MathCalculate Primary Directory
Statistics and Probability Calculators
Explore 66 public calculators and reference tables that fit MathCalculate's current statistics and probability scope, organized into four working areas: describing data, modeling distributions, testing hypotheses, and computing probabilities. 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.
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.
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.
Binomial Distribution Calculator
Compute exact and cumulative binomial probabilities with mean, variance, and standard deviation.
Poisson Distribution Calculator
Turn an average event rate into exact and cumulative Poisson probabilities.
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.
Hypergeometric Distribution Calculator
Compute exact probabilities for sampling without replacement from a finite population.
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 and chi-square check differences across groups and categories, p-values and effect sizes describe how convincing and how large those differences are, the pooled standard deviation combines group spreads for those procedures, and regression and correlation model relationships between variables.
Confidence Interval Calculator
Estimate confidence intervals for means and proportions with visible assumptions.
P-Value Calculator
Estimate p-values for common hypothesis-testing scenarios.
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.
ANOVA Calculator
Run one-way ANOVA calculations and inspect variance across groups.
Chi-Square Calculator
Perform chi-square goodness-of-fit and independence calculations.
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.
Regression Calculator
Run linear regression and inspect slope, intercept, and fit metrics.
Correlation Calculator
Measure the strength and direction of a relationship between variables.
Covariance Calculator
Measure how paired variables move together with sample or population covariance and Pearson r.
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
Calculate combinations, events, and basic probability outcomes.
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).
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.
Reference Support
Pair calculators with concept pages and public standards so results are easier to interpret and verify.