Statistics Calculators

Summaries, distributions, sample-size planning, probability, combinations, and z-scores with stated conventions.

Describe data and reason about chance: averages, standard deviation, normal and uniform distributions, z-scores, confidence intervals, proportion sample-size planning, correlation, regression, binomial, Poisson, hypergeometric, and exponential probability, plus combinations and permutations with and without repetition.

214 free tools · each with formula, worked example & methodology notes

Category context

How statistical calculations should be interpreted

Statistics tools describe data or evaluate a stated probability model. They do not turn an observed summary into causation, certainty, or a forecast without additional evidence.

Method and background

Data analysis developed from summaries of observations into probability, estimation, and decision measures. The essential habit remains the same: define the population, sample, variable, and convention before calculating.

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Calculator directory

Choose the tool that matches your question

214 tools arranged by purpose, so you can scan the right group before opening a calculator.

60 tools

Descriptive statistics

Means, medians, spread, weighted summaries, and ways to describe a dataset.

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Cohen's d Effect Size Calculator

Calculate the standardized mean difference between two independent groups using pooled sample standard deviation.

You enter: Group 1 mean · Group 1 sample SD · Group 1 sample size · Group 2 mean · Group 2 sample SD · Group 2 sample size

Example: Pooled SD ≈ 9.142; Cohen's d ≈ 0.547.

Open Cohen's d Effect Size Calculator →

One-Way ANOVA F Statistic Calculator

Calculate between-group and within-group mean squares and the one-way ANOVA F statistic from summary sums of squares and degrees of freedom.

You enter: Between-group sum of squares · Within-group sum of squares · Between-group degrees of freedom · Within-group degrees of freedom

Example: MS between=40; MS within=8.333; F=4.8.

Open One-Way ANOVA F Statistic Calculator →

Pooled Variance Calculator

Calculate pooled variance and pooled standard deviation for two independent groups.

You enter: Group 1 standard deviation · Group 1 sample size · Group 2 standard deviation · Group 2 sample size

Example: Pooled variance ≈121.214; pooled SD ≈11.010.

Open Pooled Variance Calculator →

Sum of Squares Calculator

Calculate the squared-deviation total, mean squared deviation, and root-mean-square distance from a reference value.

You enter: Values · Reference value

Example: Sum of squares = 30; mean squared distance = 7.5; RMS distance ≈ 2.739.

Open Sum of Squares Calculator →

Third Quartile Calculator

Sort a raw dataset and calculate its third quartile, median, first quartile, and interquartile range using a stated median-of-halves convention.

You enter: Data values

Example: Ordered values are 4, 7, 10, 12, 15, 19, 21; Q3 is 19, Q1 is 7, and IQR is 12.

Open Third Quartile Calculator →

Geometric Mean

Calculate the geometric mean of a list of positive values using logarithmic accumulation for stability.

You enter: Positive values

Example: Geometric mean 4.

Open Geometric Mean →

Exponential Distribution

Evaluate the density, cumulative probability, survival probability, mean, and variance of an exponential waiting-time model.

You enter: Rate (lambda) · Value (x)

Example: f(2) = 0.183940; F(2) = 0.632121; survival = 0.367879; mean = 2; variance = 4.

Open Exponential Distribution →

68 tools

Probability and distributions

Discrete and continuous probability models, quantiles, and distribution calculations.

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Binomial Probability

Exact and cumulative probabilities for a fixed number of independent trials.

You enter: Trials (n) · Successes (k) · Success probability per trial

Example: P(X = 5) = 0.2461; P(X <= 5) = 0.6230.

Open Binomial Probability →

One-Sample Normal Power Calculator

Estimate one-sided or two-sided normal-test power from an effect, standard deviation, significance level, and sample size.

You enter: Significance level · Expected mean difference · Population standard deviation · Sample size · Alternative

Example: Noncentral shift = 2.5; approximate two-sided power ≈ 70.542%.

Open One-Sample Normal Power Calculator →

OR Probability Calculator

Calculate the probability of at least one of two events, exactly one event, and neither event from an overlap.

You enter: Probability of A · Probability of B · Probability of A and B

Example: P(A or B) = 0.70; exactly one = 0.50; neither = 0.30.

Open OR Probability Calculator →

Two-Envelope Scenario Calculator

Evaluate a transparent two-envelope switching scenario under explicit up/down ratios and a stated probability.

You enter: Amount in held envelope · Larger-envelope ratio · Smaller-envelope ratio · Probability of the larger case

Example: Expected switch value = 125; expected change = 25; break-even larger-case probability ≈ 33.33%.

Open Two-Envelope Scenario Calculator →

Wilcoxon Rank-Sum Statistic

Rank two independent samples, calculate the Wilcoxon rank-sum and U statistics, and show a large-sample normal approximation.

You enter: Sample A values · Sample B values · Normal approximation correction

Example: The pooled ranks give Rₐ = 16, Uₐ = 6, expected U = 8, and z ≈ −0.577.

Open Wilcoxon Rank-Sum Statistic →

Lottery Match Probability Calculator

Calculate the chance of meeting a chosen lottery match threshold from a pool, ticket size, draw size, and number of tickets without assuming a particular country's game rules.

You enter: Numbers in the pool · Numbers selected per ticket · Numbers drawn · Minimum matches of interest · Tickets in the scenario

Example: There are 13,983,816 possible six-number draws; one fixed ticket has a jackpot chance of about 0.00000715%, or about 1 in 13,983,816.

Open Lottery Match Probability Calculator →

Geometric Distribution

Calculate the probability that the first success occurs on a selected trial and the cumulative probability by that trial.

You enter: Success probability p · Trial of first success k

Example: P(X=3)=0.128; P(X<=3)=0.488.

Open Geometric Distribution →

Hypergeometric Distribution

Calculate an exact and cumulative probability for successes drawn without replacement from a finite population.

You enter: Population size (N) · Successes in population (K) · Sample size (n) · Observed successes (x)

Example: P(X = 2) = 0.476190; P(X <= 2) = 0.738095.

Open Hypergeometric Distribution →

23 tools

Inference and confidence

Confidence intervals, tests, corrections, sample sizes, and uncertainty.

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Sample Size for a Proportion

Estimate how many observations a survey needs for a target proportion margin of error and confidence level.

You enter: Planning proportion · Margin of error · Confidence level · Population size (optional)

Example: 1,068 observations needed before any nonresponse adjustment.

Open Sample Size for a Proportion →

Fisher's Exact Test Calculator

Calculate an exact two-sided Fisher probability for a 2×2 contingency table with fixed margins.

You enter: Row 1, column 1 · Row 1, column 2 · Row 2, column 1 · Row 2, column 2

Example: Observed table probability ≈ 0.2652; lower-tail p-value ≈ 0.3106; two-sided exact p-value ≈ 0.5581.

Open Fisher's Exact Test Calculator →

Post-Test Probability Calculator

Use prevalence, sensitivity, and specificity to estimate positive and negative post-test probabilities with Bayes' theorem.

You enter: Pre-test prevalence · Sensitivity · Specificity

Example: Positive post-test probability is about 33.1034%; negative post-test probability of no condition is about 99.3531%.

Open Post-Test Probability Calculator →

One-Sample z Hypothesis Test Calculator

Calculate a one-sample z statistic and tail-specific p-value when the population standard deviation is supplied.

You enter: Null-hypothesis mean μ₀ · Observed sample mean · Known population standard deviation σ · Sample size n · Significance level α · Alternative hypothesis

Example: z ≈ 11.1803, the right-tail p-value is effectively 0%, and the null is rejected at 5% in this model.

Open One-Sample z Hypothesis Test Calculator →

Bonferroni Correction

Calculate a Bonferroni-adjusted significance threshold and adjusted p-value for multiple comparisons.

You enter: Unadjusted alpha · Number of comparisons · Observed p-value

Example: Adjusted alpha 0.01; adjusted p-value 0.05.

Open Bonferroni Correction →

15 tools

Correlation and regression

Association, covariance, correlation, regression, and model-fit summaries.

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9 tools

Quality and classification

Confusion-matrix measures, reliability, process capability, and quality rates.

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Sensitivity Calculator

Calculate sensitivity, miss rate, and the number of actual positive cases from true positives and false negatives.

You enter: True positives · False negatives

Example: Sensitivity: 90%; miss rate: 10%; actual positives: 100.

Open Sensitivity Calculator →

Specificity Calculator

Calculate specificity, false-positive rate, and the number of actual negative cases from true negatives and false positives.

You enter: True negatives · False positives

Example: Specificity: 90%; false-positive rate: 10%; actual negatives: 200.

Open Specificity Calculator →

39 tools

More Statistics Calculators tools

Additional tools in this category that do not yet need a narrower navigation label.

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Password Combination Calculator

Count the exact number of passwords possible from an alphabet size and length, with or without character reuse.

You enter: Available characters · Password length · May a character repeat?

Example: 62¹² = 3,226,266,762,397,899,821,056 possible strings, an approximately 71.45-bit search space.

Open Password Combination Calculator →

Exponential Growth and Decay Calculator

Project a positive starting value under discrete compounding or continuous exponential growth and display the change and doubling time.

You enter: Initial value · Rate per time unit · Elapsed time · Growth model · Compounding periods per time unit

Example: The final value is about 1,628.895, a growth factor of 1.628895, after ten annual periods.

Open Exponential Growth and Decay Calculator →

Gender Pay Gap Percentage Calculator

Calculate an unadjusted pay gap, comparison-group pay share, and absolute difference from two user-entered earnings figures without bundling stale country data.

You enter: Reference-group earnings · Comparison-group earnings

Example: The unadjusted gap is 10%; the comparison group earns 90% of the reference-group amount, a difference of 500 pay units.

Open Gender Pay Gap Percentage Calculator →

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Most-used Statistics Calculators tools

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How to use these tools

Each calculator shows its formula, assumptions, and a worked example. Enter your values, choose Calculate, and copy results for reports or planning. Financial and health tools are planning estimates with stated limits, not professional advice.

Frequently asked questions

Should I use population or sample standard deviation?

Use population when your list is the entire group. Use sample when estimating population variability from a sample of at least two values.

What does independence mean for probability?

One event does not change the probability of the other. The joint probability is then the product; mutually exclusive events are a different concept.