Statistics & Probability

189 tools · page 2 of 4

Fractional to Decimal Odds Converter Fractional odds like 11/4 restated as decimal odds (a ÷ b + 1), with the implied probability alongside.
Binomial Coefficient Calculator Computes the binomial coefficient C(n, k) = n! / (k!(n−k)!) along with the permutation count P(n, k).
Expected Pulls Calculator Estimates the average number of gacha pulls until your first success and how many are needed for a target confidence level.
Pascal's Triangle Generator Generate any number of rows of Pascal's triangle with exact integer arithmetic, where each value is the sum of the two above it.
Multinomial Distribution Calculator Computes the exact multinomial probability of observing a given set of category counts across a number of independent trials.
Z-Score to Raw Score Calculator Convert a standard score (z-score) back to a raw score using x = μ + zσ, from the mean and standard deviation of the distribution. The inverse of standardisation.
Mutually Exclusive Events Calculator For two mutually exclusive events, computes P(A or B) = P(A) + P(B) and the probability that neither occurs.
Random Walk Probability Calculator Computes the probability of a 1D random walk ending at a given position after n steps with a chosen step probability.
Relative Standard Deviation Calculator Computes the relative standard deviation (coefficient of variation) by expressing the standard deviation as a percentage of the mean.
Multinomial Probability Calculator Computes the probability of a specific combination of outcomes across independent trials using the multinomial distribution.
License Plate Combinations Calculator Calculate how many unique license plates a format can produce from the number of letter positions and digit positions: 26^letters × 10^digits. Useful for understanding plate-scheme capacity.
Least Squares Line Calculator Fits a least-squares regression line to your paired X and Y data, returning the equation, slope, intercept and correlation coefficient.
M/M/1 Queue Calculator Calculate the key metrics of an M/M/1 queue — utilization, average number in system and in queue, and average time in system and waiting — from the arrival rate λ and service rate μ. A foundation of queueing theory.
Maximin Strategy Calculator Applies the maximin decision rule to a payoff matrix, choosing the strategy whose worst-case outcome is highest.
M/G/1 Queue Calculator Uses the Pollaczek–Khinchine formula to compute utilization, average queue length, and waiting times for an M/G/1 queue from arrival rate, service rate, and service-time variability.
Linear Regression Calculator Fit a least-squares line to your X and Y data and get the slope, intercept, correlation coefficient and R² value.
Shapley-Shubik Index Calculator Computes the Shapley-Shubik power index for each voter in a weighted voting game by counting pivotal positions across all orderings.
Assignment Problem (Hungarian) Calculator Solves the 3×3 assignment problem by checking all permutations to find the minimum-cost matching of agents to tasks (Hungarian method result).
Each-Way Bet Calculator Work out the total return and profit on an each-way bet from the stake, decimal odds, place fraction, and result (won, placed, or lost).
Permutation Sign Calculator Determines the sign (parity) of a permutation of 1..n by counting inversions; even gives +1, odd gives −1.
Trimmed Mean Calculator Calculate a trimmed mean by removing a given percentage of the lowest and highest values before averaging, alongside the regular mean. A robust average that resists outliers.
Multinomial Coefficient Calculator Computes the multinomial coefficient n! / (k1! k2! ...) for a list of group sizes.
Quartile Deviation Calculator Sorts your data set and computes the first and third quartiles, the interquartile range and the quartile deviation (semi-interquartile range).
Beta-Binomial Distribution Calculator Computes the probability mass P(k), mean and variance of the beta-binomial distribution for given trials n, successes k and shape parameters α and β.
Difference of Means Confidence Interval Calculator Compute the difference between two sample means and its confidence interval from each group's mean, standard deviation and size.
Truncated Normal Distribution Calculator Compute the probability density of a normal distribution truncated to a lower and upper bound at a given point.
Wheel Probability Calculator For a wheel with equal segments, find the chance per segment, expected number of hits over many spins, and the probability of at least one hit.
Bet Expected Value Calculator Calculates the expected value of a bet from your win probability, decimal odds and stake, plus EV as a percent of stake and the implied probability.
Derangement Calculator Computes the number of derangements (!n) of n items — permutations where no element stays in its original position — and the probability of a random permutation being a derangement.
Prisoner's Dilemma Payoff Calculator Given T>R>P>S payoffs and both players' choices, reports each player's payoff and the resulting outcome.
Regression Prediction Calculator Predict the response y for a new x from a fitted linear regression line, y = a + b·x.
Zero-Sum Game Value Calculator Finds the value of a 2x2 zero-sum game: the saddle point if one exists, otherwise the mixed-strategy value of the payoff matrix.
Distribution Variance Calculator Computes the variance, expected value (mean) and standard deviation of a discrete random variable from its values and probabilities.
Poker Outs Calculator Converts your number of outs into the exact probability of hitting on the flop or turn, plus the rule-of-2-and-4 estimate.
Dice Notation Calculator Computes the average, minimum, and maximum result for dice notation NdM+K — rolling N dice with M sides plus a modifier K.
Gini Coefficient Calculator Computes the Gini coefficient of income or wealth inequality from a comma-separated list of values, along with the mean and sample size.
House Edge Calculator Work out the house edge, return to player (RTP), and your expected value from a bet's win probability and payout odds.
Restricted Partition Calculator Compute p(n,k), the number of ways to write a positive integer n as a sum of exactly k positive parts, using the classic partition recurrence.
Skellam Distribution Calculator Compute the Skellam probability P(K=k) for the difference of two independent Poisson variables with means μ1 and μ2, plus its mean and variance.
Population & Sample Variance Calculator Calculates both the population variance and the sample variance of a list of numbers, along with the mean and count.
Half-Normal Distribution Calculator Compute the probability density, cumulative probability and mean of the half-normal distribution for a value x and scale σ.
Parlay Odds Calculator Multiply decimal odds across up to three legs to find combined odds and payout for a parlay/accumulator bet.
Crit Damage Multiplier Calculator Calculate average damage and the effective damage multiplier from base damage, critical hit chance, and critical damage multiplier.
Hit Probability Calculator Computes the chance to hit a target from your accuracy and the target's evasion, clamped to a floor and cap.
Residual Calculator Computes the residual (observed − predicted) of a data point, plus its absolute value and percent residual relative to the observed value.
Deck Shuffle Combinations Calculator Calculates the number of distinct orderings (n!) of a deck of cards, shown in scientific notation. Defaults to a standard 52-card deck.
Northwest Corner Method Calculator Finds the initial basic feasible solution of a balanced 2x2 transportation problem with the northwest corner rule and its total cost.
Expected Payoff Matrix Calculator Computes the expected payoff of a 2×2 matrix from row and column probabilities, plus the best and worst pure outcomes.
Fisher Exact Test Calculator Compute the exact hypergeometric point probability of an observed 2x2 contingency table, plus the total and odds ratio.
Interquartile Range Calculator Calculate the interquartile range and outlier fences from the first and third quartiles.
Rayleigh Distribution Calculator Computes the probability density and cumulative distribution of the Rayleigh distribution at a point, plus its mean, variance, and mode.
Little's Law Calculator Applies Little's Law (L = λ·W) to find the average number of items in a system from the arrival rate and the average time each item spends in the system.
Newsvendor Optimal Order Calculator Finds the profit-maximizing order quantity for the newsvendor model using the critical ratio and the inverse normal of demand (μ, σ).
Sample Size Calculator Determine the survey sample size needed for a given confidence level, margin of error, and population.
Erlang Distribution Calculator Computes the probability density and cumulative distribution of the Erlang distribution for given shape and rate.
Chi-Square Independence Calculator Performs a Pearson chi-square test of independence on a 2×2 contingency table, returning the χ² statistic, p-value and Cramér's V effect size.
Lattice Path Counter Calculator Counts the number of monotonic lattice paths from one corner to the opposite corner of an m × n grid, moving only right and up.
Mahalanobis Distance Calculator Computes the Mahalanobis distance of a two-variable point from a distribution mean using its covariance matrix.
Repeated Measures ANOVA Calculator Computes the repeated-measures ANOVA F statistic from sums of squares and degrees of freedom: F = (SS_conditions/df_conditions) / (SS_error/df_error).
Risk Ratio (Relative Risk) Calculator Calculate the risk ratio (relative risk) between an exposed group and a control group from event counts and group totals — a key statistic in epidemiology and clinical studies.