Probability Calculator

  • Permutation Calculator
    Calculate permutations P(n,r) = n!/(n-r)! instantly. Find the number of ordered arrangements of r items chosen from n distinct items.
  • Joint Probability Calculator
    Calculate the joint probability P(A and B) of two independent events by multiplying their individual probabilities. Free, instant, with worked examples.
  • False Positive Paradox Calculator
    Calculate the true probability of disease after a positive test using Bayes' theorem. Enter prevalence, sensitivity and specificity to see the false positive paradox.
  • Implied Probability Calculator
    Convert decimal or American (moneyline) betting odds into implied probability. Free calculator showing the percentage chance behind any odds.
  • Dice Probability Calculator
    Calculate the probability of rolling a target sum with any number of dice and sides. Get favorable outcomes, total combinations, percentage and odds.
  • Expected Value Calculator
    Compute the expected value (mean) of a discrete random variable from outcome values and their probabilities using E(X) = Σ xᵢ·pᵢ. Free and instant.
  • Coin Toss Streak Calculator
    Calculate the probability of getting a streak of k identical coin flips within n tosses, plus p^k and the expected number of runs. Works for biased coins.
  • Dice Average Calculator
    Calculate the average (expected) total when rolling any number of dice with any number of sides. Free dice average calculator with min/max totals.
  • Combination Calculator
    Calculate combinations C(n,r) = n!/(r!(n-r)!) instantly. Find how many ways to choose r items from n when order doesn't matter, plus permutations.
  • Conditional Probability Calculator
    Calculate conditional probability P(A|B) instantly. Enter P(A and B) and P(B) to find the probability of A given B, shown as a value and percentage.
  • Coin Flip Probability Calculator
    Calculate the probability of getting exactly k heads in n coin flips using the binomial formula. Supports fair and biased coins, plus cumulative odds.
  • Chebyshev's Theorem Calculator
    Use Chebyshev's Theorem to find the minimum proportion of data within k standard deviations of the mean. Works for any distribution shape.
  • Diagnostic Test Accuracy Calculator
    Compute sensitivity, specificity, false positive/negative rate, PPV, NPV and prevalence from a 2x2 diagnostic confusion matrix. Universal epidemiology tool.
  • Chi-Squared Distribution Random Number Generator
    Generate pseudo-random numbers drawn from a chi-squared distribution with any positive degrees of freedom v. Returns up to 1000 non-negative values plus theoretical mean, variance and SD.
  • Gamma Distribution Random Number Generator
    Generate pseudo-random numbers following a Gamma distribution with shape a and scale b. Uses the Marsaglia-Tsang method; reports sample mean and variance.
  • Student's t-Distribution Random Number Generator
    Generate pseudo-random numbers from a Student's t-distribution with your chosen degrees of freedom. Set the count (1-1000) and get instant t-distributed samples.
  • Log-Normal Distribution Random Number Generator
    Generate pseudo-random numbers from a log-normal distribution using the Box-Muller transform. Set mu, sigma and count; see theoretical mean, median and variance.
  • Lévy Distribution Calculator
    Compute and graph the Lévy distribution: probability density f(x), lower cumulative P(x) and upper cumulative Q(x) over a range of x values you define.
  • Levy Distribution Percentile (Quantile) Calculator
    Find the percentile (quantile) x of a Levy distribution from a lower or upper cumulative probability, with location parameter mu and scale parameter c.
  • Levy Distribution Calculator
    Compute the Levy distribution PDF f(x), lower cumulative probability P(x) and upper cumulative probability Q(x) from location mu and scale c.
  • Student's t-Distribution Graph Calculator
    Compute and plot the Student's t-distribution: probability density f, lower cumulative P and upper cumulative Q over a range of x for given degrees of freedom.
  • Generalized Pareto Distribution Percentile (Quantile) Calculator
    Compute the percentile (quantile / inverse CDF) of the Generalized Pareto Distribution from a lower or upper cumulative probability and parameters mu, sigma, xi.
  • Pareto Distribution Percentile (Quantile) Calculator
    Compute the Pareto Type I percentile (quantile) x for a lower-tail P or upper-tail Q probability given scale a and shape b by inverting the CDF.
  • Pareto Distribution Calculator
    Compute the Pareto (Type I) distribution: probability density f, cumulative probability P (CDF), and survival function Q for any x, scale xm and shape alpha.

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