Probability Calculator

  • Beta Distribution Calculator
    Compute the Beta distribution mean, variance, standard deviation, mode and probability density f(x) from shape parameters α and β. Free online tool.
  • Beta Distribution Calculator
    Compute the Beta distribution PDF f(x), lower cumulative probability P(x) and upper cumulative probability Q(x) for shape parameters a and b, with a table and graph.
  • Benford's Law Calculator
    Calculate the Benford's Law probability for any leading digit 1-9 using P(d)=log10(1+1/d), plus the expected count within a sample size.
  • Bayes' Theorem Calculator
    Calculate the posterior probability P(A|B) using Bayes' theorem from the prior, likelihood, and false-positive rate. Free, instant, with worked examples.
  • One-Sample Z-Test for Significance
    Test whether a sample mean differs significantly from a known population mean. Computes the z statistic, critical z, p-value, and reports significance.
  • Inverse Chi-Square Distribution Percent Point Calculator
    Find the chi-square distribution quantile (percentage point) from a lower- or upper-tail probability and degrees of freedom by inverting the CDF. Free online tool.
  • Inverse Chi-Squared Distribution Calculator
    Compute the PDF, lower and upper cumulative probability of the inverse chi-squared distribution for any point x and degrees of freedom nu.
  • Stirling Numbers of the Second Kind Table Calculator
    Compute an exact table of Stirling numbers of the second kind S(n,k) for k = 0..n, with arbitrary-precision integers and the Bell number row sum.
  • Stirling Numbers of the First Kind (Table)
    Compute the full row of signed Stirling numbers of the first kind s(n,k) for k = 0..n. Enter n and get a clean table plus signed and absolute sums.
  • Stirling Numbers of the Second Kind S(n,k) Calculator
    Compute the Stirling number of the second kind S(n,k): the number of ways to partition n labeled elements into k non-empty unlabeled subsets.
  • Stirling Number of the First Kind Calculator
    Compute the signed Stirling number of the first kind s(n,k) for non-negative integers n and k, the falling-factorial coefficients, with a worked example.
  • Subset Calculator
    Count the total number of subsets of an n-element set (2ⁿ) and the number of subsets of size k using the combination formula C(n,k).
  • Probability Someone Shares Your Birthday Calculator
    Find the chance that at least one other person in a group shares YOUR exact birthday using p = 1 - (364/365)^(n-1). The "matches mine" birthday problem.
  • IQ Percentile Calculator
    Convert any IQ score to its percentile rank using the normal distribution. Supports SD 15, 16 and 24 scales with the standard normal CDF.
  • Probability of At Least k Successes (Binomial)
    Calculate P(X ≥ k) for a binomial distribution — the probability of at least k successes in n trials with success probability p. Free, instant, exact.
  • Incomplete Beta Function & Regularized Incomplete Beta Function Table Calculator
    Build a table of the lower incomplete beta function Bx(a,b) and the regularized incomplete beta Ix(a,b) over a range of x for given shape parameters a and b.
  • Permutations with Repetition Table Calculator
    Build a table of permutations with repetition nΠr = n^r for a fixed set size n while r ranges from a start to an end value, with big-integer precision.
  • Combinations nCr Table Calculator
    Tabulate the binomial coefficients nCr for every r from 0 to n. Computes combinations with exact big-number arithmetic and the 2^n row sum, n up to 300.
  • Permutations nPr Table Calculator
    Generate a full table of permutations nPr for r = 0 to n using nPr = n!/(n-r)!. Exact big-integer results for ordered arrangements of distinct objects.
  • Combinations with Repetition Table Calculator
    Compute a table of combinations with repetition H(n, r) = C(n+r-1, r) for n distinct items, with r ranging over any integer interval. Exact big-integer results.
  • Poisson Lambda from Cumulative Probability Calculator
    Solve for the Poisson mean lambda from a known cumulative probability and percentile point x. Supports lower P(X less or equal x) and upper Q(X greater or equal x) modes.
  • Punnett Square Calculator
    Free Punnett square calculator for a monohybrid cross. Enter both parents' alleles to get offspring genotype and phenotype ratios and probabilities.
  • Rock-Paper-Scissors Decisive Round Probability Calculator
    Compute the probability a rock-paper-scissors (janken) game with n players is decided within r rounds, and rounds needed for a 99% chance of a decision.
  • Incomplete Beta Function Calculator
    Compute the lower incomplete beta function B_x(a,b) by numerically integrating t^(a-1)(1-t)^(b-1) with Gauss-Legendre quadrature. Set x=1 for the complete beta function.

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