Statistics & Probability

Statistics and probability tools: averages and spread, confidence intervals, sample sizes, hypothesis tests, distributions and odds. Enter your data or summary figures and each tool explains which formula it applies.

189 tools · page 1 of 4

Z-Score Calculator Calculate the z-score (standard score) of a value.
Combinations & Permutations (nCr, nPr) Calculate combinations (nCr), permutations (nPr) and the factorial n! from n and r.
Binomial Probability Calculator Calculate the binomial probability P(X=k) for n trials.
Kelly Criterion Calculator Use the Kelly criterion to find the fraction of your bankroll to wager given decimal odds and your win probability.
Percentile from Z-Score Calculator Converts a z-score into a percentile using the standard normal cumulative distribution function.
Bell Number Calculator Computes the Bell number Bn, the number of ways to partition a set of n elements, using the Bell triangle.
Binomial Distribution Calculator Calculate binomial probabilities — exact, cumulative ≤k and ≥k — for n trials with success probability p.
D&D Roll Odds Calculator Calculate the chance to meet a DC on a d20 with normal, advantage and disadvantage rolls.
Lottery Odds Calculator Calculate the number of combinations and your odds of winning a lottery.
Betting Odds Converter Enter decimal odds and instantly convert them to implied probability percentage, fractional odds, and American (moneyline) odds. A quick reference for comparing odds formats across sportsbooks.
Probability Calculator Calculate the probability of an event from favorable and total outcomes.
Mean, Median, Mode Calculator Calculate the mean, median and mode of a list of numbers.
Percentile Calculator Calculate the kth percentile of a dataset.
Mean Absolute Deviation Calculator Calculate the mean absolute deviation of a dataset.
Midrange Calculator Calculate the midrange and range of a data set from its maximum and minimum values.
Correlation Coefficient Calculator Calculate the Pearson correlation of paired data.
Combinations with Repetition Calculator Calculate the number of multiset combinations — choosing r items from n types with repetition allowed.
Standard Deviation Calculator Calculate the sample and population standard deviation, variance, and mean of a data set.
Statistics Calculator (Mean, Median…) Calculate the mean, median, mode, min/max, range and standard deviation of a list of numbers.
Poisson Probability Calculator Calculate Poisson probabilities — exact, cumulative ≤k and ≥k — for an average rate λ.
Subfactorial Calculator Calculate the subfactorial !n — the number of derangements (permutations with no element in its place).
Variance Calculator Calculate the population and sample variance and standard deviation of a list of numbers.
Cohen's d Calculator Calculate Cohen's d effect size from two means and the pooled standard deviation.
Odds Ratio Calculator Calculate the odds ratio from a 2×2 contingency table.
Margin of Error Calculator Calculate the margin of error of a survey from the sample proportion, size and confidence level.
Percentile Rank Calculator Calculate the percentile rank of a score from how many values fall below it.
Bayes' Theorem Calculator Calculate the posterior probability with Bayes' theorem from a prior, sensitivity and false-positive rate.
Coefficient of Variation Calculator Calculate the coefficient of variation (CV) as the ratio of standard deviation to the mean, in percent.
R-Squared Calculator Calculate the coefficient of determination (R²) from a correlation coefficient.
Geometric Distribution Calculator Calculate geometric distribution probabilities — exact, cumulative ≤k and ≥k — for the trial of the first success.
Standard Error Calculator Calculate the standard error of the mean from the standard deviation and sample size.
A/B Test Significance Calculator Test whether the difference between two conversion rates is statistically significant.
Five Number Summary Calculator Compute the five-number summary — minimum, first quartile (Q1), median, third quartile (Q3) and maximum — from a list of numbers, using the exclusive (Tukey) quartile method.
Expected Damage Roll Calculator Compute the average, minimum and maximum damage for dice notation of the form NdS+M (N dice with S sides plus a modifier).
Normal Distribution Calculator Find the z-score and cumulative probability (percentile) of a value in a normal distribution.
Z-Score from Percentile Calculator Finds the standard-normal z-score corresponding to a given percentile using the inverse normal distribution.
Gacha Pity Calculator Calculate the probability of getting at least one drop over a number of attempts at a given drop rate.
Random Number Generator Generate any number of random integers between a minimum and maximum value.
Confidence Interval Calculator Calculate the confidence interval and margin of error for a sample mean using its standard deviation and size.
Permutations with Repetition Calculator Count the number of ordered arrangements of length r drawn from n items when repetition is allowed (n to the power r). Useful for passwords, PINs and lock combinations.
Expected Value Calculator Compute the expected value of a wager from win probability, amount won and amount lost.
Coin Flip Probability Calculator For a fair coin, find the probability of getting exactly k heads and at least k heads in n flips, plus the expected number of heads.
Combinatorial Probability Calculator Compute a simple probability as the ratio of favorable outcomes to total equally-likely outcomes, with odds.
Gacha Pull Probability Calculator Find the probability of getting at least one of a rated item across a number of independent gacha pulls.
Normal Distribution Probability Calculator Find the probability that a normally distributed variable falls between two values, P(a < X < b), from its mean and standard deviation using the normal CDF.
Conditional Probability Calculator Compute the conditional probability P(A|B) = P(A ∩ B) / P(B) from the joint probability of A and B and the marginal probability of B.
DPS Calculator Compute effective damage per second from hit damage, attack speed, critical chance and critical multiplier.
American to Decimal Odds Converter Converts American (moneyline) betting odds to decimal odds, shows the implied win probability, and gives the equivalent fractional odds.
Skewness Calculator Calculates the sample and population skewness of a data set to measure distribution asymmetry.
Dice Probability Calculator Calculate the probability of rolling an exact total with any number of dice and sides.
Expected Number of Trials Calculator Uses the geometric distribution to find the expected, median and 90%-confidence number of trials until the first success.
Negative Binomial PMF Calculator Computes the negative binomial probability of k failures before the r-th success, plus its mean and standard deviation.
PIN Combinations Calculator Calculate how many possible PIN codes exist for a given length, with or without repeated digits. Understand the keyspace and security of a numeric PIN.
Range Calculator Finds the range of a data set by subtracting the minimum value from the maximum value, with min, max and count.
Stars and Bars Calculator Counts the number of ways to distribute identical items into distinct groups, with or without allowing empty groups, using the stars and bars theorem.
P-Value from Z-Score Calculator Calculate one-tailed and two-tailed p-values from a z-score using the normal distribution.
Bootstrap Confidence Interval Calculator Estimates a confidence interval for the mean by bootstrap resampling your data many times.
Dominant Strategy Finder Compares the row player's two strategies across both opponent moves to identify a dominant strategy in a 2×2 game.
Standard Error of Median Calculator Computes the asymptotic standard error of the sample median (1.2533·SD/√n) along with the median and sample size.
Decimal to American Odds Converter Convert decimal odds to American (moneyline) odds. Decimal to American Odds Converter gives you the result instantly from a simple input.