Statistics calculators that show their work

Free statistics calculators with steps, charts and clear explanations. Every calculator gives step-by-step solutions, the formulas behind them and a chart of your own data.

Browse all calculators

Popular calculators

4 Event Probability Calculator: All, None, At Least One, Exactly k

Work out the probability that all four, none, at least one, or exactly one, two or three of four independent events happen.

One-Way ANOVA Calculator with ANOVA Table, Effect Size and Post-Hoc

Compare the means of three or more groups. Paste each group on its own line to get the full ANOVA table, F test, effect sizes and pairwise comparisons.

Average Deviation Calculator (Mean and Median) with Steps

Find the average deviation of a data set about its mean or its median, with the full deviation table and both versions side by side.

Binomial Distribution Table Calculator (Full PMF and CDF Table for n and p)

Generate a complete binomial probability table for any n and p, with the cumulative columns you would look up in a textbook and charts of the shape.

Binomial Probability Calculator with Steps (Exact, Cumulative, Mean and SD)

Calculate exact and cumulative binomial probabilities, with every step of the formula shown and the distribution plotted.

Birthday Paradox Calculator: Shared Birthday Probability and Group Size

Discover how likely it is that two people in a group share a birthday, and how many people you need for any target probability. It works for any number of days, not only 365.

Chi-Square Calculator: Goodness of Fit and Test of Independence

Run a chi-square goodness-of-fit test or a test of independence on a contingency table. See expected counts, residuals, the p-value and an effect size.

Cochran’s Formula Calculator: Sample Size for Proportions and Means

Find the sample size you need with Cochran’s formula, for categorical or continuous data, then adjust for a finite population, design effect and non-response.

Coefficient of Variation Calculator (CV) from Data or Mean and SD

Compute the coefficient of variation from raw data or from a mean and standard deviation, and see what the result means in practice.

Combination and Permutation Calculator (nCr, nPr)

Work out how many ways you can choose r items from n, in any order (combinations) or in a specific order (permutations), with or without repetition.

Combinations with Repetition Calculator (Multichoose, Stars and Bars)

Count the ways to choose r items from n types when the same type can be picked more than once and order does not matter, with the stars-and-bars working.

Confidence Interval Calculator for a Mean or Proportion (t, z, Wilson)

Calculate a confidence interval for a mean or a proportion. Choose the right method, see the margin of error and compare methods side by side.

Confusion Matrix Calculator: Accuracy, Precision, Recall, F1, MCC

Turn the four cells of a confusion matrix into every classification metric you need, with a heat-mapped matrix and confidence interval for accuracy.

Cosine Similarity Calculator for Two Vectors (with Angle and Distance)

Compare the direction of two vectors. Get cosine similarity, the angle between them and cosine distance, with the full dot-product working.

Curve Fitting Calculator: Linear, Polynomial, Exponential, Power, Logarithmic

Find the curve that best describes your data. Fit six model families at once, compare them fairly and get equations you can use for predictions.

Descriptive Statistics Calculator: Mean, Median, SD, Quartiles, Skewness

Paste a list of numbers to get every common summary statistic at once, plus a box plot, a histogram and an outlier check.

Doubling Time Calculator: From Growth Rate, Two Values, or Rule of 70 and 72

Find how long it takes for something to double at a steady growth rate, or work out the growth rate from a known doubling time. It also covers population, investments, cases and bacteria.

Shannon Entropy Calculator: Bits, Nats, Gini Impurity and Perplexity

Measure the uncertainty of a probability distribution in bits, nats or hartleys, with normalised entropy, Gini impurity and perplexity.

F1 Score Calculator: F-Measure from Precision and Recall or TP, FP, FN

Get the F1 score, the harmonic mean of precision and recall, plus F-beta variants that weight recall or precision more.

Gamma Distribution Calculator: PDF, CDF, Percentiles, Mean and Variance

Work with the gamma distribution: probabilities for any x or interval, density, percentiles, mean, variance and shape measures, with the curve plotted.

Geometric Distribution Calculator: Trials Until First Success

Model the number of trials until the first success. Get exact and cumulative probabilities, the expected wait and how many tries give a 95% chance.

Histogram Maker and Calculator

Paste your data and get an instant histogram, a frequency table and the bin width, using an automatic bin count or your own.

Hypothesis Testing Calculator with Steps (z, t and Proportion Tests)

Work through a hypothesis test step by step. Enter your sample summary and get hypotheses, test statistic, p-value, critical value, interval and a conclusion in words.

Kurtosis Calculator: Excess Kurtosis, G2 and Normality Tests

Measure how heavy or light the tails of your data are. Shows excess kurtosis in all three common forms, a z-test and a Jarque-Bera normality check.

Level of Significance (Alpha) Calculator: Critical Values, Type I/II Error, Power

See what your chosen significance level α means: critical values, the rejection region, the Type I error rate and, optionally, the power and Type II error for a given effect size and sample size.

Mean Absolute Deviation (MAD) Calculator

Enter a list of numbers to find the mean absolute deviation, the average distance of the values from their mean, with every step shown.

Mean and Standard Deviation Calculator

Paste your data to get the mean, standard deviation, variance and standard error in one step, with the full working shown.

Mean, Median, Mode and Range Calculator

Enter a list of numbers to find the mean, median, mode and range in one go, with the working shown.

Mean Squared Error (MSE) Calculator with RMSE, MAE and MAPE

Score a forecast or regression model with MSE, then read RMSE, MAE, MAPE, bias and R² side by side so you know which metric to trust.

nCr Calculator: Combinations C(n, r) with Steps, Pascal’s Triangle and Formula

Calculate nCr, the number of ways to choose r items from n when order does not matter, with exact big-number arithmetic and full working.

Nonlinear Regression Calculator: Exponential, Logistic, Michaelis-Menten, Gompertz

Fit curved models by true non-linear least squares with the Levenberg-Marquardt algorithm. Get parameters with standard errors, R² and a residual plot.

nPr Calculator: Permutations P(n, r) with Steps, Factorials and Circular Arrangements

Count ordered arrangements: how many ways can r items be picked from n and arranged in order? Exact answers with the working shown.

P-Value from Chi-Square Calculator (χ², df) with Critical Value Table

Convert a chi-square statistic and its degrees of freedom into an exact p-value, with the critical value, a shaded graph and a reference table.

Percentage Error Calculator: Percent Error Formula with Steps

Compare a measured value with the true value to get the percentage error, shown signed and absolute with the full working.

Probability of 3 Events Calculator: All, None, At Least One, Exactly

Enter the probabilities of three independent events to find the chance that all happen, none happen, at least one happens, or exactly one or two happen.

Probability Calculator: Chance, Odds, At Least Once and Exactly k Times

Find the chance of an event, convert it to odds, and see what happens over repeated tries: at least once, exactly k times and how many tries you need.

Raosoft-Style Sample Size Calculator (Margin of Error, Confidence, Population)

Work out how many survey responses you need, using the same inputs and formula as the Raosoft sample size calculator, plus a lookup table and a chart.

Regression Equation Calculator: Linear Regression Line, R², p-value and Prediction

Find the least squares regression line from your data. Get the equation, correlation, R², slope significance, a prediction with intervals and a residual plot.

RSD Calculator (Relative Standard Deviation)

Enter repeated measurements to find the relative standard deviation: the standard deviation expressed as a percentage of the mean.

Sample Variance Calculator (with Population Variance and Steps)

Calculate sample and population variance side by side, with the full squared-deviation table and a confidence interval for the true variance.

Sample Size Calculator: Estimate a Mean or Proportion, or Compare Two Groups

Plan your study size. Choose whether you are estimating a value or comparing two groups, and get the number of participants you need.

SEM Calculator: Standard Error of the Mean with Confidence Interval

Find the standard error of the mean from raw data or from summary statistics, with a confidence interval and a chart of how the SEM shrinks as n grows.

Skewness Calculator: g1, G1 and b1 with Significance Test

Measure how asymmetric your data are. All three common skewness formulas are shown, with a significance test and a plain-English reading.

SSE Calculator: Sum of Squared Errors, MSE, RMSE and R²

Compare actual and predicted values to get the sum of squared errors along with MSE, RMSE, MAE and R², plus charts that show where the error comes from.

Standard Deviation for Grouped Data Calculator (Frequency Table)

Enter a frequency table as class intervals and counts to get the mean, variance and standard deviation, with the complete working table.

Statistical Significance Calculator for A/B Tests (Two Proportions)

Check whether the difference between two conversion rates is statistically significant, with p-value, uplift, confidence interval and power.

T-Test Calculator: One-Sample, Two-Sample (Welch), Paired with Steps

Run a one-sample, paired or two-sample t-test from raw data or summary statistics. You get the t statistic, p-value, confidence interval, effect size and a ready-to-paste APA sentence.

Z Test Statistic Calculator: z-Score, Mean, Proportion, Two Proportions

Compute the z test statistic for a single value, a sample mean, a proportion or the difference of two proportions, with all the p-values you may need.

Z-Table Calculator: Z-Score to Probability and Back (Normal Distribution)

Look up standard normal probabilities without a printed table. Go from a z-score or a raw value to areas, or from a probability back to z.

Z-Test Calculator (One-Sample)

Test whether a sample mean differs from a claimed population mean when the population standard deviation is known. You get the z-score, p-value, critical values and a decision.

Browse by topic

Descriptive Statistics

Mean, spread, variation and data summaries.

Probability & Counting

Combinations, permutations, tests and distributions.

Algebra

Factoring, expanding, simplifying and solving.

GeometryComing soon

Areas, volumes, triangles and shapes.

Linear AlgebraComing soon

Matrices, determinants and vectors.

Logic & Discrete MathComing soon

Boolean algebra, truth tables and algorithms.

CalculusComing soon

Limits, derivatives and differential equations.

Trigonometry & FunctionsComing soon

Trig functions, logs and graphs.

Why use StatisticsCalc?

Each calculator is built to teach as well as to answer. You get the result, the working, the formula in plain notation and a chart, so you can check your own homework, understand a method or sanity-check a report. Everything runs in your browser: the numbers you enter are never sent to a server.