Statistics and probability calculators
Descriptive statistics, normal and other distributions, confidence intervals, hypothesis tests, regression, correlation, combinations and probability, with p-values and charts explained.
18 calculators, 116 checked worked examples.
Find the right calculation
- Why quartile calculators give different answers
Compare R-7, R-6 and Tukey conventions on the same sample, including how the selected method changes an outlier boundary.
- Sample or population standard deviation?
Choose the divisor that matches whether you have the whole group or a sample, then inspect the worked calculation.
- Mean, median and mode for uneven data
Compare the average with the middle and most common values before using one number to describe the data.
Describing data
- Descriptive statistics calculator
Descriptive statistics calculator: mean, median, mode, standard deviation, variance, quartiles, IQR, outliers, skewness and kurtosis, with a histogram.
- Grade curve calculator
Grade curve calculator: rescale a class's scores to a target mean and standard deviation, or add flat points, with z-scores and percentile ranks.
Distributions
- Binomial & Poisson distribution calculator
Binomial distribution calculator: exact P(X = k), P(X ≤ k), tails and ranges for binomial, Poisson, geometric, negative binomial and hypergeometric.
- Normal distribution & z-score calculator
Normal distribution calculator: z-scores, the probability below, above or between values, and the value at any percentile (inverse normal).
- t, chi-square & F distribution calculator
t, chi-square and F distribution calculator: tail areas, p-values, densities and critical values, plus exponential and uniform distributions.
Inference
- Confidence interval calculator
Confidence interval calculator for a mean (t or z), a proportion (Wilson or Wald) or a difference of two means, with the margin of error and both bounds.
- Sample size and power calculator
Sample size calculator for surveys and studies: n for a margin of error on a proportion or mean, and the per-group n for a target power.
- t-test and z-test calculator
t-test calculator for one-sample, two-sample (Welch or pooled) and paired tests, plus z-tests for a mean or proportion: p-value, critical value, decision.
- Chi-square test calculator
Chi-square test calculator for goodness of fit and independence in a contingency table: χ², p-value, expected counts and Cramér's V.
- One-way ANOVA calculator
One-way ANOVA calculator: the F statistic, p-value, sums of squares, mean squares and η² for two or more groups, with the full ANOVA table.
Relationships
- Linear regression calculator (line of best fit)
Linear regression calculator: least-squares line of best fit with R², standard errors, p-values and predictions, plus polynomial and exponential fits.
- Correlation coefficient calculator (Pearson and Spearman)
Correlation coefficient calculator: Pearson's r or Spearman's rank correlation for paired data, with r², a t statistic and a two-sided p-value.
Probability
- Permutation and combination calculator (nPr, nCr)
Calculate nCr and nPr exactly: combinations and permutations with or without repetition, for poker hands, lottery odds and PIN codes.
- Probability calculator (events & Bayes' theorem)
Calculate P(A or B), P(A and B) and P(A | B) for two events, or apply Bayes' theorem to a test result, with a probability tree and Venn diagram.
- Dice, coin and card probability calculator
Exact probability of dice sums, coin-flip heads and streaks, drawing special cards from a deck and each 5-card poker hand, as a fraction and 1 in N.
- Expected value calculator
Calculate expected value E[X], variance and standard deviation for a bet, game or decision from its outcomes and their probabilities or weights.
- Odds converter (fractional, decimal, American, probability)
Convert odds between fractional, decimal and American (moneyline) formats and get the implied probability, worked in exact fractions.
- Random number generator (seeded)
Generate random numbers from a seed: integers in a range, decimals, lottery-style draws without repeats and dice rolls, repeatable with xoshiro256**.
How to choose a statistics calculator
Describe the data before testing a claim
Begin with descriptive statistics to inspect sample size, center and spread. Mean, median and mode answer different questions when data are skewed or have outliers. Choose sample or population standard deviation according to what the dataset represents. Quartile methods can give different answers for the same small sample, so keep the convention consistent when comparing software. A graph is useful for spotting patterns that one summary number misses.
Descriptive statistics guide · Normal distribution and z-scores
Match the test to the study
Paired observations require a different comparison from independent groups. Check whether the selected procedure models a mean, proportion, count or relationship, and read its assumptions before entering data. Set the confidence level or hypothesis before interpreting the output. A p-value is not the probability that a hypothesis is true, and correlation does not establish causation. Report effect size and uncertainty alongside a test result when the tool supplies them.