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Statistics & Probability Calculators

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Statistics & Probability Calculators with Steps

Every calculator in this section shows its working: the formula, your numbers substituted into it, each intermediate value and a plain-English conclusion you can copy into an assignment or report. Enter raw data or summary statistics, choose the options your course uses (sample or population, one- or two-tailed, Welch or pooled) and the result updates with a full worked solution.

The tools cover a first course in statistics end to end: measures of centre and spread, z-scores and percentiles, the z, t, chi-square, ANOVA and non-parametric tests, correlation and regression, confidence intervals and sample size planning, the standard discrete and continuous probability distributions, printable statistical tables and graph makers for histograms, box plots and scatter plots.

All calculations run in your browser and have been checked against SciPy on more than 300 test cases. Nothing you enter is sent to a server. Each tool page also has a pre-filled example, so you can see what a complete worked solution looks like before you paste your own data.

Jump to: Descriptive statistics · Hypothesis tests · Confidence intervals and sample size · Probability distributions · Statistical tables · Graph makers

Descriptive statistics

Summarise a data set: centre, spread, position and shape.

Mean, Median and Mode CalculatorCentre of a data set: arithmetic mean, middle value and most frequent value.Variance and Standard Deviation CalculatorSample (n − 1) or population (n) variance and standard deviation with the deviation table.Quartiles and IQR CalculatorQ1, Q3, interquartile range and outlier fences with three quartile conventions.Five Number Summary CalculatorMinimum, Q1, median, Q3, maximum — the numbers behind a box plot.Z-Score Calculator (With Percentile)Standardise a raw score and read its percentile from the normal curve.Percentile Calculator (Rank and Value)Value at the kth percentile, or the percentile rank of a score, from raw data.Coefficient of Variation CalculatorRelative spread: standard deviation as a percentage of the mean.Mean Absolute Deviation CalculatorAverage distance of the values from their mean, with the deviation table.Weighted Mean CalculatorWeighted average of values with given weights, e.g. category grades or survey weights.

Hypothesis tests

Test a claim about means, proportions, variances, counts, ranks or correlation, with every step shown.

One Sample Z-Test Calculator (With Steps)Test a mean when the population standard deviation is known.One Sample T-Test Calculator (With Steps)Test a mean from a small sample when σ is unknown.Two Sample T-Test Calculator (Welch, Pooled)Compare the means of two independent groups (Welch or pooled).Paired T-Test Calculator (With Steps)Before-and-after or matched-pair comparison using the differences.One Proportion Z-Test CalculatorTest whether a proportion (pass rate, yes share) equals a claimed value.Two Proportion Z-Test CalculatorCompare success rates between two independent groups.Chi-Square Goodness of Fit CalculatorDo observed category counts match an expected distribution?Chi-Square Test of Independence CalculatorAre two categorical variables associated? Any r × c contingency table.One-Way ANOVA Calculator (With Steps)Compare three or more group means with an F test and full ANOVA table.F-Test for Two Variances CalculatorTest whether two samples have the same variance (F = s₁²/s₂²).Mann-Whitney U Test CalculatorNon-parametric comparison of two independent groups using ranks.Wilcoxon Signed-Rank Test CalculatorNon-parametric paired test based on signed ranks of the differences.Pearson Correlation Coefficient CalculatorLinear correlation r between two variables with a significance test.Spearman Rank Correlation CalculatorRank-based correlation for monotonic or ordinal relationships.Linear Regression Calculator (With Steps)Least-squares line ŷ = b₀ + b₁x with residuals, r², slope test and prediction.

Confidence intervals and sample size

Estimate a parameter with a margin of error, or work out how many observations you need.

Confidence Interval for a Mean CalculatorInterval estimate of a mean with t or z critical values.Confidence Interval for a ProportionInterval for a percentage or proportion (Wald and Wilson score).CI for the Difference of Two MeansInterval for μ₁ − μ₂ between two independent groups.CI for the Difference of Two ProportionsInterval for the gap between two percentages.Sample Size Calculator for a MeanObservations needed to estimate a mean within ±E.Sample Size Calculator for a ProportionSurvey size needed for a percentage within ±E, with finite population correction.Margin of Error Calculator±E for a survey percentage or a sample mean at a given confidence level.

Probability distributions

Probabilities, percentiles and critical values for the common discrete and continuous distributions.

Normal Distribution CalculatorAreas under any normal curve: below, above or between values.Inverse Normal Calculator (Percentile to X)From an area or percentile back to the cut-off value and z.Binomial Distribution CalculatorExact probabilities for k successes in n independent trials.Poisson Distribution CalculatorProbabilities for counts of events at an average rate λ.Geometric Distribution CalculatorNumber of trials until the first success.Hypergeometric Distribution CalculatorSuccesses when drawing without replacement from a finite population.Exponential Distribution CalculatorWaiting time between events that occur at a constant rate.Uniform Distribution CalculatorEqual likelihood over an interval [a, b].T Distribution Calculator (p & Critical t)p-values and critical values for Student's t with any df.Chi-Square Distribution Calculatorp-values and critical values of χ² for any degrees of freedom.F Distribution Calculator (p & Critical F)p-values and critical values of F for ANOVA and variance tests.

Statistical tables

Printable z, t, chi-square and F tables generated from the same formulas the calculators use.

Z-Table (Standard Normal Distribution)Cumulative areas Φ(z) for z from −3.49 to 3.49.T-Table (Critical Values of t Distribution)Critical t values by degrees of freedom and α.Chi-Square Table (Critical Values)Critical χ² values by degrees of freedom and right-tail area.F-Table (Critical Values at 0.05 and 0.01)Upper critical F values at α = 0.05 and 0.01 for common df pairs.

Graph makers

Draw a histogram, box plot or scatter plot from your data and download it as a PNG.

Histogram Maker (Free, Downloadable PNG)Frequency histogram from raw data with a frequency table and PNG download.Box Plot Maker (Box and Whisker, PNG)Box-and-whisker plots for one or more groups with outliers marked.Scatter Plot Maker (With Trend Line, PNG)x–y scatter plot with optional least-squares line and r.

Frequently asked questions

Are these statistics calculators free?
Yes. Every tool on this page is free to use with no sign-up, and the worked steps are shown in full.
Do the calculators show the steps?
Yes. Each one prints the formula, the substitution with your numbers, every intermediate result and an interpretation of the outcome.
Which hypothesis test should I use?
One mean: z-test (σ known) or t-test. Two independent means: two-sample t-test or Mann-Whitney U. Paired data: paired t-test or Wilcoxon signed-rank. Proportions: one- or two-proportion z-test. Counts in categories: chi-square. Three or more means: one-way ANOVA. Relationship between two numeric variables: Pearson or Spearman correlation, or linear regression.
Are the results accurate?
The numerical routines were validated against SciPy across all calculators, matching to at least seven significant figures on the test cases.

More calculators on this site

Last reviewed: September 25, 2026. 49 tools, all validated against SciPy.

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