Probability Calculator

  • 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.
  • Birthday Paradox Probability Table Calculator
    Build a birthday paradox table: for each group size n, see the probability that at least one pair shares a birthday. Find where it crosses 50%.
  • 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.
  • 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.
  • Permutations with Repetition Calculator (nĪ r)
    Calculate permutations with repetition (nĪ r = 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.
  • 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.
  • 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.
  • Gamma Function Calculator
    Compute the Gamma function Ī“(z) for any real number using the Lanczos approximation. Handles negative non-integer values via the reflection formula.
  • 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.
  • Binomial Coefficient Calculator
    Calculate the binomial coefficient C(n,k) ā€” "n choose k" ā€” using the formula n! / (k!(nāˆ’k)!). Find combinations instantly with a worked example.
  • Gamma Distribution Graph Calculator
    Compute the Gamma distribution PDF f(x), lower cumulative P(x) and upper cumulative Q(x) over an x grid using shape a and scale b parameters.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Cauchy Distribution Calculator
    Compute the Cauchy (Lorentz) distribution probability density, lower cumulative P(X less than or equal x) and upper cumulative P(X greater than x) from x, location x0 and scale gamma.

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