Statistics and Probability Calculators
Explore 141 public calculators and reference tables that fit MathCalculate's statistics and probability scope, organized into working areas for describing data, modeling distributions, testing hypotheses, analyzing categories and ranks, fitting relationships, computing probabilities, and simulating randomness. Every tool shows its formula, a worked example, and interpretation guidance.
Descriptive Statistics
Descriptive tools summarize a data set you already have: where its center sits, how far values spread, and which points fall outside the pattern. Start with mean, median, and mode to establish the center, or the weighted mean when values carry unequal importance, then use variance, standard deviation, or the underlying sum of squares to measure spread around it. Percentiles, quartiles, and the five number summary describe position and shape: exactly what you need before sketching a box plot or comparing groups. Robust spread and shape tools round out the set: the IQR, outlier screen, and box plot generator handle suspect extremes, the coefficient of variation and MAD offer alternative spread measures, skewness and kurtosis quantify shape, the geometric and harmonic means average growth rates and rates correctly, and percent error scores a measurement against its accepted value.
Standard Deviation Calculator
Calculate standard deviation, variance, and spread with clear statistical outputs.
Descriptive Statistics Calculator
Summarize data with mean, median, range, variance, and related statistics.
Mean, Median, Mode Calculator
Find mean, median, mode, range, sum, and count with a full step-by-step solution.
Variance Calculator
Compute population or sample variance with every deviation and squared term shown.
Percentile Calculator
Find the value at any percentile or a value's percentile rank using linear interpolation.
Quartile Calculator
Calculate Q1, Q2, Q3, IQR, and Tukey fences with automatic outlier detection.
Five Number Summary Calculator
Get the minimum, Q1, median, Q3, and maximum of a data set for box plots.
Interquartile Range Calculator
Find the IQR with Q1, Q3, the median, and 1.5 × IQR fences via the median-split method.
Outlier Calculator
Detect outliers with Tukey's 1.5 × IQR fences or a z-score threshold, plus a cleaned data preview.
Box Plot Generator
Draw a labeled box and whisker plot with Tukey whiskers and outlier dots, downloadable as SVG.
Coefficient of Variation Calculator
Express the standard deviation as a percentage of the mean to compare variability across scales.
Mean Absolute Deviation (MAD) Calculator
Calculate the average distance from the mean step by step, plus the median absolute deviation.
Skewness and Kurtosis Calculator
Measure distribution shape with sample and population skewness and excess kurtosis, with plain-language labels.
Geometric Mean Calculator
Average growth rates, returns, and ratios multiplicatively with the numerically stable log method.
Harmonic Mean Calculator
Average rates and speeds correctly and see the AM ≥ GM ≥ HM ordering on your own data.
Class Width Calculator
Divide a data range into equal histogram classes with boundaries, frequencies, and Sturges' rule.
Weighted Mean Calculator
Average values with unequal importance using weights: grades, GPAs, and weighted scores with full working.
Sum of Squares Calculator
Compute the total sum of squared deviations with both the definitional and computational formulas shown.
Percent Error Calculator
Compare a measured value against the accepted value with absolute, relative, and percent error.
Histogram Maker
Turn raw data into a histogram with a frequency table, relative and cumulative frequencies, and SVG download.
Stem and Leaf Plot Generator
Build an ordered stem-and-leaf display from raw data, with split stems and a summary of the data's shape.
Moving Average Calculator
Simple, weighted and exponential moving averages of a series for any window, with the working, a chart and the forecast errors MAD, MSE and MAPE.
Range Calculator
Find the range of a data set as maximum minus minimum, with the minimum, maximum, midrange, the range rule of thumb and a number line.
Frequency Distribution Calculator
Make a frequency table from numbers, classes or categories with relative and cumulative frequency, percent, the working and a bar chart or histogram.
Chebyshev's Theorem Calculator
Find the minimum share of values within k standard deviations of the mean for any distribution, the k for a share or an interval, with the interval, counts and working.
Grouped Data Calculator
Find the mean, median, mode, variance, standard deviation and quartiles of grouped data from classes and frequencies, with class marks, boundaries and the working.
Distributions & Critical Values
These calculators work with probability models rather than raw data. Use the normal distribution and z-score tools when values follow a bell curve, the binomial tool for successes in a fixed number of trials, and the Poisson tool for event counts over an interval. The exponential tool times the waits between those events, the geometric tool finds when the first success arrives, and the hypergeometric tool handles draws without replacement. The empirical rule gives quick 68-95-99.7 ranges, while the critical value tool returns the exact cutoffs that hypothesis tests are judged against. For classic table lookups, the printable z-table, t-table, chi-square table, and F-table list the same cumulative probabilities and critical values in the format textbooks use. Working from a TI-84? The normalcdf, normalpdf, invNorm, tcdf, invT, χ²cdf, binompdf, poissonpdf, and geometpdf calculators reproduce each DISTR-menu function with the same arguments and show the steps behind the answer.
Normal Distribution Calculator
Work with the normal curve, cumulative probabilities, and related z-score outputs.
Z-Score Calculator
Convert values to z-scores and estimate probability within a normal model.
Central Limit Theorem Calculator
Find the sampling distribution of a sample mean or sum: the standard error, the probability below, above or between values, and percentiles, with a finite population correction.
Binomial Distribution Calculator
Exact, at-most, at-least and range probabilities for the number of successes in n independent trials, with the mean, variance, a bar chart and a table.
Poisson Distribution Calculator
Turn an average event rate into exact, cumulative and range Poisson probabilities, with a bar chart and a probability table.
Empirical Rule Calculator
Apply the 68-95-99.7 rule to get one, two, and three standard deviation ranges.
Critical Value Calculator
Find Z, t, chi-square, and F critical values for any significance level and tail choice.
Z-Table (Standard Normal Distribution)
Look up cumulative standard normal probabilities for any z-score from −3.49 to 3.49.
T-Table (Student's t Critical Values)
Look up Student's t critical values by degrees of freedom and one- or two-tail significance level.
T-Table for α = 0.10
One- and two-tail t critical values at the 0.10 level for every degree of freedom 1–1000.
T-Table for α = 0.05
The workhorse t critical values at the 5% level (one- and two-tail) for every degree of freedom 1–1000.
T-Table for α = 0.025
The 0.025-level t values, including the familiar 95% confidence interval multipliers, for df 1–1000.
T-Table for α = 0.01
The strict 1%-level t critical values (one- and two-tail) for every degree of freedom 1–1000.
Chi-Square Table (χ² Critical Values)
Look up chi-square critical values for degrees of freedom 1 to 100 across ten common tail areas.
Chi-Square Table for α = 0.10
Upper and lower χ² critical values at the lenient 0.10 level for every degree of freedom 1–100.
Chi-Square Table for α = 0.05
The standard 5%-level χ² critical values for every degree of freedom 1–100, with lower-tail pairs.
Chi-Square Table for α = 0.025
The per-tail χ² pair behind 95% variance confidence intervals, for every degree of freedom 1–100.
Chi-Square Table for α = 0.01
The strict 1%-level χ² critical values for every degree of freedom 1–100, with lower-tail pairs.
F-Table (F-Distribution Critical Values)
Look up F critical values by numerator and denominator degrees of freedom for α = 0.10, 0.05, 0.025, and 0.01.
F-Table for α = 0.10
F critical values at the lenient 0.10 level, for screening ANOVA and 20% two-tailed variance tests.
F-Table for α = 0.05
The standard ANOVA critical values: upper-tail F cutoffs at the conventional 5% significance level.
F-Table for α = 0.025
Per-tail F cutoffs for 5% two-tailed variance-ratio tests and 95% variance-ratio confidence intervals.
F-Table for α = 0.01
The strict 1%-level F critical values for highly significant ANOVA and regression tests.
Exponential Distribution Calculator
Turn an event rate or mean waiting time into exact exponential probabilities and percentiles.
Geometric Distribution Calculator
Find the probability that the first success lands on a given trial, in either textbook convention, with cumulative and range results.
Negative Binomial Distribution Calculator
Find the probability that the r-th success arrives on a given trial, or after a given number of failures: exactly, at most, at least or between.
Hypergeometric Distribution Calculator
Exact probabilities for sampling without replacement: exactly, at most, at least and between k successes from a finite population.
normalcdf Calculator
Evaluate normalcdf(lower, upper, μ, σ) exactly like a TI-84, with the shaded area and keystrokes shown.
invNorm Calculator
Find the value or z-score for a given area with invNorm(area, μ, σ): left, right, or center tail.
binompdf & binomcdf Calculator
Evaluate binompdf(n, p, k) and binomcdf(n, p, k) like a TI-84, plus a full probability table.
normalpdf Calculator
Evaluate normalpdf(x, μ, σ) (the height of the bell curve at a point) with steps and a graph.
tcdf Calculator
Evaluate tcdf(lower, upper, df) and turn any t statistic into one- and two-tailed p-values.
invT Calculator
Find t critical values with invT(area, df) for left, right, or two-tailed areas.
Chi-Square CDF Calculator (χ²cdf)
Evaluate χ²cdf(lower, upper, df) and get the p-value for any chi-square statistic.
poissonpdf & poissoncdf Calculator
Evaluate poissonpdf(λ, x) and poissoncdf(λ, x) like a TI-84, with at-least and more-than versions.
geometpdf & geometcdf Calculator
Evaluate geometpdf(p, x) and geometcdf(p, x) for the trial of the first success, TI-84 style.
Z-Score to Percentile Calculator
Convert a z-score to a percentile with the areas to the left and right, the two-tailed p-value and a shaded normal curve.
Percentile to Z-Score Calculator
Convert a percentile, top percent or middle percent to a z-score, and to a raw score from a mean and standard deviation.
Uniform Distribution Calculator
Uniform distribution probabilities below, above, between or outside values, plus the inverse, mean, variance and median from a minimum and maximum, with a shaded chart.
Student t Distribution Calculator
Student's t probabilities, two-tailed p-values, critical values and quantiles from the degrees of freedom, with mean, variance and a shaded density chart.
Chi-Square Distribution Calculator
Chi-square cumulative probabilities, right-tail p-values and critical values from the degrees of freedom, with mean, variance, mode and a shaded chart.
F Distribution Calculator
F distribution p-values, cumulative probabilities and critical values from the numerator and denominator degrees of freedom, with a shaded density chart.
Gamma Distribution Calculator
Gamma distribution probabilities and quantiles from the shape and scale or rate, with mean, variance, mode, skewness and a shaded density chart.
Weibull Distribution Calculator
Weibull probabilities, reliability and percentile life from the shape and scale, with mean, variance, mode and a shaded density chart.
Lognormal Distribution Calculator
Lognormal probabilities and quantiles from the log mean and log SD, or from the mean and SD of the data itself, with a shaded density chart.
Beta Distribution Calculator
Beta distribution probabilities and quantiles for a proportion from α and β, with mean, variance, mode, skewness and a shaded density chart.
Inference & Hypothesis Testing
Inference tools answer questions about a population using only a sample. Before collecting data, plan with the sample size and margin of error calculators; afterward, quantify precision with standard error and confidence intervals. T-tests and z-tests compare means and proportions, ANOVA extends the comparison to three or more groups, p-values and effect sizes describe how convincing and how large those differences are, and the pooled standard deviation combines group spreads for those procedures. The one-sample t-test, t and proportion intervals, and the F-test for two variances mirror the TI-84 STAT TESTS menu, reporting the same values the calculator screen shows.
Confidence Interval Calculator
Build a z confidence interval for a population mean at 90%, 95%, or 99% confidence.
P-Value Calculator
Find the one- or two-tailed p-value of a z, t, chi-square or F test statistic and the decision at your significance level.
T-Test Calculator
Compare sample means with common t-test workflows and interpretable outputs.
Z-Test Calculator
Run one-sample, two-sample, and proportion z-tests with z statistics, p-values, and critical values.
One-Sample t-Test Calculator
Test a mean against a hypothesized value from data or x̄, Sx, and n: the TI-84 T-Test output.
t Confidence Interval Calculator
Build t intervals for one mean or two means (pooled or Welch), matching TInterval and 2-SampTInt.
Confidence Interval for a Proportion Calculator
Estimate one proportion or the difference of two from counts with the Wald (1-PropZInt, 2-PropZInt), Wilson, Agresti–Coull, Clopper–Pearson, Jeffreys and Newcombe methods compared.
F-Test for Two Variances
Compare two variances with F, p-value, and df from data or Sx and n: the TI-84 2-SampFTest.
ANOVA Calculator
Run one-way ANOVA calculations and inspect variance across groups.
Sample Size Calculator
Plan surveys with a confidence level, margin of error, and finite population correction.
Margin of Error Calculator
Measure sampling error for proportions and means at common confidence levels.
Standard Error Calculator
Compute the standard error of a mean or proportion from raw data or summary statistics.
Effect Size Calculator (Cohen's d)
Quantify the difference between two groups with Cohen's d, Hedges' g, and pooled SD.
Pooled Standard Deviation Calculator
Combine two or more group standard deviations into the pooled estimate used by t-tests and effect sizes.
Two Sample T-Test Calculator
Compare two independent means with Welch (default) or pooled Student t-tests from raw data or summary statistics, with both methods side by side.
Paired T-Test Calculator
Dependent-samples t-test on before/after or matched pairs, with difference table, correlation, Cohen's d_z, and confidence interval for the mean change.
Degrees of Freedom Calculator
Compute degrees of freedom for t, chi-square, F, and regression tests with the formula shown, plus the critical value at your alpha.
One Proportion Z-Test Calculator
Test a sample proportion against a hypothesized value: z statistic, one- or two-tailed p-value, the exact binomial p-value and a Wilson confidence interval.
Two Proportion Z-Test Calculator
Compare two proportions with the pooled z-test: z statistic, p-value and a confidence interval for the difference (Wald, Newcombe or Agresti–Caffo).
A/B Test Calculator
Check whether variant B beats A: conversion rates, relative uplift with its confidence interval, z-test p-value and a traffic-split (sample ratio) check.
Statistical Power Calculator
Compute power or required sample size for t tests, two proportions, ANOVA, and correlation with step-by-step noncentral distributions.
A/B Test Sample Size Calculator
Plan fixed-horizon A/B tests: sample size per variant from baseline conversion, MDE, α, and power.
Tukey HSD Calculator
Pairwise comparisons after ANOVA with Tukey HSD or Tukey-Kramer from raw data or an ANOVA table: differences, q statistics, adjusted p-values, and simultaneous confidence intervals.
Two-Way ANOVA Calculator
Balanced two-factor ANOVA with or without replication: main effects, interaction, partial eta squared, a variance check, and an interaction plot.
Levene's Test Calculator
Test equal variances across groups with Levene (mean), Brown-Forsythe (median) or a 10% trimmed mean: W, p-value, F critical value, group SDs and the ANOVA on absolute deviations.
Bonferroni Correction Calculator
Adjust multiple p-values with Bonferroni, Holm, Šidák, Hochberg, Benjamini-Hochberg, or Benjamini-Yekutieli, or find the corrected alpha for m tests.
Categorical & Nonparametric Tests
Categorical and nonparametric tests work with counts, categories, and ranks instead of the mean of normally distributed data. The chi-square calculator compares observed counts with expected counts to test whether a distribution fits or two categorical variables are related.
Chi-Square Calculator
Test observed counts against expected counts with a chi-square goodness-of-fit test.
Chi-Square Test of Independence Calculator
Run Pearson's chi-square test on an r×c contingency table with expected counts, residuals, Cramér's V, and p-value.
Cramér's V Calculator
Cramér's V, bias-corrected V, phi, Tschuprow's T and the contingency coefficient for any 2×2 to 10×10 table, with the chi-square p-value and Cohen's size label.
Chi-Square Goodness of Fit Calculator
Test whether observed category counts match expected proportions or counts with χ², df, residuals, and p-value.
Fisher's Exact Test Calculator
Exact two-sided and one-sided p-values for 2×2 tables via the hypergeometric distribution, with odds ratio.
Odds Ratio Calculator
Odds ratio with a Woolf confidence interval, chi-square and Fisher p-values, and a Haldane-Anscombe option for zero cells.
Relative Risk Calculator
Risk ratio with a Katz confidence interval, risk difference, relative risk reduction, and number needed to treat from a 2×2 table.
Sensitivity and Specificity Calculator
Sensitivity, specificity, PPV, NPV, likelihood ratios and accuracy from counts or from rates and prevalence, with confidence intervals.
Cohen's Kappa Calculator
Inter-rater agreement κ with standard error, 95% CI, weighted κ, and test of κ = 0 from an agreement table.
McNemar's Test Calculator
Test paired binary outcomes: chi-square, corrected, exact and mid-p p-values, and the odds ratio of the discordant pairs.
Mann-Whitney U Test Calculator
Compare two independent samples with the Mann-Whitney U (Wilcoxon rank-sum) test: exact or asymptotic p-value, rank table, and effect sizes.
Wilcoxon Signed-Rank Test Calculator
Paired or one-sample Wilcoxon signed-rank test with zero handling, tie correction, exact p for small n, and a signed-rank table.
Kruskal-Wallis Test Calculator
Nonparametric one-way comparison of 2–10 groups: H statistic, chi-square p-value, epsilon-squared, and Dunn post hoc with Bonferroni adjustment.
Sign Test Calculator
Paired or one-sample sign test for a median: exact binomial p-values, zero-drop count, and optional median confidence interval.
Shapiro-Wilk Test Calculator
Shapiro-Wilk normality test (Royston AS R94): W, p-value, skewness and kurtosis, plus a normal Q-Q plot with Blom positions.
Regression & Correlation
Regression and correlation tools describe how two variables move together. Correlation and covariance measure the strength and direction of a linear relationship, the regression calculator fits the least-squares line, LinRegTTest tests whether its slope differs from zero, and R-squared reports how much of the variation the model explains.
LinRegTTest Calculator
Test whether a regression slope is zero, with t, p, a, b, s, r², r, and a slope interval.
R-Squared Calculator
Get R², adjusted R², r, and the SSR/SSE/SST breakdown from X–Y data or observed vs predicted values.
Linear Regression Calculator
Fit a least-squares line and get the equation, R², coefficient tests, ANOVA table, confidence and prediction intervals, residuals and a plot.
Line of Best Fit Calculator
Find the least-squares line of best fit for X–Y data with the equation, slope, intercept, correlation, working table, residuals and a scatter plot.
Correlation Coefficient Calculator
Calculate Pearson's r with its p-value, Fisher z confidence interval, R², covariance, worked steps and a scatter plot.
Spearman Correlation Calculator
Calculate Spearman's rank correlation ρ with tie-corrected average ranks, the rank table, the t-based p-value and a scatter plot.
Quadratic Regression Calculator
Fit a least-squares parabola y = ax² + bx + c to X–Y data with R², the vertex, predictions, the normal equations, residuals and a plot.
Exponential Regression Calculator
Fit y = a·b^x to X–Y data with the growth rate, doubling time or half-life, R² on both scales, predictions, the log-linear steps and a plot.
Mean Squared Error Calculator
Score predictions against observed values: MSE, RMSE, MAE, MAPE, R² and the mean error, with the working, an observed-vs-predicted plot and every error.
Residual Calculator
Find the residuals of a least-squares line, of a line you supply or of predictions, with standardized residuals, leverage, Cook's distance and a residual plot.
Covariance Calculator
Measure how paired variables move together with sample or population covariance and Pearson r.
Cronbach's Alpha Calculator
Calculate Cronbach's alpha for a scale with a confidence interval, standardized alpha, corrected item-total correlations, alpha if item deleted and reverse scoring.
Probability & Combinatorics
These tools handle chance directly by counting outcomes and weighing how likely each one is. Combinations count selections where order does not matter and permutations count arrangements where it does: the foundation of most probability problems. Expected value turns outcomes and probabilities into a long-run average, Bayes' theorem updates a probability when new evidence arrives, the at-least-one calculator applies the complement rule to repeated tries, and the dice and coin flip calculators put all of it to work on concrete, checkable examples.
Probability Calculator
Find the probability, fraction, percentage and odds of an event, or count combinations and permutations exactly.
Expected Value Calculator
Calculate E(X), variance, and standard deviation of a discrete random variable.
Combination Calculator (nCr)
Count combinations exactly with big-integer nCr results, even for very large n.
Permutation Calculator (nPr)
Count ordered arrangements with exact nPr and n^r results, with or without repetition.
Bayes' Theorem Calculator
Update a prior probability with new evidence to get the posterior P(A|B) and total P(B).
Conditional Probability Calculator
Find P(A|B) from probabilities or a two-way table, with P(B|A), the union and an independence test.
Probability of Multiple Events Calculator
Find P(A and B) and P(A or B) for two events, or the chance that all, none or at least one of several events happen.
Dice Probability Calculator
Find exact odds of rolling a dice sum exactly, at least, or at most a target value.
Coin Flip Probability Calculator
Find the probability of any number of heads in a series of fair or biased coin flips.
Probability of At Least One Calculator
Compute the chance an event happens at least once in n tries, or the tries needed to hit a target.
Birthday Paradox Calculator
Find the chance that two people share a birthday, or how many people a target chance needs, for any number of days, exact.
Lottery Odds Calculator
Find the exact jackpot odds of any lottery with or without a bonus ball, the chance of matching some numbers, and the chance with many tickets.
Random Generators & Simulators
Generators and simulators let you see randomness instead of only calculating it. The random number generator draws integers or decimals from any range, with or without repeats, for raffles, sampling, and classroom picks. The coin flipper and dice roller run anything from a single toss to thousands of trials, then set the observed frequencies next to the exact theoretical probabilities, so you can watch the law of large numbers work on your own screen. The systematic sampling calculator picks every k-th member of a list after a random start. Every draw uses the browser's cryptographic random source rather than a predictable formula.
Random Number Generator
Generate cryptographically secure random integers or decimals in any range, with or without repeats.
Flip a Coin
Flip a fair virtual coin once or up to 10,000 times and watch the running share of heads settle toward 50%.
Dice Roller
Roll any number of d4, d6, d8, d10, d12, or d20 dice and compare the observed totals with the exact odds.
Systematic Sampling Calculator
Find the sampling interval k, draw a random start, and list every selected position or item from your list.
Reference Support
Pair calculators with concept pages and public standards so results are easier to interpret and verify.