Probability Calculator

  • Combination with Replacement Calculator
    Calculate combinations with replacement (multisets) using C(n+r-1, r). Enter the number of item types and items chosen to get the count instantly.
  • Mean, Median, Mode, Range Calculator
    Calculate the mean, median, mode, range, sum, min and max of any data set. Free online statistics calculator — just paste your numbers.
  • Permutation and Combination Calculator
    Free permutation and combination calculator. Compute P(n,r) ordered arrangements and C(n,r) selections from n items instantly with formulas and examples.
  • Drake Equation for Love Calculator
    Use the Drake Equation for love to estimate how many potential partners exist in your city. Enter population and percentages to find your dating odds.
  • Three-Way Playoff (Tomoe-sen) Win Probability Calculator
    Compute each contestant's chance of winning a three-way sumo playoff (tomoe-sen, Japan). Fair case gives 5/14, 5/14, 4/14; supports uneven strengths.
  • Estimate the True Value Range from Sample Mean and Standard Deviation
    Estimate the range a true value lies in from a sample mean and standard deviation using a normal distribution. Computes mean +/- z*sd for any confidence level.
  • Dice Fairness Chi-Square Calculator
    Test if a six-sided die is fair with a chi-square goodness-of-fit test. Enter the count of each face (1-6) to get the test statistic and fairness probability.
  • Permutations with Repetition Calculator (nΠr)
    Calculate permutations with repetition (nΠr = n^r): ordered selections of r items from n distinct items where each item may be reused. Exact big-integer output.
  • Combinations with Repetition Calculator
    Calculate combinations with repetition (nHr), the multiset coefficient C(n+r-1, r). Choose r items from n distinct types when repetition is allowed and order is ignored.
  • Standard Normal Distribution Calculator
    Compute the standard normal N(0,1) probability density and lower, upper, and two-sided cumulative probabilities for any z-score x. Free online tool.
  • Error Function Table Calculator
    Generate a table of the Gauss error function erf(x) and complementary error function erfc(x) over a range of x defined by start, increment and number of rows.
  • Error Function Calculator
    Compute the Gauss error function erf(x) and complementary error function erfc(x) for any real x using the Abramowitz-Stegun approximation.
  • AND Probability Calculator
    Calculate P(A and B), the probability that both events happen, for independent or dependent events. Enter P(A) and P(B) or P(B|A).
  • Birthday Paradox Probability Calculator
    Calculate the probability that at least two people in a group share a birthday. Solve the classic birthday paradox for any group size using 365 days.
  • Noncentral F-Distribution Calculator
    Compute the noncentral F-distribution density f(x), lower cumulative P(x) and upper cumulative Q(x) for given degrees of freedom and noncentrality, with a table and plot.
  • Normal Distribution Graph Calculator
    Generate a table of the normal (Gaussian) distribution: probability density f(x), lower cumulative P(x), or upper cumulative Q(x) over a range of x values.
  • Standard Normal Distribution Percentile Calculator
    Compute the standard normal percent point (inverse CDF / probit z-value) from a lower, upper, or central two-sided cumulative probability between 0 and 1.
  • Normal Distribution Calculator
    Compute the normal distribution probability density f(x), lower cumulative P(X <= x) and upper cumulative P(X > x) for any mean and standard deviation.
  • Negative Binomial Distribution Calculator
    Compute the negative binomial distribution: probability mass f, lower cumulative P, and upper survival Q for x failures before the k-th success, with a table and stats.
  • F-Distribution Graph Calculator
    Tabulate and graph the F-distribution: probability density f, lower cumulative P, or upper cumulative Q over a series of x values for degrees of freedom v1 and v2.
  • Cauchy Distribution Graph Calculator
    Compute the Cauchy (Lorentz) distribution density, lower cumulative P, or upper cumulative Q over a sequence of x values and build a plot-ready table.
  • F-Distribution Calculator
    Compute the F-distribution probability density f(x) and the lower and upper cumulative probabilities for numerator df v1 and denominator df v2.
  • F-Distribution Percent Point (Inverse F / Quantile) Calculator
    Find the F-distribution percent point (inverse F / quantile / critical value) from a lower-tail P or upper-tail Q probability and degrees of freedom d1, d2.
  • Cauchy Distribution Percentile (Quantile) Calculator
    Compute the percentile (quantile / percent point) of a Cauchy distribution from a lower or upper cumulative probability, with custom location x0 and scale gamma.

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