Statistics Calculators

What is the probability?

Probability

Single event, two-event, conditional (Bayes), and repeated trial probabilities.

How do I calculate probability of 3 events?

Probability of 3 Events

P(A∩B∩C), P(A∪B∪C), inclusion-exclusion for three events.

What is the probability?

Conditional Probability

P(A|B) from direct input, contingency tables, or probability values.

How do I calculate bayes' theorem?

Bayes' Theorem

Update beliefs with prior, likelihood, and evidence. Step-by-step Bayesian reasoning.

How do I calculate expected value?

Expected Value

Compute E(X) = Σ x·P(x) for any discrete random variable with custom outcomes.

What is the probability?

Joint Probability

P(A∩B) for independent and dependent events with joint probability tables.

How do I calculate venn diagram?

Venn Diagram

Set operations with interactive Venn diagrams. 2 and 3 set unions, intersections, complements.

How do I calculate odds?

Odds

Convert between probability, decimal odds, fractional odds, and American odds.

What is the probability?

Implied Probability

Extract true probability from betting odds. Remove vig/overround.

How do I calculate risk?

Risk

Cumulative risk over time, Poisson event probabilities, and risk comparison.

How do I calculate relative risk?

Relative Risk

Risk ratio, ARR, NNT, and confidence intervals from 2×2 tables.

How do I calculate roulette payout?

Roulette Payout

Probabilities, payouts, expected value, and house edge for all roulette bets.

How do I calculate lottery?

Lottery

Calculate lottery odds for any pick-k-from-n format with powerball bonus.

What is the probability?

Coin Flip Probability

Exact P(k heads in n flips) with PMF/CDF charts for fair or biased coins.

How do I calculate coin toss streak?

Coin Toss Streak

Probability of consecutive heads/tails streaks within n flips.

What is the probability?

Dice Probability

Exact sum probabilities for any combination of dice (d4–d20).

How do I calculate dice average?

Dice Average

Expected value, variance, and distribution for dice rolls. D&D damage calculator.

How do I calculate password combination?

Password Combination

Total password combinations and brute-force time for any character set.

How do I calculate random number generator?

Random Number Generator

Generate random numbers from uniform, normal, exponential, and Poisson distributions.

How do I calculate monty hall problem?

Monty Hall Problem

Should you switch doors? Interactive simulation proves switching wins 2/3 of the time.

How do I calculate birthday paradox?

Birthday Paradox

Why 23 people gives >50% chance of a shared birthday. Interactive probability curve.

How do I calculate bertrand's box paradox?

Bertrand's Box Paradox

Three boxes, gold/silver coins — why P(other gold) = 2/3, not 1/2.

How do I calculate bertrand's paradox?

Bertrand's Paradox

Random chord in a circle: three methods give 1/3, 1/2, or 1/4.

How do I calculate boy or girl paradox?

Boy or Girl Paradox

Two-child problem: how asking differently changes P(both boys) from 1/2 to 1/3.

How do I calculate false positive paradox?

False Positive Paradox

Why a 99% accurate test gives mostly false positives for rare conditions.

How do I calculate parrondo's paradox?

Parrondo's Paradox

Two losing games combine to make a winning strategy. Simulation and proof.

How do I calculate two envelopes paradox?

Two Envelopes Paradox

Why the naive switching argument fails. Bayesian resolution and simulation.

How do I calculate sensitivity and specificity?

Sensitivity and Specificity

TPR, TNR, PPV, NPV, LR+, LR−, Youden Index from confusion matrix.

What is the probability?

Post-Test Probability

Fagan nomogram — post-test probability from pre-test probability and likelihood ratios.

How do I calculate false positive paradox?

False Positive Paradox

Why a positive test for a rare condition is usually wrong. Base rate analysis.

How do I calculate accuracy?

Accuracy

Confusion matrix metrics: Accuracy, Precision, Recall, F1, MCC.

How do I calculate relative risk?

Relative Risk

Risk ratio, absolute risk reduction, NNT from 2×2 epidemiological tables.

How do I calculate normal distribution?

Normal Distribution

Bell curve probabilities, percentiles, z-scores with interactive shaded chart.

How do I calculate inverse normal distribution?

Inverse Normal Distribution

Find the x-value (quantile) given a probability. Probit function.

How do I calculate binomial distribution?

Binomial Distribution

P(X=k), P(X≤k), P(X≥k) with PMF/CDF charts and probability tables.

How do I calculate poisson distribution?

Poisson Distribution

P(X=k) for count data. Model events per interval with PMF/CDF charts.

How do I calculate exponential distribution?

Exponential Distribution

PDF, CDF, mean, memoryless property for time-between-events.

How do I calculate geometric distribution?

Geometric Distribution

Trials until first success. PMF, CDF, mean 1/p, memoryless property.

How do I calculate negative binomial distribution?

Negative Binomial Distribution

Trials until rth success. Generalizes geometric distribution.

How do I calculate hypergeometric distribution?

Hypergeometric Distribution

Sampling without replacement. Drawing k successes from N with K total.

How do I calculate beta distribution?

Beta Distribution

PDF, CDF, mean, mode for Beta(α,β). Bayesian priors and A/B testing.

How do I calculate lognormal distribution?

Lognormal Distribution

PDF, CDF for lognormal. Models income, stock prices, particle sizes.

How do I calculate uniform distribution?

Uniform Distribution

Continuous and discrete uniform: PDF, CDF, mean, variance.

How do I calculate weibull distribution?

Weibull Distribution

Reliability engineering: PDF, CDF, hazard rate, MTTF, B-life.

How do I calculate rayleigh distribution?

Rayleigh Distribution

Magnitude of 2D Gaussian vectors. Wind speed, wave height modeling.

How do I calculate central limit theorem?

Central Limit Theorem

Interactive CLT demo — see sampling means converge to normal.

How do I calculate chebyshev's theorem?

Chebyshev's Theorem

Minimum % within k standard deviations for ANY distribution shape.

How do I calculate empirical rule?

Empirical Rule

68-95-99.7 rule for normal distributions with bell curve visualization.

How do I calculate continuity correction?

Continuity Correction

Normal approximation with ±0.5 correction for binomial and Poisson.

How do I calculate benford's law?

Benford's Law

Test data against first-digit law. Chi-square and fraud detection.

How do I calculate exponential growth prediction?

Exponential Growth Prediction

Model growth/decay, doubling time, half-life. Fit from data.

How do I calculate normal probability for sampling distributions?

Normal Probability for Sampling Distributions

P(X̄ ≤ x), standard error, CLT-based sampling distribution of means.

How do I calculate sampling distribution of sample proportion?

Sampling Distribution of Sample Proportion

Distribution of p̂, standard error, normality conditions, probabilities.

How do I calculate sum distribution?

Sum Distribution

ΣX distribution: mean nμ, SD σ√n, probabilities for sums.

How do I calculate p-hat?

P-Hat

Sample proportion, margin of error, confidence interval for surveys.

How do I calculate standard error?

Standard Error

SE of mean, proportion, diff of means, diff of proportions, correlation, regression.

What is the average?

SD of Sample Mean

σ_x̄ = σ/√n with FPC, sample size planning, CLT visualization.

How do I calculate relative standard error?

Relative Standard Error

RSE = (SE/estimate)×100%. Survey reliability metric with design effect.

How do I calculate sampling error?

Sampling Error

Expected sampling error for means/proportions. SE vs n curve, MOE, FPC.

How do I calculate margin of error?

Margin of Error

MOE for surveys/polls. Required sample size. Finite population correction.

How do I calculate sample size?

Sample Size

Required n for surveys, mean estimation, t-tests, proportion tests. FPC, dropout.

How do I calculate descriptive statistics?

Descriptive Statistics

All-in-one: mean, median, mode, SD, skewness, kurtosis, quartiles, and more.

What is the standard deviation?

Standard Deviation

Mean, variance, SD, median, quartiles, IQR with histogram and box plot.

What is the variance?

Variance

Sample and population variance with 5 input modes. Step-by-step computation.

What is the variance?

Population Variance

Population σ² vs sample s². Bessel's correction explained step by step.

What is the mode?

Mean Median Mode

All central tendency measures: arithmetic, geometric, harmonic, trimmed, weighted.

What is the median?

Median

Median with step-by-step sorting, weighted median, and running median.

What is the mode?

Mode

Unimodal, bimodal, multimodal detection. Raw and grouped data.

How do I calculate five number summary?

Five Number Summary

Min, Q1, Median, Q3, Max with IQR, fences, and box plot.

How do I calculate quartile?

Quartile

Q1, Q2, Q3 with 4 methods. IQR, midhinge, Bowley skewness.

How do I calculate iqr?

IQR

Interquartile range, fences, mild/extreme outlier detection.

How do I calculate percentile?

Percentile

Find percentile rank of a value or value at a percentile. Multiple methods.

How do I calculate percentile rank?

Percentile Rank

What percent of values fall below a score? Standard, inclusive, exclusive methods.

How do I calculate decile?

Decile

All 9 deciles (D1-D9), interdecile range, and decile ratios.

How do I calculate range?

Range

Range, IQR, interdecile range, relative range, coefficient of range.

How do I calculate dispersion?

Dispersion

Range, IQR, variance, SD, MAD, CV — all measures of spread compared.

How do I calculate coefficient of variation?

Coefficient of Variation

CV = SD/mean × 100%. Compare variability across different scales.

What is the standard deviation?

Relative Standard Deviation

RSD% = (SD/mean)×100%. Precision metric for analytical chemistry and QC.

How do I calculate mean absolute deviation?

Mean Absolute Deviation

MAD about mean or median. Robust alternative to standard deviation.

How do I calculate median absolute deviation?

Median Absolute Deviation

MAD(median) — robust spread measure. Modified Z-scores for outliers.

How do I calculate skewness?

Skewness

Fisher-Pearson, Pearson's 1st/2nd, Bowley skewness. Symmetry analysis.

How do I calculate midrange?

Midrange

Midrange = (min+max)/2. Simple central tendency with outlier sensitivity.

How do I calculate minimum and maximum?

Minimum and Maximum

Min, max, range, k-th smallest/largest, running min/max.

How do I calculate outlier?

Outlier

Detect outliers: IQR, Z-score, Modified Z, Grubbs', Dixon's Q test.

How do I calculate upper and lower fence?

Upper and Lower Fence

Inner/outer fences for outlier boundaries. Custom IQR multiplier.

How do I calculate least to greatest?

Least to Greatest

Sort, rank, percentile rank, and z-score for each value.

How do I calculate sum of squares?

Sum of Squares

SS total, between, within for ANOVA. Step-by-step deviation table.

What is the standard deviation?

Pooled Standard Deviation

Pooled SD from multiple groups. Used in t-tests, ANOVA, meta-analysis.

How do I calculate grouped data sd?

Grouped Data SD

Mean, variance, SD from frequency distribution tables.

How do I calculate average rating?

Average Rating

Weighted average, Bayesian average, Wilson score for star ratings.

How do I calculate mse?

MSE

MSE, RMSE, MAE, MAPE, R² for regression and forecast errors.

How do I calculate error propagation?

Error Propagation

Propagate uncertainties through math operations. Monte Carlo option.

How do I calculate simpson's diversity index?

Simpson's Diversity Index

Simpson's D, Shannon-Wiener H', species richness for biodiversity analysis.

How do I calculate index of qualitative variation?

Index of Qualitative Variation

IQV, Simpson's D, Shannon entropy for categorical data variation.

How do I calculate constant of proportionality?

Constant of Proportionality

Find k in y=kx or y=k/x. Test proportional relationships.

How do I calculate raw score?

Raw Score

Convert between raw scores, z-scores, percentiles, T-scores, IQ, SAT.

How do I calculate relative error?

Relative Error

Absolute, relative, and percentage error. Single or multiple measurements.

How do I calculate shannon entropy?

Shannon Entropy

Shannon H, joint/conditional entropy, mutual information, perplexity.

How do I calculate box plot?

Box Plot

Box-and-whisker plots with quartiles, IQR, fences, and outlier detection.

How do I calculate histogram?

Histogram

Customizable histograms with multiple binning methods and normal overlay.

How do I calculate dot plot?

Dot Plot

Cleveland dot plots from raw data with frequency analysis.

How do I calculate stem and leaf plot?

Stem and Leaf Plot

Stem-and-leaf displays with back-to-back comparison support.

How do I calculate pie chart?

Pie Chart

Interactive pie/doughnut charts from categorical data with percentages.

How do I calculate frequency distribution?

Frequency Distribution

Build frequency tables: absolute, relative, cumulative frequencies.

How do I calculate frequency polygon?

Frequency Polygon

Line plots through midpoints. Multi-dataset comparison.

What is the frequency?

Relative Frequency

Relative and cumulative relative frequencies from data or tables.

How do I calculate class width?

Class Width

Optimal bin width using Sturges, Scott, Freedman-Diaconis, Rice, √n.

How do I calculate correlation coefficient?

Correlation Coefficient

Pearson r, Spearman ρ, Kendall τ with scatter plot and CI.

How correlated are these variables?

Pearson Correlation

Dedicated Pearson r with step-by-step computation and t-test.

How correlated are these variables?

Spearman's Correlation

Non-parametric rank correlation ρ. Step-by-step ranks and d² table.

What is the variance?

Covariance

Sample and population covariance. Covariance matrix for multiple variables.

How correlated are these variables?

Matthews Correlation

MCC for binary classification. Better than accuracy for imbalanced data.

How do I calculate cohen's d?

Cohen's D

Effect size: Cohen's d, Hedges' g, Glass's Δ with overlap visualization.

How do I calculate hypothesis testing?

Hypothesis Testing

Z-test, t-test, paired t, proportion tests. Test stat, p-value, decision.

How do I calculate t-test?

t-test

Full t-test: raw or summary data, assumptions check, CI, effect size, power.

How do I calculate t-statistic?

t-statistic

Compute t-stat for one-sample, two-sample, Welch, paired designs.

How do I calculate z-test?

Z-test

One/two-sample z-test, proportion z-test. CI, effect size, power.

How do I calculate p-value?

p-value

P-values from z, t, chi-square, F statistics. Distribution curve with shaded area.

How do I calculate power analysis?

Power Analysis

Sample size, power, or effect size for t-tests, proportions, ANOVA, correlation.

How do I calculate ab test?

AB Test

A/B test significance, sample size, power, Bayesian P(B beats A).

How do I calculate mcnemar's test?

McNemar's Test

Paired nominal data test (before/after). Exact binomial and chi-square.

How do I calculate mann-whitney u test?

Mann-Whitney U Test

Non-parametric test for two independent groups. Rank-based alternative to t-test.

How do I calculate wilcoxon signed-rank test?

Wilcoxon Signed-Rank Test

Non-parametric paired test. Signed ranks, W+/W-, normal approximation.

How do I calculate youden index?

Youden Index

J = Sensitivity + Specificity - 1. Optimal ROC cutoff, diagnostic metrics.

How do I calculate anova?

ANOVA

One-way ANOVA: F-statistic, p-value, eta squared, and full ANOVA table.

How do I calculate f-statistic?

F-statistic

F-stat and p-value for ANOVA, regression, and variance ratio tests.

How do I calculate fisher's exact test?

Fisher's Exact Test

Exact p-value for 2×2 tables. Preferred for small samples over chi-square.

How do I calculate critical value?

Critical Value

Z, t, chi-square, and F critical values for any α and df.

How do I calculate degrees of freedom?

Degrees of Freedom

df for t-test, chi-square, ANOVA, Welch's, regression. Conceptual guide.

How do I calculate bonferroni correction?

Bonferroni Correction

Adjust α for multiple comparisons: Bonferroni, Šidák, Holm, BH (FDR).

How do I calculate normal approximation?

Normal Approximation

Approximate binomial, Poisson, hypergeometric with normal. Continuity correction.

How do I calculate point estimate?

Point Estimate

Sample mean, proportion (Wilson, Agresti-Coull, Jeffreys), MLE estimators.

What is the z-score?

Z-Score

Z-scores, percentiles, and probabilities with interactive normal curve.

How do I calculate chi-square?

Chi-Square

Goodness-of-fit and independence tests. χ², p-value, Cramér's V.

How do I calculate confidence interval?

Confidence Interval

CI for means (z/t), proportions, differences. Sample size planning.

How do I calculate absolute uncertainty?

Absolute Uncertainty

Absolute and relative uncertainty from measurements. GUM-compliant propagation.

How do I calculate linear regression?

Linear Regression

y = a + bx: slope, intercept, R², ANOVA table, CI/PI bands.

How do I calculate quadratic regression?

Quadratic Regression

Fit y = ax² + bx + c. Vertex, axis of symmetry, F-test vs linear.

How do I calculate cubic regression?

Cubic Regression

Fit y = ax³ + bx² + cx + d. Compare linear/quadratic/cubic fits.

How do I calculate polynomial regression?

Polynomial Regression

Fit degree 1-6 polynomials. R², AIC, BIC model selection comparison.

How do I calculate exponential regression?

Exponential Regression

Fit y = ae^(bx). Doubling time, half-life, R², growth rate.

How do I calculate residual?

Residual

Residual diagnostics: standardized, studentized, Cook's D, leverage, DW.

How do I calculate coefficient of determination (r²)?

Coefficient of Determination (R²)

R², adjusted R² from data, correlation, or SS values. Model fit assessment.

How do I calculate process capability index?

Process Capability Index

Cp, Cpk, Pp, Ppk, Cpm for manufacturing. Six Sigma metrics and DPMO.

How do I calculate standard deviation index?

Standard Deviation Index

SDI for lab proficiency testing. CLIA/CAP quality assessment metrics.

How do I calculate upper control limit?

Upper Control Limit

UCL, LCL, CL for X̄, R, S, p, np, c, u control charts (SPC).