probability Calculators
Coin Flip Probability Calculator
Find the exact probability of getting a chosen number of heads in a set of coin flips. Useful for statistics homework, game design, or verifying fair-coin assumptions.
Dice Roll Probability Calculator
Compute the probability of rolling any target sum with any number of multi-sided dice. Perfect for tabletop RPG designers, board game players, and statistics students.
Lottery Odds Calculator
Find the odds of winning a lottery by calculating how many possible ticket combinations exist. Use it before buying a ticket to understand just how unlikely a jackpot win is.
Poker Hand Probability Calculator
Calculate the probability of being dealt any classic poker hand from a standard 52-card deck. Great for learning poker math or verifying hand rankings.
Birthday Paradox Calculator
Discover the surprisingly high probability that at least two people in a group share a birthday. Use it to demonstrate the birthday paradox in classrooms or trivia nights.
Bayes' Theorem Calculator
Compute the posterior probability P(A|B) using Bayes' theorem. Use it when you want to update a prior belief about event A after observing new evidence B — common in medical testing, spam filtering, and risk analysis.
Hypergeometric Probability Calculator
Calculate the exact probability of drawing exactly k successes from a finite population without replacement. Ideal for quality control sampling, card game odds, and any scenario where items are not returned to the pool after selection.
Poisson Probability Calculator
Find the probability that exactly k events occur in a fixed interval, given a known average rate λ. Use it for modeling rare events like customer arrivals, server requests, manufacturing defects, or radioactive decay counts.
Normal Distribution Probability Calculator
Compute the cumulative probability P(X ≤ x) for a normal distribution with a given mean and standard deviation. Use it to find the percentage of a population below a test score, measurement threshold, or quality specification limit.
Geometric Probability Calculator
Find the probability that the first success occurs on exactly the nth trial, given a constant success probability per trial. Use it for modeling first-time events like the first defective item on a production line or the first sale made by a salesperson.
Binomial Probability Calculator
Find the probability of getting exactly k successes, at most k, or more than k in n independent trials. Ideal for quality control, genetics, and game-theory scenarios.
Normal Distribution Calculator
Compute left-tail, right-tail, or two-tail probabilities for any normal distribution given its mean and standard deviation. Widely used in statistics, finance, and scientific research.
Multiple Dice Probability Calculator
Calculate the probability that multiple dice produce a specific sum, or a sum greater or less than a target. Perfect for tabletop RPG players and probability students.
Lottery Odds Calculator
Compute your exact odds of winning a lottery jackpot based on pool size, numbers drawn, and bonus ball rules. Helps you understand just how unlikely a jackpot win really is.
Conditional Probability Calculator
Apply Bayes' theorem to find conditional probabilities, intersections, and unions of two events. Useful in medical testing, risk analysis, and machine learning evaluation.
Sports Betting Odds Calculator
Convert American, decimal, or fractional odds into implied probability or potential payout. Use it before placing a bet to compare lines across sportsbooks or spot value in the market.
Birthday Paradox Calculator
Calculate the probability that at least two people in a group share a birthday. Useful for teaching probability concepts or settling that classic party debate.
Hypothesis Testing Calculator
Run a one-sample t-test to decide whether a sample mean differs significantly from a hypothesised population mean. Returns 1 (reject the null hypothesis) or 0 (fail to reject) at your chosen confidence level using the one-sample t-statistic and a critical-value lookup.
Monte Carlo Simulation Calculator
Use repeated random sampling to estimate probabilities for coin flips, dice rolls, or π. Ideal for understanding how simulation converges to theoretical values as trial count increases.
Bayes' Theorem Calculator
Compute the posterior probability P(A|B) from a prior belief, a likelihood, and a false-positive rate. Use it for medical testing, spam filtering, or any scenario where you update beliefs with new evidence.
Hypergeometric Distribution Calculator
Calculates exact probabilities when drawing items from a finite population without replacement. Use it in quality control, card games, or any scenario where sampling changes remaining proportions.
Confidence Interval Calculator
Computes the range of values likely to contain a true population mean at your chosen confidence level. Use it when reporting survey results, clinical trial outcomes, or any estimate derived from a sample.
Statistical Power Calculator
Calculates the statistical power of a hypothesis test or the sample size needed to detect a given effect. Use it when designing experiments to ensure your study can reliably detect meaningful differences.
Chi-Square Goodness of Fit Calculator
Tests whether your observed frequency counts match a theoretically expected distribution. Use it to check if a die is fair, verify that survey responses follow a predicted pattern, or validate a statistical model.
Poisson Probability Calculator
Computes the probability of observing exactly k events in a fixed interval when events occur at a known average rate. Use it for call-centre arrivals, equipment failures, or any count of rare, independent events.
Expected Value Calculator
Compute the expected value (mean) of a discrete probability distribution by entering up to three outcomes and their probabilities. Ideal for decision analysis, gambling odds, and statistics coursework.
Chi-Square Test Calculator
Calculate the chi-square (χ²) test statistic and compare it against a critical value to test goodness of fit or independence. Used in research, biology, marketing, and quality control.
Hypothesis Test Calculator
Run a one-sample z-test or t-test to determine whether a sample mean significantly differs from a hypothesized population mean. Essential for quality control, clinical trials, and academic research.
Combinations and Permutations Calculator
Calculate combinations (nCr) and permutations (nPr), with or without replacement, for counting and probability problems. Use it for lottery odds, team selection, and combinatorics assignments.
Sample Size Calculator
Determine the minimum sample size needed for a survey or experiment given your confidence level, margin of error, and population size. Prevents under-powered studies and over-budgeted data collection.