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Statistics Calculators

Use deterministic statistics calculators for center and spread, percentiles, correlation, regression, standardized scores, sampling uncertainty and sample-size planning. Each tool states the formula, convention or approximation that matters for classroom and research-methods work.

Start with your question

Which statistics calculator do I need?

Choose the task before choosing a formula. Open a task below to see the available tools and the inputs to check.

Summarize one set of numbersWhat is typical, and how much do the values vary?

Use center and spread together. A median can help you describe an uneven dataset; standard deviation measures spread around the mean.

Before calculating: Check whether your values are a sample or the entire population before choosing an SD result.

Compare group meansOne mean, two groups, or matched before-and-after values?

The T-Test Calculator offers one-sample, independent-sample Welch and paired modes. Use paired mode only when each first measurement matches one second measurement. One-way ANOVA compares three or more independent groups.

Before calculating: Review sampling, outliers and distribution assumptions. A significant ANOVA result does not identify which groups differ.

Study a relationshipDo two numeric variables move together?

Pearson correlation summarizes linear association. Simple linear regression fits a line and can estimate Y at an entered X. Keep each X value matched with its Y value.

Before calculating: Inspect the pattern and outliers first. Correlation does not establish causation; predictions outside the observed X range are extrapolations.

Compare categorical countsAre you working with frequencies instead of measurements?

Use the Chi-Square Calculator for a contingency table or observed-versus-expected category counts. Its goodness-of-fit mode expects fully specified expected counts.

Before calculating: Enter counts, not percentages. Sparse expected cells can weaken the approximation; this tool does not calculate Fisher’s exact test.

Estimate uncertaintyIs the target a mean or a population proportion?

Standard error describes uncertainty around a mean. Lynara’s mean interval uses z and requires an appropriate known-population-SD model. Margin of Error and Sample Size use a proportion model.

Before calculating: The mean-interval tool does not provide a Student t interval. A proportion sample-size result is not a power calculation for a t-test.

Calculate a model probabilityFixed trials, event counts, or a continuous normal model?

Binomial uses a fixed trial count and success probability. Poisson uses an expected event count over a specified interval. Normal probability uses a mean and SD.

Before calculating: Choose the model from the experiment and its assumptions. A calculator cannot determine a distribution from a short list of observations.

Method reference: NIST statistical techniques. Tool-specific formulas and limitations are explained on each calculator page.

Learn the method

Statistics guides and worked examples

Check assumptions, see a worked method and choose the matching calculator for your dataset or coursework.

Population vs Sample Standard DeviationCompare population and sample variance and standard deviation and understand why sample calculations divide squared deviations by n minus 1.Normal Distribution Probability GuideCalculate normal left-tail, right-tail and interval probabilities, z-scores and inverse percentiles from a mean and standard deviation.How to Calculate and Read a P-ValueConvert z, t and chi-square statistics into the correct tail probability and avoid common mistakes when interpreting a p-value.One-Way ANOVA GuideUnderstand one-way ANOVA, between- and within-group variation, the F statistic, p-value, eta squared and the limits of an omnibus test.How to Calculate a Mean Confidence IntervalBuild a normal-approximation confidence interval around a mean using standard error and 90%, 95% or 99% z critical values.Sample Size for a Proportion GuideEstimate proportion sample size from confidence and margin of error, with optional finite-population correction for a known population.Pearson Correlation and Covariance GuideCalculate Pearson r, r squared and covariance for paired numeric data while separating standardized association from scale-dependent covariance.Binomial Probability GuideCalculate exact, at-most and at-least binomial probabilities and check whether a fixed-trial probability model fits the problem.

Browse all study and statistics guides →

Available tools

Mean Median Mode CalculatorCalculate mean, median, mode, minimum and maximum from a list of numeric values.CalculatorStandard Deviation CalculatorCalculate population and sample variance and standard deviation from a numeric data set.CalculatorFive Number Summary & Outlier CalculatorCalculate min, Q1, median, Q3, max, IQR, 1.5×IQR fences, box-plot whiskers and flagged outliers from numeric data.CalculatorNormal Distribution CalculatorCalculate normal-distribution left-tail, right-tail and between-values probabilities, density, z-scores and inverse percentiles.CalculatorT-Test CalculatorRun one-sample, Welch two-sample or paired two-tailed t tests with t statistic, degrees of freedom and p-value.CalculatorChi-Square Test CalculatorRun chi-square independence or goodness-of-fit calculations with expected counts, degrees of freedom and upper-tail p-value.CalculatorP-Value CalculatorConvert a z, t or chi-square test statistic into the matching one- or two-tailed p-value with explicit distribution assumptions.CalculatorOne-Way ANOVA CalculatorRun a one-way ANOVA across 3 to 20 numeric groups with F statistic, degrees of freedom, p-value, sums of squares and eta squared.CalculatorBinomial Probability CalculatorCalculate exact, at-most and at-least binomial probabilities from trials, successes and a fixed success probability.CalculatorPoisson Distribution CalculatorCalculate exact, at-most and at-least Poisson probabilities from an average event rate and an observed event count.CalculatorPermutation & Combination CalculatorCalculate exact nPr permutations and nCr combinations with or without repetition, using integer arithmetic instead of rounded factorial math.CalculatorPercentile Rank CalculatorCalculate the percentile rank of a target value within a numeric data set using a stated midrank convention.CalculatorCoefficient of Variation CalculatorCalculate population and sample coefficient of variation from a numeric data set with a nonzero mean.CalculatorZ-Score & Normal Percentile CalculatorCalculate a z-score from value, mean and standard deviation, plus normal-model percentile and right-tail probability.CalculatorPearson Correlation & Covariance CalculatorCalculate Pearson r, r squared, sample covariance and population covariance from two paired numeric data sets.CalculatorSimple Linear Regression & Prediction CalculatorFit a least-squares line, calculate slope, intercept, Pearson r and r squared, and optionally predict Y for a chosen X value.CalculatorStandard Error CalculatorCalculate the standard error of a sample mean from standard deviation and sample size.CalculatorMean Confidence Interval CalculatorCalculate a normal-approximation confidence interval for a mean from the mean, standard deviation, sample size and confidence level.CalculatorMargin of Error CalculatorCalculate a normal-approximation margin of error for a proportion from sample size, estimated proportion and confidence level.CalculatorSample Size CalculatorEstimate sample size for a proportion margin-of-error target, with optional finite-population correction for a known population.Calculator

Use statistical formulas with the assumptions visible

Statistics calculators are most useful when the method matches the data and assignment. Lynara keeps the formula, sample-size assumptions and approximation method visible rather than presenting one statistical procedure as universal.

Related: Compare subgroups and pooled success rates · Correlation vs causation guide · Check a research graph axis and denominator · Read graphs in research papers · Check which statistical test fits your design · Verify an AI-suggested statistical test · Mean Median Mode Calculator · Pearson Correlation Calculator · Simple Linear Regression Calculator · Standard Deviation Calculator · Z-Score Calculator · Standard Error Calculator · Mean Confidence Interval Calculator · Margin of Error Calculator · Sample Size Calculator · statistics and study guides