Statistics

Calculate when to stop exploring and start committing with the 37% optimal stopping rule.

Calculate the posterior probability P(A|B) with Bayes' theorem from a prior P(A) and the two likelihoods P(B|A) and P(B|¬A).

Calculate the binomial probability P(X = k) = C(n, k) · pᵏ · (1 − p)^(n − k) — the chance of exactly k successes in n independent trials each with success probability p.

Calculate the coefficient of variation from a mean and a standard deviation — CV% = (σ ÷ μ) × 100.

Calculate the number of combinations C(n, r) — how many ways to choose r items from n when order does not matter, using C(n, r) = n! ÷ (r! × (n − r)!).

Calculate the number of combinations with repetition C(n + r − 1, r) — how many ways to choose r items from n distinct types when repeats are allowed and order does not matter.

Calculate the conditional probability P(A|B) = P(A∩B) ÷ P(B) — the probability of event A given that event B has occurred.

Calculate the margin of error and the confidence interval for a mean from the sample mean, standard deviation, sample size, and z critical value.

Calculate the geometric distribution probability that the first success occurs on trial k — P(X = k) = (1 − p)^(k − 1) × p.

Calculate the margin of error for a proportion from the sample proportion p, the sample size n, and a z-score — MoE = z × √(p(1 − p) ÷ n) × 100.

Calculate the odds ratio (OR) from a 2×2 contingency table — OR = (a × d) ÷ (b × c) — to compare the odds of an outcome between two groups.

Convert odds such as 1 to 4 into a probability instantly. This odds to probability calculator returns both a percentage and a decimal probability value.

Convert a z, t, chi-square, or F test statistic into its exact p-value and check significance at your alpha level.

Calculate the number of permutations P(n, r) — how many ways to arrange r items chosen from n when order matters, using P(n, r) = n! ÷ (n − r)!.

Calculate the number of ordered selections n^r — how many arrangements of r positions you can make from n distinct items when items may repeat.

Calculate the Poisson probability P(k; λ) = (λ^k × e^(−λ)) / k! of exactly k events in a fixed interval from the average rate λ.

Calculate the probability of the union of two events with the addition rule, P(A∪B) = P(A) + P(B) − P(A∩B).

Calculate LIX, Flesch Reading Ease, and WSTF scores to evaluate text readability.

Calculate the sample size needed for a survey or poll from your confidence level (z-score), expected proportion, and margin of error: n = (z²·p·(1−p))/E².

Calculate the standard error of the mean from standard deviation and sample size. Supports bidirectional solving.

Convert a raw score or a z-score into a T-score on the 50 ± 10 metric and see the matching percentile.

Calculate the one-sample t-statistic, t = (x̄ − μ) / (s / √n), from a sample mean, hypothesized population mean, sample standard deviation, and sample size.

Calculate a z-score from a raw value, the mean, and the standard deviation — z = (x − μ) ÷ σ.