Probability Calculator

  • Sampling Distribution of the Sample Mean Calculator
    Compute the mean and standard error (σ/√n) of the sampling distribution of the sample mean from population mean, std dev, and sample size.
  • Permutations and Combinations Calculator
    Calculate permutations (nPr) and combinations (nCr) instantly. Enter n and r to find how many ways to arrange or choose items, with formulas and examples.
  • Odds to Probability Calculator
    Convert odds (a:b) into a probability and percentage instantly. Supports odds in favor and odds against using P = a/(a+b). Free and accurate.
  • Poisson Probability Calculator
    Calculate Poisson probability P(X=k) from a mean rate λ. Get exact, less-than, cumulative, and at-least probabilities instantly with this free tool.
  • Permutations & Combinations Calculator
    Calculate permutations (nPr) and combinations (nCr) instantly. Enter n and r to find ordered arrangements and unordered selections using factorials.
  • Probability of At Least One Calculator
    Calculate the probability of at least one success in n independent trials using P = 1 - (1-p)^n. Free, instant, with worked examples.
  • Variance of a Probability Distribution Calculator
    Compute the variance and standard deviation of a discrete probability distribution from outcomes xᵢ and probabilities pᵢ using Var(X)=Σpᵢxᵢ²−(Σpᵢxᵢ)².
  • One-Proportion Z-Test Calculator
    Run a one-proportion z-test online. Enter successes, sample size, and hypothesized proportion to get the z statistic, standard error, and p-value.
  • Exact Binomial Test Calculator
    Compute the exact binomial test p-value (two-sided and one-sided) for k successes in n trials against a hypothesized probability p.
  • Z-Score Calculator
    Free z-score calculator: find the standardized value of a data point, a sample mean, or a data sample using the population mean and standard deviation.
  • Random Playing Card Generator
    Draw random playing cards from a shuffled deck. Choose with or without replacement, customize ranks, suits and jokers, and pick how many cards to deal.
  • Random Number Generator (1 to 100)
    Free random number generator from 1 to 100. Click Pick for a uniform random integer (each number 1% likely), with a running pick counter and Reset.
  • Percentile Calculator (Linear Interpolation Method)
    Find any percentile of a data set using linear interpolation (the same R-7 method as Excel and Google Sheets PERCENTILE / PERCENTILE.INC), with an optional percentile table.
  • Random Number Generator 1-10
    Generate a random integer from 1 to 10 instantly. Each pick is fair and independent with a 10% chance per number, plus a pick counter and probability breakdown.
  • Random Number and Letter Set Generator
    Generate a random set of numbers or letters from any inclusive range. Control sample size, duplicates, and comma separators. Great for PINs, sampling, and lots.
  • Coin Flipper (Heads or Tails Simulator)
    Free online coin flipper. Simulate 1 to 100,000 fair coin tosses, see each Heads or Tails result, and get exact totals and percentages.
  • Lottery Number Generator
    Generate random quick-pick lottery numbers for Powerball, Mega Millions, EuroMillions, Lotto 6/49, Pick games and more. Force in your favorite numbers.
  • Poker Hand Rankings Evaluator
    Enter any 5 cards and instantly see which poker hand they make, from Royal Flush to High Card, with its rank (1-10) and the key cards explained.
  • Dice Roller (1 to 6 Dice)
    Free online dice roller. Roll 1 to 6 fair six-sided dice and see each face plus the total. Great for board games, craps, Yahtzee and probability lessons.
  • Sample Size from Margin of Error Calculator
    Calculate the survey sample size needed for a target margin of error and confidence level using n = z² p(1−p)/E², with optional finite population correction.
  • Shannon Entropy Calculator
    Compute Shannon entropy H = -Σ pᵢ·log₂(pᵢ) from a probability distribution. Supports bits, nats and dits, plus max entropy and efficiency.
  • Confidence Interval for Difference of Two Means Calculator
    Compute a confidence interval for the difference between two independent sample means using the Welch t-method. Enter means, SDs, sizes and confidence level.
  • Confidence Interval for Difference of Two Proportions
    Compute a confidence interval for the difference between two sample proportions (p̂₁−p̂₂) at 90%, 95%, or 99% using the normal approximation.
  • Cohen's Kappa Calculator
    Calculate Cohen Kappa (κ) for inter-rater agreement from a 2x2 table. Get observed and expected agreement and interpret reliability instantly.

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