculators/bootstrap-mean-interval-calculator.md): Resample your data thousands of times to get a percentile bootstrap confidence interval and standard error for the mean, with a seed for repeatable runs.
- [Percentile Rank Calculator](https://calculators.geekmidst.com/calculators/percentile-rank-calculator.md): Find 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.
- [Moving Average Calculator](https://calculators.geekmidst.com/calculators/moving-average-calculator.md): Calculate simple (SMA), exponential (EMA) and linearly weighted (WMA) moving averages for any window, with the full series in a table and chart.
- [Exponential Smoothing Calculator](https://calculators.geekmidst.com/calculators/exponential-smoothing-calculator.md): Forecast 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 Calculator](https://calculators.geekmidst.com/calculators/time-series-growth-calculator.md): Paste 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.
- [Churn Cohort Retention Calculator](https://calculators.geekmidst.com/calculators/churn-cohort-retention-calculator.md): Track 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 Calculator](https://calculators.geekmidst.com/calculators/data-missingness-percentage-calculator.md): Work out the percentage of missing cells in a data set and how many complete rows are left for a complete-case (listwise deletion) analysis.
- [Class Imbalance Ratio Calculator](https://calculators.geekmidst.com/calculators/class-imbalance-ratio-calculator.md): Enter class counts to get the imbalance ratio (majority ÷ minority), each class’s share, entropy-based balance and balanced class weights.
- [Precision Recall F1 Calculator](https://calculators.geekmidst.com/calculators/precision-recall-f1-calculator.md): Calculate 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 Calculator](https://calculators.geekmidst.com/calculators/confusion-matrix-accuracy-calculator.md): From 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 Calculator](https://calculators.geekmidst.com/calculators/roc-sensitivity-specificity-calculator.md): Calculate sensitivity, specificity, false-positive rate, Youden’s J, likelihood ratios and predictive values at any prevalence from a 2 × 2 table.
- [Shannon Entropy Calculator](https://calculators.geekmidst.com/calculators/entropy-shannon-calculator.md): Calculate the Shannon entropy of a probability distribution or set of counts in bits, nats or hartleys, with maximum entropy, evenness and perplexity.
- [Gini Impurity Calculator](https://calculators.geekmidst.com/calculators/gini-impurity-calculator.md): Calculate 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 Calculator](https://calculators.geekmidst.com/calculators/information-gain-calculator.md): Enter 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 Calculator](https://calculators.geekmidst.com/calculators/kl-divergence-calculator.md): Calculate the Kullback–Leibler divergence D(P‖Q) and D(Q‖P) between two discrete distributions, plus cross-entropy and Jensen–Shannon divergence.