Statistics Calculators

Calculate arithmetic, weighted, geometric, or harmonic averages from a list of numbers with steps and summary statistics.

Find mean, median, mode, range, count, sum, minimum, and maximum for a list of numbers with sorted values and steps.

Compute the posterior probability P(A|B) from a prior P(A) and the likelihoods P(B|A) and P(B|not A). Shows the joint-probability table, the total probability of B, odds form, and the Bayes factor.

Find P(χ² ≤ x) and P(χ² ≥ x) for any degrees of freedom, invert a probability to get x, or look up the critical chi-square value for a significance level. Includes mean, variance, mode, and density.

Run a chi-square goodness-of-fit test (observed vs expected) or a test of independence on a contingency table. Get χ², df, p-value, critical value, expected counts, per-cell contributions, and Cramér's V.

Calculate sample or population covariance from paired x and y data. Shows the full (x - x̄)(y - ȳ) table, the sum of products, both covariance formulas, and the correlation coefficient.

Apply the 68-95-99.7 empirical rule to any mean and standard deviation: get the one, two, and three standard deviation ranges, the exact normal percentages, and where a chosen value falls, drawn on a bell curve.

Calculate the margin of error for a survey proportion or a sample mean at any confidence level, with z or t critical values and a finite population correction. Reverse it to find the sample size for a target margin.

Find P(X < x), P(X > x), P(a < X < b), z-scores, and percentiles for any normal distribution, or work backward from a probability to x. Includes a shaded bell curve and full steps.

Find outliers in a data set with the 1.5 × IQR fence rule or the z-score rule. Shows Q1, Q3, IQR, the lower and upper fences, every outlier, and the mean, median, and standard deviation with outliers removed.

Convert a z or t test statistic into a p-value with two-tailed, left, or right tails — includes reject/fail-to-reject decisions at alpha = 0.05 and 0.01 plus the full CDF work.

Find Q1, Q2, and Q3 for any data set using the exclusive, inclusive, median-split, or Tukey-hinge method, see how the methods differ, and get the IQR, fences, outliers, and a box plot.

Find R² (coefficient of determination) from paired data or from a correlation coefficient, plus adjusted R² for any number of predictors. Shows the fitted line, SSR, SSE, SST, and interpretation.

Compute skewness and kurtosis for a data set with both the population (moment) formulas and the sample-adjusted formulas used by Excel and SPSS. Reports excess kurtosis, the central moments, and a plain-English shape reading.

Find left-tail, right-tail, and two-tailed probabilities for a t value, invert a probability to get t, or look up critical t values for any degrees of freedom and significance level.

Run a one-sample, two-sample (Welch or pooled), or paired t test from raw data, summary statistics, or a t value you already have. Get t, df, one- or two-tailed p-value, confidence interval, Cohen's d, a hypothesized difference Δ, and a decision at your α.

Run a one-proportion z test or a one-mean z test (known σ). Get the z statistic, one- or two-tailed p-value, critical value, confidence interval (Wald and Wilson for proportions), and the decision at your α.

Calculate sample or population standard deviation, variance, mean, and z-score-ready summary statistics from a data list.

Calculate combinations and permutations for counting problems where order may or may not matter.

Calculate event probability, complement probability, odds, and repeated independent event probabilities.

Calculate confidence intervals for a mean or proportion with margin of error and z critical value.

Calculate z-score, percentile estimate, and distance from mean using value, mean, and standard deviation.

Estimate survey sample size from confidence level, margin of error, and expected proportion.

Calculate sample or population variance from a data list with mean and squared-deviation steps.

Calculate Q1, median, Q3, and interquartile range from a data list.

Find a percentile value from a data list using linear interpolation.

Find minimum, Q1, median, Q3, maximum, and IQR from a data list with sorted-data steps.

Calculate how often a target value appears in a data list as a count and percentage.

Calculate the geometric mean of positive values with log-safe product-root steps.

Calculate mean absolute deviation from a data list with mean and absolute-distance steps.

Calculate root mean square from a list of positive, negative, or mixed values.

Calculate coefficient of variation from a data set using standard deviation divided by mean.

Calculate standard error of the mean from standard deviation and sample size.

Calculate exact binomial probability for k successes in n independent trials.

Calculate exact Poisson probability for k events with average rate lambda.

Calculate expected value from outcome and probability lists.

Convert between odds in favor, odds against, probability, complement, and percentage chance.

Calculate Pearson correlation coefficient r from paired x and y data.

Calculate least-squares regression line y = mx + b from paired x and y data.