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.

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Popular calculators

1.5 IQR Rule Calculator: Find Outliers and Fences

Apply the 1.5 IQR rule to your data. You get the quartiles, the IQR, the two outlier fences and a list of the values that fall outside them.

2 SEM Calculator: Mean ± 2 Standard Errors Interval

Calculate the standard error of the mean (SEM), 2 × SEM and the mean ± 2 SEM interval.

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.

Accept or Reject Null Hypothesis Calculator (p-value & Critical)

Decide whether to reject the null hypothesis. Enter a p-value, or a test statistic and degrees of freedom, and compare it with your significance level.

Add and Subtract Binomials Calculator with Steps

Add or subtract two binomials and get the combined result, with the sign change for subtraction and like terms grouped for you.

Add the Proper Constant to the Binomial Calculator

Find the constant that makes x² + bx a perfect square trinomial. This is the key step in completing the square, shown with exact fractions.

Adding Binomials Calculator: Add Two or Three Binomials

Add two or three binomials in one step. The calculator groups the like terms and gives the simplified sum.

Adding Machine vs Calculator: Tape Total With Running Sum

Add a list of numbers the way an adding machine does, with a running total on a tape, and see how that differs from a standard calculator.

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.

ANOVA Table Calculator From Means, SDs and Sample Sizes

Build a complete one-way ANOVA table from each group’s sample size, mean and standard deviation.

Area Model Calculator for Multiplication and Binomials

Draw the area model for a multiplication problem and see each partial product before they are added.

Area Model Multiplication Calculator With Estimate Check

Multiply large numbers with the area model, see each row of the grid and check the answer against a quick estimate.

Average and Standard Deviation Calculator: Mean, Median, Mode

Find the average and standard deviation of your data, and see which kind of average best describes it.

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.

Basis for the Range of a Matrix Calculator (Column Space)

Find a basis for the range (column space) of a matrix, along with its rank and pivot columns.

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 Distribution Calculator With Steps and Terms

See every term of the binomial distribution you add up, for exact, at most, at least and between probabilities.

Binomial Expansion of (1 + x)^n Calculator With Steps

Expand (1 + x)ⁿ for any n: a finite expansion for whole numbers and an infinite series for fractional or negative powers.

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.

Multiply Radical Binomials Calculator With Steps

Multiply binomial radical expressions and get the answer in simplest radical form. Every partial product is shown, with perfect squares pulled out and like radicals combined.

Binomial Squared Calculator: Expand (a + b)² With Steps

Square any binomial and see the three parts of the answer: the first term squared, twice the product, and the last term squared.

Binomial Calculator with Steps: Percentile, Mode, Find n

Work backwards from a probability: find the binomial percentile k, the most likely number of successes, or how many trials you need, with each step shown.

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.

Bivariate Regression Calculator: y on x, x on y, r and Covariance

Analyse two variables together: get the regression line of y on x, the line of x on y, the correlation coefficient and the covariance in one step.

Box Plot Range Calculator: Range, IQR and Whiskers

Find the range of a box plot in three ways: the full range from minimum to maximum, the range of the box (the IQR), and the span of the whiskers.

CDF Probability Calculator: Less, More, Between

Turn a CDF into the probability you need: less than, more than, between two values, or outside them. Works for normal, t, chi-square, binomial and Poisson.

Cell Doubling Time Calculator: Growth Rate and Generations

Calculate the doubling time of a cell culture from starting and final counts, with the growth rate and number of generations.

Central Limit Theorem Calculator: Simulate Sample Means

Choose a skewed, uniform or two-humped population and watch the sample means turn bell-shaped as n grows, with the exact standard error and a normal-approximation probability.

Chi-Square Table Calculator: Critical Values by df and α

Look up any chi-square critical value without paging through a printed table, and read the whole table below the calculator.

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.

Chi Test Calculator: Chi-Square Test Statistic and P-Value

Calculate the chi-square test statistic, degrees of freedom and p-value for a goodness-of-fit or independence test.

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 Skewness Calculator: Pearson, Bowley and Moment

Calculate the coefficient of skewness of your data using the Pearson, Bowley and moment formulas side by side.

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.

Combination Notation Calculator: C(n,k), nCr and (n choose k)

Type a combination in whatever notation you have, C(10,3), 10C3 or 10 choose 3, and get the value with the equivalent notations and steps.

Combination Probability Calculator: Choose r From N Items

Use combinations to find the probability of picking exactly k special items when you choose r items without replacement.

Combination Sum Calculator: Σ C(n, k) Over a Range of k

Add up combinations C(n, k) over a range of k, such as the number of ways to choose at most r items from n.

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.

Covariance Matrix Calculator With Correlation Matrix

Paste columns of data to get the covariance matrix and correlation matrix for up to 12 variables.

Covariance Calculator Online: Sample, Population and r

Calculate the covariance of two variables online. Get the sample and population values, the correlation, and the table that shows each product of deviations.

Critical Value for a Confidence Level (z and t)

Find the critical value for any confidence level. You get the z* value, and the t* value too when you enter degrees of freedom, with a table of common levels.

Critical Value of z Calculator: One- and Two-Tailed

Find the critical value of z for any confidence level or significance level, for left, right or two-tailed tests.

Cross-Entropy Loss Calculator (Binary and Multiclass)

Calculate the cross-entropy loss of a classifier. Use labels with predicted probabilities for binary log loss, or enter two full distributions for multiclass.

Cumulative Distribution Function (CDF) Calculator

Find the cumulative distribution function value F(x) = P(X ≤ x) for five common distributions. You also get the upper tail and the density or probability at x.

Curve Fit Calculator: Try Every Model and Rank by R²

Try every common curve on your x and y data at once, rank them by R² and predict a new value.

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.

d and SD Calculator: Deviations, SD and Paired Difference

Work out d and SD in two ways: the deviation d of each value from the mean with the standard deviation, or the paired differences d̄ and s_d for before and after data.

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.

Distance Between Skew Lines Calculator in 3D

Find the shortest distance between two lines in 3D. Enter a point and a direction vector for each line, and see whether they are skew, parallel or intersecting.

Distinguishable Permutations Calculator (Repeated Items)

Count the distinguishable permutations of a word or a set with repeated items. Enter letters or group sizes and get the number of different arrangements.

Distributive Property Calculator: Expand and Multiply

Expand a product with the distributive property, from a single factor times a bracket to two full polynomials.

Distribution Mean Calculator: Expected Value and Variance

Find the mean of a probability distribution. Enter a table of values and probabilities, or pick a standard distribution and its parameters.

Domain and Range of a Circle Calculator With Graph

Find the domain and range of a circle graph from its center and radius, or from its general equation. The result is in interval notation, with a plot of the circle.

Domain and Range of a Parabola Calculator With Steps

Find the domain and range of a parabola in interval notation. Works for parabolas that open up or down, and for ones that open left or right.

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.

Entropy Calculator for Decision Trees: Information Gain

Calculate entropy and information gain for a decision tree split. Enter the class counts at a node and at each child to see which split is best.

Equation of the Line That Passes Through the Points Calculator

Find the equation of the line that passes through two points. You get slope-intercept, point-slope and standard form, plus intercepts, distance and midpoint.

Expected Value and Variance Calculator for Discrete Data

Enter outcomes and their probabilities to get the expected value, variance and standard deviation with a full working table.

Experimental vs Theoretical Probability Calculator

Compare theoretical probability with the experimental probability from your trials. You get both values, the difference, the expected count and a quick check of whether the gap is unusual.

Exponential Decay Model Calculator: k, Half-Life and Time

Build an exponential decay model from a decay constant, a half-life or two measurements, and use it to predict.

Exponential Distribution Calculator: Probability and Mean

Calculate waiting-time probabilities from a rate or a mean, with median, variance, percentiles and density charts.

F Distribution Calculator: F Table and P-Value

Look up critical F values for any pair of degrees of freedom, or convert an F statistic into a p-value for ANOVA and variance tests.

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.

Factoring Binomials Calculator With Steps

Factor any two-term expression such as 9x² − 25 or 8x³ + 27, with the pattern used and every step.

Find Probability Calculator: Normal, Binomial, Poisson and More

Find a probability under the normal, binomial, Poisson, uniform, exponential or t distribution in one place.

Find the Margin of Error Calculator for Means and Proportions

Find the margin of error for a mean, a proportion or an existing confidence interval.

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.

Genotype Probability Calculator: Punnett Square for 1 to 3 Genes

Enter the genotype of each parent to get the probability of every offspring genotype and phenotype. Supports one, two or three genes with complete dominance.

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.

Histogram Mean Calculator: Estimate Mean, Median and Mode

Estimate the mean of a histogram from its classes and frequencies, together with the median, mode and standard deviation.

How to Find Population Variance: Calculator With Steps

Learn how to find population variance and get the answer with steps. Choose the exact population variance, or the estimated population variance from a sample.

How to Find the Mean Calculator: Steps, Frequency and Target

See how to find the mean step by step for a list, a frequency table, or a target average.

Hypothesis Calculator: H0, H1, Critical Value and Power

Set up a hypothesis test: write H0 and H1, find the critical value, then check the power and the sample size you need.

Hypothesis Test for a Mean Calculator (z and t) With Steps

Test a claim about a population mean. Enter your sample mean, hypothesised mean, standard deviation and size to get the statistic, p-value and decision.

Hypothesis Test Calculator: z, t, Proportion, Two-Sample

Run a hypothesis test from summary statistics. Choose a one-sample z or t test, a one-proportion test, or a two-sample test, and get the statistic, p-value and decision.

Hypothesis Test Calculator: One- and Two-Tailed Tests

Run a one-tailed or two-tailed hypothesis test for means, paired data and proportions from summary numbers.

P-Value Calculator: From Z, T, Chi-Square or F Statistic

Turn a test statistic into a p-value for z, t, chi-square and F tests, with the decision at your α.

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.

Increment Method Calculator: Δy, Δy/Δx and the Limit as h → 0

Find the increment Δy and the difference quotient Δy / Δx for any f(x), then watch the quotient settle on the derivative as h shrinks.

Independent Event Probability Calculator: And, Or, At Least

Combine the probabilities of any number of independent events to get P(all), P(none), P(at least one) and P(exactly k).

Critical Value Calculator: z, t, Chi-Square, F

Find the indicated critical value for a z, t, chi-square or F test. Enter the significance level, the tail and any degrees of freedom to get the cut-off and the rejection region.

Indicated Probability Calculator: Chance of the Event You Pick

Find the probability of the event you indicate from a list of outcomes and how many of each there are.

Inverse Z Score Calculator: Find Z From a Probability

Turn a probability or confidence level into a z-score cut-off, and into a raw value for any mean and standard deviation.

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.

Least Squares Calculator: Line of Best Fit with Steps

Fit the least-squares line to your data and see every sum, the normal equations, the sum of squared errors and each residual.

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.

Linear Correlation Coefficient Calculator (Pearson r)

Paste paired x and y values to get the linear correlation coefficient r, its significance test and a confidence interval, with a scatter plot.

Linear Equations With Distribution Calculator With Steps

Solve a linear equation that needs the distributive property, with every step from distributing to checking.

Logistic Regression Sample Size Calculator (EPV & Hsieh)

Work out the sample size for a logistic regression three ways: the events-per-variable rule, a binary predictor, or a continuous predictor with an odds ratio.

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.

MAD in Math Calculator: Mean Absolute Deviation With Steps

Find the MAD (mean absolute deviation) in math with every step, and compare how spread out two data sets are.

Mean Absolute Value Calculator (and Mean Absolute Deviation)

Find the mean absolute value of a list of numbers, and see how it compares with the mean absolute deviation, the ordinary mean and the root mean square.

Mean and MAD Calculator: Mean Absolute Deviation and Median

Calculate the mean and the MAD (mean absolute deviation and median absolute deviation) for any data set.

Mean and SD Calculator: Average, Sample and Population SD

Get the mean and SD of your data, with sample and population values side by side.

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 and Stdev Calculator With Excel STDEV.S and STDEV.P

Calculate the mean and stdev of your numbers and see the matching Excel and Google Sheets functions.

Mean Average Deviation Calculator: One or Two Data Sets

Calculate the mean average deviation of one data set, or compare two sets by their means and spreads.

Mean, Median and Standard Deviation Calculator + Outlier Test

Calculate the mean, median and standard deviation together and see how an extreme value affects each.

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 Mode Calculator: Find the Average and Most Common Value

Find the mean and mode of a list of numbers, including data with more than one mode or none.

Mean of a Random Variable Calculator (Expected Value)

Find the mean of a discrete random variable from its values and probabilities. The mean is the expected value, and you can also get the mean of aX + b.

Mean, SD and CV Calculator: Compare Variability Between Sets

Calculate the mean, SD and coefficient of variation together, and compare the relative spread of two data sets.

Mean Square Calculator: Mean of Squares, RMS and MS

Find the mean square of your data, the average of the squared values, along with the root mean square and the mean sum of squares about the mean.

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.

Quartile Calculator: Q1, Median, Q3, IQR and Outliers

Find Q1, the median, Q3, the interquartile range and outliers for any data set, using the method your course or software uses.

Median Score Calculator: Median, Quartiles and Percentile Rank

Find the median score of a class or data set, and see where any one score stands.

Min, Q1, Median, Q3, Max Calculator (Five-Number Summary)

Get the minimum, Q1, median, Q3 and maximum of your data, plus the IQR, outlier fences and a box plot, using the quartile method you need.

Moment Generating Function Calculator: M(t), Mean, Variance

Choose a distribution, enter its parameters and a value of t to get the moment generating function, plus the mean and variance it implies.

Monte Carlo Probability Calculator (Dice, Coins, Birthday)

Estimate a probability by simulation. Pick dice, coins or the birthday problem, set the number of trials, and compare the Monte Carlo estimate with the exact answer.

Multiple Regression Calculator: Coefficients, R² and P-Values

Fit a multiple linear regression with up to 8 predictors and get coefficients, p-values, R², adjusted R² and the overall F test.

Multiply Binomials by Polynomials Calculator With Steps

Multiply a binomial by any polynomial. The calculator lists every partial product, then adds like terms to give the final expanded answer.

Multiplying Binomials With Fractional Coefficients

Multiply two binomials whose coefficients are fractions. You get each FOIL product as an exact fraction, then the combined answer in lowest terms.

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.

Normal Approximation to the Binomial Calculator

Approximate binomial probabilities with a normal curve and compare them with the exact answer, with and without continuity correction.

Normal Distribution Calculator: Probability, Z-Score and Area

Find normal probabilities for any mean and standard deviation, with z-scores and a shaded bell curve.

Normal Sampling Distribution Calculator (Sample Mean)

Find the standard error and the probabilities for a sample mean when the population is normal or the sample is large. Choose less than, greater than or between.

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.

OLS Regression Calculator: Slope, R², t Test, CI

Run an ordinary least squares regression on paired data. You get the fitted line, R², standard errors, the t and F tests for the slope and a confidence interval.

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.

P Value Two Tailed Test Calculator for z and t Statistics

Find the p-value for a two-tailed test from a z or t statistic, with the one-tailed values, critical values and the reject or fail-to-reject decision.

P Value Calculator With Steps: z, t, Chi-Square and F

Find a p-value from a z, t, chi-square or F statistic, with each step shown. Choose a two-tailed, left-tailed or right-tailed test.

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.

Percentile of Normal Distribution Calculator (Both Ways)

Find the percentile of any value in a normal distribution, or go the other way and find the value that sits at a chosen percentile.

Poisson Distribution Calculator: Exact and Cumulative

Calculate the probability of k events in a fixed interval from the average rate λ.

Polynomial Curve Fitting Calculator: Degree 1 to 6 With R²

Fit a polynomial of the degree you choose to your data and see how each degree compares.

Probability Calculator for 1 Event: Single and Repeated Trials

Work out the probability of one event, and how that chance builds up when you repeat it.

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.

Conditional Probability Calculator: P(A|B), P(A and B), Bayes

Find the probability of A given B, the joint and union probabilities, and whether the events are independent.

Probability of A or B Calculator (Union of Two Events)

Find the probability of A or B. Choose independent, mutually exclusive or overlapping events and get the union, the intersection and the other regions.

Probability of a Sample Proportion Calculator (z and Exact)

Find the probability that a sample proportion falls below, above or between values, given the true population proportion and the sample size.

Probability Z Score Calculator: Left, Right and Two-Tail

Convert a z-score, or a raw score with its mean and standard deviation, into a normal probability.

Proof Table Calculator: Truth Tables, Tautology and Equivalence

Build a proof table for any logical statement. See every row, find out if it is a tautology or contradiction, and test equivalence with a second statement.

Range of a Function Calculator With Domain and Steps

Find the range of a function in interval notation, with the vertex, the domain used and a graph.

Range Symbol on Calculator: What R Means and How to Find It

See what the range symbol means, calculate the range of your data and read the other common statistics symbols with your own values.

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.

Raosoft Sample Size Calculator Citation: Formula and Methods Text

Working out how to cite a Raosoft sample size calculation? This tool gives the number, the formula behind it and a methods sentence listing every input a reviewer expects to see.

Rearrange Equations Calculator: Make Any Variable the Subject

Rearrange a formula to make any variable the subject, see each algebra step, and calculate the answer from known values.

Rearrange Formula Calculator for Statistics With Steps

Rearrange a statistics formula to solve for the variable you need, with every algebra step and the numeric answer.

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.

Relative Average Deviation Calculator: % and ppt

Calculate the relative average deviation of repeated measurements as a percentage or in parts per thousand.

Relative Cumulative Frequency Calculator With Table & Ogive

Build a relative cumulative frequency table from your data. See each frequency, relative frequency, cumulative frequency and the running percentage, plus an ogive.

RSD Calculator (Relative Standard Deviation)

Enter repeated measurements, or just a standard deviation and a mean, to find the relative standard deviation: the standard deviation as a percentage of the mean.

Sample Mean and Sample Standard Deviation Calculator

Find the sample mean x̄ and sample standard deviation s, plus the standard error and a confidence interval for the population mean.

Sample Mean Probability Calculator (Central Limit Theorem)

Find the probability that a sample mean falls below, above or between values, using the mean, standard deviation and sample size of the population.

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.

SD Formula Calculator: Standard Deviation From Sums

Use the SD formula without the raw list: enter Σx, Σx² and n, a frequency table or a variance.

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.

Significant Figure Rounding Calculator With Steps

Round a number to the significant figures you need. The calculator also counts the sig figs in your input and shows the result in scientific notation.

Simple Regression Calculator: Equation, R², Slope Test, ANOVA

Run a simple linear regression of y on x and get the equation, the slope test and the ANOVA table in one place.

Simplify Expressions with Distribution Calculator (Step by Step)

Simplify any expression that needs the distributive property. See each bracket distributed, then like terms combined into the final answer.

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.

Square of a Binomial Calculator: (a + b)² With Steps

Square a binomial such as (3x + 5)² with every step, or check whether a trinomial is a perfect square.

Square Root Regression Calculator: y = a + b√x With R²

Fit a square root curve to your data. The calculator finds a and b in y = a + b√x, reports R² and compares the fit with a straight line.

Least Squares Regression Line Calculator: Slope, Intercept, r

Find the least squares regression line from raw data or from summary statistics. You get the slope, intercept, equation, r and a prediction.

Squaring a Binomial Calculator (Simple and Two-Variable)

Square a binomial with one or two variables. Enter the two terms and see the three parts of the answer worked out separately.

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.

SSR, SST, SSE Calculator and R² (Sum of Squares)

Split the variation in y into explained and unexplained parts. You get SST, SSR, SSE and R² from raw data, or from observed and predicted values.

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.

Standard Deviation Formula Calculator With Steps

Apply the standard deviation formula step by step and see every deviation, square and total.

Standard Deviation From Mean and Sample Size Calculator

Find a standard deviation when you know the sample size and a summary such as the standard error, a confidence interval, the CV or Σx².

Standard Deviation Index (SDI) Calculator for Lab Comparison

Calculate the standard deviation index (SDI) of a result against a group mean and standard deviation.

Standard Error Calculator: Mean (SEM) and Proportion

Calculate the standard error of the mean from your data, from a standard deviation and sample size, or for a proportion.

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.

Statistical Sampling Calculator: Random, Systematic, Stratified

Select a simple random, systematic or stratified sample from a population and see the sampling fraction and margin of error.

Statistics Confidence Interval Calculator: Mean and Proportion

Get a confidence interval from summary statistics for a mean or a proportion, and see how the level changes its width.

Sxx Calculator: Sxx, Syy, Sxy, Slope and Correlation

Calculate Sxx, Syy and Sxy for one or two variables and see how they build the regression slope and correlation.

T Critical Value Calculator (Two-Tailed) With Steps

Find the two-tailed critical value of the t distribution from your significance level and degrees of freedom. It also shows the matching z value for comparison.

T Distribution Calculator: Critical Values and P-Values

Look up critical t values for any degrees of freedom and confidence level, or turn a t statistic into a p-value.

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.

Test Statistic Calculator for z, t, Proportion, χ², F and r

Compute the test statistic for the most common hypothesis tests, with the formula filled in and the p-value.

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.

Uniform Distribution Calculator: Probability, Mean, Variance

Find probabilities, the mean and the variance for a continuous uniform distribution on [a, b].

Variance of a Probability Distribution Calculator

Find the variance of a named probability distribution straight from its parameters.

Variance of a Random Variable Calculator + Steps

Find the variance and standard deviation of a discrete random variable from its values and probabilities. It also gives the variance after a linear change aX + b.

Variance Symbol Calculator: s² vs σ² With Your Own Data

Find out which variance symbol to use, s² or σ², and calculate both for your data.

Variance Calculator with Frequency: Mean, s² and σ² From a Table

Find the variance of a frequency table. Enter each value with its frequency and get the mean, variance and standard deviation with the full working.

Calculator With Standard Deviation: One-Variable Statistics

A calculator with standard deviation that shows the full one-variable statistics screen for your list of numbers.

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.

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Descriptive Statistics

Mean, spread, variation and data summaries.

Probability & Counting

Combinations, permutations, tests and distributions.

Algebra

Factoring, expanding, simplifying and solving.

Logic & Discrete Math

Boolean algebra, truth tables and algorithms.

Calculus

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.