Statistics Calculators

Turn a raw value into a z-score — how many standard deviations it sits above or below the mean — with its percentile under a normal curve.

Build a confidence interval for a mean from your sample mean, standard deviation and size — with the margin of error and the interval bounds.

Find the standard error of the mean from a sample standard deviation and size — how much the sample mean is expected to vary.

Work out how many people to survey for a target margin of error and confidence level, with an optional finite-population correction.

Find the margin of error for a survey proportion or a mean from the sample size and confidence level, with the finite population correction and design effect. Or work backwards to the sample size you need. Includes Wilson and exact intervals, tables, a chart and the steps.

Compute the Pearson correlation coefficient r between two lists of numbers, with r-squared and a plain-language reading of the relationship.

Find the percentile rank of a value in a data set, or the value at any percentile, with the Excel, nearest-rank and (n + 1) methods side by side, a full percentile table, quartiles and the worked steps.

Compute the coefficient of variation (CV, or relative standard deviation) from a mean and standard deviation, or paste raw data. Get sample and population CV, the small-sample unbiased CV, a confidence interval for the CV, a two-set comparison and the full working.

Convert a z-score into a p-value from the normal distribution for a left, right or two-tailed test, with a significance verdict at 0.05.

Get the five-number summary — minimum, Q1, median, Q3 and maximum — plus the interquartile range and outlier fences for any data set.

Calculate relative risk (the risk ratio) from a 2×2 table with its confidence interval, plus the odds ratio, absolute risk difference, NNT or NNH, chi-square and Fisher exact p-values, and the worked steps.

Paste a list of numbers to get the mean absolute deviation (MAD), plus the mean, variance and standard deviation.

Paste a list of numbers to get the sample and population variance, plus the standard deviation, mean and count — with the n vs n−1 difference explained.

Find the range of a data set — the gap between the highest and lowest value — along with the minimum, maximum, midrange and count.

Fit a least-squares line y = a + bx to paired X and Y data — with the slope, intercept, correlation r and r-squared.

Find the probability that a normally distributed value falls below or above a point — with its z-score and probability density.

Find binomial probabilities — exactly k, at most k and at least k successes in n independent trials — plus the mean and standard deviation.

Compute Poisson probabilities — exactly k, at most k and at least k occurrences for a given average rate λ — with the mean and standard deviation.

Compute the expected value of a discrete probability distribution from its outcomes and probabilities — with the variance and standard deviation.

Run a one-sample, two-sample (Welch or pooled Student) or paired t-test from pasted data or summary statistics — t, degrees of freedom, one- or two-tailed p-value, confidence interval, effect size, variance and normality checks, and every step.

Run a chi-square goodness-of-fit or test of independence — get the χ² statistic, degrees of freedom, p-value and a plain-language verdict at α = 0.05.

Run a one-way ANOVA across two or more groups — get the F statistic, between- and within-group degrees of freedom, the p-value and a verdict at α = 0.05.

Compute a weighted average from a list of values and their weights — where some numbers count more than others — with the sum of weights.

Find the geometric mean of positive numbers or the average growth rate of percentage returns — with weights, the geometric standard deviation, a confidence interval, arithmetic and harmonic means for comparison, a table, chart and worked steps.

Compute the harmonic mean of positive numbers — the correct average for rates and speeds — alongside the arithmetic and geometric means.

Find the interquartile range of a data set — the spread of the middle 50% — with Q1, Q3, the median and the 1.5×IQR outlier fences.

Detect outliers in a data set using Tukey’s 1.5×IQR rule — see which values fall outside the fences, plus the quartiles and fence bounds.

Find the midrange of a data set — the midpoint between the smallest and largest value — along with the minimum, maximum and range.

Measure effect size between two groups with Cohen’s d from their means, standard deviations and sizes — with the pooled SD and a magnitude label.

Compute the odds ratio from a 2×2 table of exposure and outcome — with the exposed and unexposed odds and a plain-language interpretation.

Calculate the number needed to treat from control and treatment event rates — with the absolute and relative risk reduction.

Evaluate a diagnostic test from its confusion matrix — sensitivity, specificity, PPV, NPV and accuracy from true/false positives and negatives.

Compute the coefficient of determination R² between two data sets — the share of variance explained — along with the Pearson correlation r.

Split a data set into quartiles — minimum, Q1, median, Q3 and maximum — with the interquartile range, using linear interpolation.

Find the probability of exactly, at most, or at least k successes in n independent trials, each with the same success probability p.

Convert a z-score into a probability under the standard normal curve — left tail, right tail, or the area between ±z — using an erf-based CDF.

Compute Poisson probabilities for the number of events in a fixed interval given an average rate λ — exactly k, at most k, and at least k.

Build a z-based confidence interval for a population mean from your sample mean, standard deviation and size — with the margin of error and bounds.

Estimate a confidence interval for a population proportion (a percentage or rate) from your successes and sample size using the Wald method.

Work out how many people to survey for a target margin of error and confidence level, with an optional finite-population correction.

Find the margin of error for a survey proportion from your sample size, confidence level and result — the ± figure quoted with poll numbers.

Express variability as a percentage of the mean — the relative standard deviation (RSD), also called the coefficient of variation, from your mean and SD.

Compute the standard error of the mean (SEM) from a sample standard deviation and size — how precisely your sample average estimates the true mean.

Find the percentile rank of a value within a data set — the percentage of scores at or below it — from a list of numbers you paste in.

Find the chance that an event happens at least once over several independent tries using the complement rule — 1 minus the probability it never happens.

Compute the expected value, variance and standard deviation of a discrete outcome from up to four value-and-probability pairs.

Fit a least-squares line y = a + bx to paired data and get the slope, intercept, correlation and the full regression equation.

Compute Pearson’s r between two paired lists, with r², the covariance and a plain-language reading of how strongly the variables move together.

Calculate the sample and population covariance between two paired lists of numbers, with the means and correlation for context.

Test whether a sample mean differs from a hypothesised value when the population standard deviation is known, with the z statistic and p-value.

Test a sample mean against a hypothesised value using the sample standard deviation, with the t statistic, degrees of freedom and a decision.

Test whether observed counts match an expected distribution with the chi-square goodness-of-fit statistic, degrees of freedom and p-value.

Turn a data set into its box-plot five-number summary — min, Q1, median, Q3, max — plus range, IQR, whisker fences and flagged outliers.

Compute R² from paired data or from observed and predicted values, showing how much of the variation your model explains.

Measure spread with the average absolute deviation from the mean, median or mode — a robust alternative to standard deviation.

Combine values with their weights into a weighted average — for grades, prices, portfolios or any figures that do not count equally.

Estimate the mean of grouped data from class midpoints or class intervals and frequencies, plus the grouped median, mode, quartiles, variance and standard deviation, with a full frequency table, histogram and worked steps.

Find the mean (expected value), variance and standard deviation of a discrete probability distribution from its values and probabilities.

Compare the means of two independent groups with the pooled (equal-variance) Student t-test — get the t statistic, degrees of freedom, two-tailed p-value and a verdict.

Paste before-and-after (paired) data or summary statistics and get the paired t-test: mean difference, t statistic, degrees of freedom, one- or two-tailed p-value, confidence interval, effect size, a Shapiro–Wilk normality check and every step worked out.

Compare two proportions (conversion rates, success rates) with a pooled z-test — get the z statistic, two-tailed p-value and a plain-language verdict.

Test whether two samples have equal variances with the F-test — get the variance ratio F, degrees of freedom and a two-tailed p-value.

Run a one-way ANOVA from each group’s mean, variance and size — get the F statistic, between/within degrees of freedom and a two-tailed p-value.

Build a confidence interval for the difference between two population means from each sample’s mean, standard deviation and size, using the pooled Student-t method.

Measure the standardized effect size between two groups with Cohen’s d from raw data — the mean difference in pooled standard deviation units, with a size label.

Turn a sample mean, standard deviation and size into a point estimate, margin of error and confidence interval using the Student-t distribution.

Compute the geometric standard deviation and geometric mean of positive data — the multiplicative spread used for growth rates, ratios and log-normal data.

Compute a trimmed (truncated) mean by dropping a percentage of the highest and lowest values — a robust average that resists outliers.

Find the mode — the most frequently occurring value(s) — of a data set, with the frequency and whether the data are unimodal, bimodal or have no mode.

Enter a list of numbers to get the minimum, maximum, range, quartiles Q1 and Q3, and the interquartile range (IQR) with outlier fences.

Find how many observations you need to estimate a population mean within a chosen margin of error at a given confidence level.

Estimate how many subjects per group you need to detect a given effect size in a two-sample comparison at your chosen power and significance.

Compute relative risk with a 95% confidence interval from the raw event counts in exposed and unexposed groups.

Turn control and treatment event rates into absolute risk reduction, relative risk reduction and number needed to treat.

Compute the number needed to treat from control and treatment event rates — how many patients to treat for one to benefit.

Compute positive and negative likelihood ratios for a diagnostic test from its sensitivity and specificity.

Enter the four cells of a diagnostic 2×2 table to get positive and negative predictive value, sensitivity and specificity.

Use Bayes theorem to convert a test’s sensitivity and specificity into predictive values at any disease prevalence.

Find the expected value, variance and standard deviation of the total when rolling fair dice (a coin is just a 2-sided die).

Convert a standard-normal z-score into a percentile, the area to its right and the two-tailed p-value.

Convert a percentile into the standard-normal z-score that sits at it — the inverse of the normal CDF.

Estimate a standard deviation quickly from the minimum and maximum using the range rule of thumb.

Check whether the difference between your control and variant conversion rates is statistically significant with a two-proportion z-test.

Find how many visitors per variant your A/B test needs to detect a given lift at your chosen confidence and power.

Turn conversions and visitors into a conversion rate with a confidence interval, so you know the true rate range, not just the point estimate.

Compare a control and variant conversion rate to get the absolute and relative uplift — the two lift numbers people constantly confuse.

Update a Beta prior with observed successes and failures to get the Bayesian posterior mean, mode and interval for a coin or conversion rate.

Convert decimal, American (moneyline) or fractional betting odds into the implied win probability they represent.

Work out the expected value of a bet in American, decimal or fractional odds. Use your own win probability or remove the vig from sharp odds (multiplicative, additive, power or Shin), then get your edge, fair odds, a Kelly stake and the chance of being ahead after many bets.

Compute the Kelly-optimal stake as a fraction of your bankroll from your win probability and odds, with the safer half-Kelly amount.

Calculate the odds of winning a lottery jackpot from the number pool, how many numbers are drawn, and an optional bonus ball.

Count how many codes a lock or PIN has from the symbols per position and length, with and without repeated symbols — plus brute-force time.

Find the probability that at least two people in a group share a birthday — the surprising result behind the birthday paradox.

Compute the probability of reaching a target before going broke in a simple gambler's ruin random walk, from your capital and per-bet win chance.

Measure how lopsided your data is — the moment coefficient of skewness plus Pearson’s median-based skewness from a list of values.

Find the kurtosis and excess kurtosis of your data — how heavy the tails are compared with a normal distribution — from a list of values.

Find what percentile a specific value sits at within a data set — the share of observations at or below it — with the count above and below.

Compute the quartile deviation (semi-interquartile range) and its coefficient from a data set — a robust, outlier-resistant measure of spread.

Run a one-sample z-test for a proportion — compare your observed success rate against a hypothesized value and get the z statistic and p-value.

Build a Wald confidence interval for a single population proportion from your successes and sample size, with the margin of error at 90/95/99%.

Compare two results from different distributions by converting each to a z-score — see which value is relatively higher despite different scales.

Curve a raw score onto a target normal distribution — set a desired class mean and spread and see the rescaled grade and its percentile.

Apply Chebyshev’s theorem to any distribution — find the minimum share of data within k standard deviations of the mean and the interval bounds.

Apply the 68-95-99.7 rule to a normal distribution — get the 1σ, 2σ and 3σ intervals around the mean and where a value falls.

Combine two samples into a single pooled variance and standard deviation — the weighted estimate used in two-sample t-tests assuming equal variances.

Compute the signal-to-noise ratio from a signal and noise level — as a plain ratio and in decibels, for amplitude or power quantities.

Find how many completed survey responses you need for a target margin of error and confidence level, corrected for a finite population, or find the margin of error a given sample gives you. Includes response rate, design effect and sample size tables.

Calculate the margin of error for a poll or survey result from its sample size, confidence level and reported percentage.

Work out the response rate you need — or the number of invitations to send — to reach a target number of completed survey responses.

Compute the post-stratification weight for a survey subgroup that is over- or under-represented relative to the population.

Turn Likert-scale response counts into a mean score plus top-box, top-2-box and bottom-box percentages.

Calculate Net Promoter Score from promoter, passive and detractor counts, with the group percentages behind it.

Build a confidence interval for the difference between two independent survey proportions and see whether it excludes zero.

Compute the design effect (DEFF) and effective sample size for a cluster survey from cluster size and intra-cluster correlation.

Split a total sample across strata by proportional or equal allocation and get the interviews needed in each stratum.

Test whether one candidate's lead over another in the same poll is statistically significant, accounting for the correlation between the two shares.

Adjust a candidate's raw support for differing turnout between two voter groups to estimate the likely-voter result.

Check a ranked-choice voting round: find the leader's share, whether anyone has a majority, and which candidate is eliminated.

See population variance (÷N) and sample variance (÷N−1) side by side from one list of numbers, with both standard deviations.

Find how many histogram bins to use with Sturges’ rule, the square-root rule and Rice’s rule, plus the class width for your data range.

Compute P(A|B) from the joint probability P(A and B) and P(B), and check whether A and B are independent.

Find P(A or B) with the addition rule — for independent, mutually exclusive or overlapping events with a known joint probability.

Probability that the first success lands on trial k, plus P(X ≤ k), P(X > k), mean and variance of the geometric distribution.

Probability of drawing exactly k successes in n draws without replacement from a population of N items containing K successes.

Probability that a waiting time falls below, above or between values for an exponential distribution with a given rate λ or mean.

Probability, mean, variance and percentiles of a continuous uniform distribution between a and b, including P(x₁ ≤ X ≤ x₂).

Compute Spearman’s ρ from two paired lists, with tie-aware ranking, a t-statistic and an approximate p-value.

Inter-rater agreement for two raters and two categories from a 2×2 table — observed agreement, expected agreement, κ and its interpretation.

Estimate the internal-consistency reliability of a scale from the number of items, the sum of item variances and the variance of total scores.

Adjust your significance level for multiple comparisons — Bonferroni and Šidák thresholds, plus the family-wise error rate you would face without correcting.

Compute Cp, Cpk, Cpu, Cpl and the expected defect rate from specification limits, process mean and standard deviation.

Convert defects, units and opportunities into DPMO, DPU, yield and sigma level (with the standard 1.5σ shift).

Measure inequality in a list of incomes or values — Gini coefficient, Lorenz-curve shares and the top/bottom split.

Score a forecast against actuals — MAPE, sMAPE, MAE and bias from two paired lists.

Compute RMSE, MSE, MAE and R² between predicted and observed values from two paired lists.

Exact p-value for a 2×2 table — one- and two-sided Fisher's exact test with the odds ratio, for small samples where chi-square is unreliable.

Compare two independent samples without assuming normality — U statistic, tie-corrected z, two-sided p-value and the rank-biserial effect size.

Paired non-parametric test — W statistic, z with tie correction and two-sided p-value for before/after or matched data.

Paired yes/no data — McNemar's chi-square with continuity correction and the exact binomial p-value from the discordant pairs.

Effect size for a contingency table — chi-square, degrees of freedom, p-value and Cramér's V (with the phi coefficient for 2×2).

Inter-rater reliability from a ratings table — ICC(1,1), ICC(2,1) absolute agreement and ICC(3,1) consistency with the ANOVA mean squares.

Power of a two-sample test from the sample size per group, effect size and alpha — for means (Cohen’s d) or two proportions, one- or two-sided.

The smallest conversion-rate lift an A/B test can reliably detect from baseline rate, visitors per variant, alpha and power — absolute and relative.

Paste a list of p-values and get Benjamini–Hochberg adjusted q-values, the BH cutoff and how many tests survive at your FDR level — with Bonferroni for comparison.

Market concentration from a list of market shares — HHI, normalised HHI, the equivalent number of equal firms and the antitrust concentration band.

Simple exponential smoothing of a time series — next-period forecast for your α, the smoothed series, MAE/MAPE and the best α found by grid search.

Non-parametric one-way comparison of three or more groups — H statistic with tie correction, degrees of freedom, p-value and epsilon-squared effect size.

From a confusion matrix get precision, recall, F1, F0.5, F2, accuracy, specificity and balanced accuracy for a classifier or a test.

MCC from a confusion matrix — the balanced classifier metric that stays honest on imbalanced data — with F1, accuracy, Cohen’s kappa and informedness alongside.

Youden’s J from sensitivity and specificity (or a 2×2 test table) — with likelihood ratios, diagnostic odds ratio and predictive values at your prevalence.

Confidence interval for a proportion that behaves at small n and near 0 or 100% — Wilson score with and without continuity correction, versus the Wald interval.

Rank correlation with Kendall’s tau-b — concordant and discordant pairs, tie handling, z-score and p-value for two paired lists.

One-way ANOVA effect sizes from raw groups — eta-squared, omega-squared and Cohen’s f, with the F statistic and p-value.

Bias-corrected standardised mean difference from two groups’ means, SDs and sizes — Hedges’ g, Cohen’s d, the correction factor and a 95% confidence interval.

Compare conversion or success rates between two groups — pooled z statistic, one- and two-sided p-values, the difference with its confidence interval and relative lift.

Shewhart X̄-R control chart limits from subgroup data — centre lines, UCL/LCL for the mean and range using the A2, D3, D4 constants, plus out-of-control points.

Paste causes with their counts and get the sorted Pareto table, cumulative percentages and the “vital few” that account for 80% of the problem.

Test a set of numbers against Benford’s first-digit law — observed vs expected digit frequencies, chi-square p-value and mean absolute deviation with Nigrini’s conformity bands.

Information entropy of a distribution from counts or probabilities — bits, nats, perplexity, maximum possible entropy and normalised entropy (evenness).

The simplest paired test — count improvements versus declines and get the exact binomial one- and two-sided p-values, with the normal approximation.

Compare two regression models from their residual sum of squares, sample size and parameter counts — AIC, corrected AICc, BIC, ΔAIC and Akaike weights.

Find the median, mode, quartiles and interquartile range of grouped data from class intervals and frequencies, using the interpolation formulas with class boundaries and a cumulative frequency table.

Turn a list of raw data into a grouped frequency distribution table: number of classes by Sturges’ rule, class width, class intervals and midpoints, absolute, relative and cumulative frequencies and percentages.

Find critical values for the Z, t, chi-square and F distributions from the significance level α, the tail and the degrees of freedom — with the rejection region for your test.

Get the p-value and cumulative probability for a t statistic and degrees of freedom — two-tailed, left-tailed or right-tailed — plus the density and a significance check.

Use the central limit theorem to find the sampling distribution of the mean: standard error σ/√n, the z-score and the probability that a sample mean falls below, above or between values.

Probability that the r-th success happens on trial x: P(X = x), P(X ≤ x) and P(X ≥ x) for the negative binomial distribution, with its mean, variance and a probability table.

Run Grubbs' outlier test on a data list: the G statistic, the critical G for your α, the suspected outlier and whether to reject it — two-sided or one-sided (max or min).

Run the Friedman test on repeated measures or blocked data — tie-corrected chi-square statistic, degrees of freedom, p-value, Kendall’s W and the mean rank of every condition.

Cochran’s Q test for three or more related yes/no outcomes — Q statistic, degrees of freedom, p-value, success rate of each treatment and the effect size η²Q.

Point-biserial correlation between a yes/no variable and a numeric score — r_pb, r², t statistic, p-value and the group means, from the two groups’ values.

Fleiss’ kappa for agreement among three or more raters — κ, observed and chance agreement, z test, p-value, per-category kappa and the Landis–Koch strength label.

Bland–Altman method comparison — mean difference (bias), SD of differences, 95% limits of agreement with confidence intervals and the points outside the limits.

Levene’s test (or the Brown–Forsythe median version) for equal variances across two or more groups — W statistic, degrees of freedom, p-value and each group’s variance.

Two-sample Kolmogorov–Smirnov test — the D statistic (largest gap between the two empirical CDFs), where it occurs, the exact or asymptotic p-value and the critical D.

Dixon’s Q test for a single outlier in 3 to 10 measurements — gap and range, Q statistic, the Rorabacher critical value at 90%, 95% or 99% and a keep/reject verdict.

Tukey’s HSD (Tukey–Kramer) post-hoc test after ANOVA — studentized range critical q, MSE, honestly significant difference and adjusted p-values and intervals for every pair.

Convert between effect sizes — Cohen’s d, correlation r, odds ratio, log odds ratio, η² and Cohen’s f — plus the common-language effect size, U3, overlap and NNT.

Area under the ROC curve from the scores of positive and negative cases — AUC, Hanley–McNeil standard error and 95% CI, Gini, the best Youden cut-off and the ROC table.

Kullback–Leibler divergence between two discrete distributions in both directions, plus Jensen–Shannon divergence, cross-entropy and entropy — in nats, bits or hartleys.

Weibull distribution from shape k and scale λ — CDF (failure probability), reliability, PDF, hazard rate, mean, median, mode, standard deviation and B10 life.

Gamma distribution with shape k and scale θ or rate β — cumulative probability P(X ≤ x), upper tail, density, mean, variance, mode and median.

Beta distribution with shape parameters α and β — cumulative probability P(X ≤ x), upper tail, density, mean, variance, mode and median for a value between 0 and 1.

Lognormal distribution from μ and σ of ln X, or from the arithmetic mean and SD — P(X ≤ x), upper tail, density, mean, median, mode, SD and the 5th–95th percentiles.

Shapiro–Wilk normality test for 3 to 5,000 values — W statistic and p-value (Royston algorithm, same as R and SciPy), with mean, SD, skewness and a verdict.