Probability Distribution Calculator — Binomial, Poisson, Normal & More
Probability Details
By Amanda Reeds, Content Researcher ·
This probability distribution calculator computes exact, cumulative, and between-range probabilities directly in your browser, no download, plugin, or app required. Pick a distribution, enter its parameters, and the calculator returns the probability along with the mean, variance, and standard deviation, plus a graph of the distribution.
It covers the six distributions that come up most often in an intro statistics or probability course: Bernoulli, Binomial, Poisson, Hypergeometric, Normal, and Exponential. That means a binomial probability calculator, a poisson distribution calculator, a hypergeometric distribution calculator, and a normal distribution calculator in one lightweight page, instead of switching between separate tools for each one.
Each mode supports exact probabilities, cumulative probabilities (a binomial cdf calculator and cumulative normal distribution calculator use case), and "between" ranges, so it works as a general probability distribution solver for homework, exam prep, or a quick sanity check on a statistics problem.
What You Can Do With This Probability Distribution Calculator
Six Distributions In One Calculator
Switch modes to move between a bernoulli distribution calculator, binomial distribution calculator, poisson distribution calculator, hypergeometric distribution calculator, normal distribution calculator, and exponential distribution calculator, without leaving the page.
- Same clean interface across every distribution
- Covers the most common discrete and continuous distributions in an intro statistics course
- No need to bookmark six separate calculator pages
Exact, Cumulative & Between-Range Probabilities
Every discrete mode supports P(X = k), P(X ≤ k), and P(X ≥ k), the same results a binomial cdf calculator or binomial pdf calculator would return, plus a P(a ≤ X ≤ b) between-range option.
- Discrete "between" ranges for binomial, poisson, and hypergeometric probabilities
- Continuous cumulative probability for the normal and exponential distributions
- A direct probability density option for finding f(x) on a continuous distribution
Instant Mean, Variance & Standard Deviation
Every calculation also returns the mean of the probability distribution, its variance, and its standard deviation, so you don't need a separate step to find the expected value of a binomial distribution or the spread of a poisson or normal distribution.
- Mean, variance, and standard deviation shown alongside every result
- z-score reported automatically in Normal mode
- Useful as a quick check for a standard deviation of probability distribution formula homework problem
Visual Probability Graphs
Each calculation draws a graph: a bar chart for discrete distributions and a curve for continuous ones, working as a binomial distribution graph generator, poisson distribution graph, and normal distribution graph maker all in one.
- The selected outcome range is highlighted directly on the graph
- Bar charts for Bernoulli, Binomial, Poisson, and Hypergeometric
- Smooth probability density curves for Normal and Exponential
Supported Distributions & Formulas
Each mode uses its own standard formula. Discrete distributions use a probability mass function (PMF); continuous distributions use a probability density function (PDF) and a cumulative distribution function (CDF).
| Distribution | Formula | Parameters |
|---|---|---|
| Bernoulli | P(X=1) = p, P(X=0) = 1 − p | p = probability of success |
| Binomial | P(X=k) = C(n,k) p^k (1−p)^(n−k) | n = trials, p = probability of success |
| Poisson | P(X=k) = e^−λ λ^k / k! | λ = average events per interval |
| Hypergeometric | P(X=k) = C(K,k) C(N−K,n−k) / C(N,n) | N = population, K = successes, n = sample size |
| Normal | f(x) = (1/σ√2π) e^−(x−μ)²/2σ² | μ = mean, σ = standard deviation |
| Exponential | f(x) = λe^−λx, P(X≤x) = 1−e^−λx | λ = rate |
How To Use The Probability Distribution Calculator
Pick the distribution that matches your problem first. Discrete counts of successes (coin flips, defective parts, calls per hour) fit Bernoulli, Binomial, Poisson, or Hypergeometric. Continuous measurements (heights, wait times, measurement error) fit Normal or Exponential.
- Choose a distribution from the row above the screen: Bernoulli, Binomial, Poisson, Hypergeometric, Normal, or Exponential.
- Enter that distribution's parameters, such as n and p for Binomial, or μ and σ for Normal.
- Enter k (or x1), and a second value for "between" calculations, then choose the calculation type: exact, ≤, ≥, or between.
- Press Calculate to see the probability, mean, variance, standard deviation, and a graph of the distribution.
- Use the Clear button to reset the current mode's fields and start a new calculation.
Quick Action Steps
- Pick a distribution and enter its parameters.
- Enter k or x1 (and k2/x2 for a between-range) and pick the calculation type.
- Press Calculate to see the probability, mean, variance, and graph.
⚠ Watch Out For This
Probabilities (p) must stay between 0 and 1, and Hypergeometric mode needs the successes in the population (K) and the sample size (n) to each be no larger than the population size (N). A k value outside what's possible for the chosen parameters returns a probability of 0 rather than an error.
How This Compares To Other Probability Tools
A graphing calculator like a TI-84, or a Casio fx-991EX, fx-9750GII, or fx-CG50, can compute binomial and normal distribution probabilities with the right built-in menu, and a tool like StatCrunch handles the same calculations online. AceCalculator's probability distribution calculator exists for the moments you want a result fast, without reaching for a physical calculator or a separate statistics platform.
- ✓ No menu-diving needed, unlike a TI-84 or Casio fx-991EX distribution menu
- ✓ No separate account or platform switch, unlike signing into StatCrunch
- ✓ Six distributions in one page: Bernoulli, Binomial, Poisson, Hypergeometric, Normal, Exponential
- ✓ Exact, cumulative, and between-range probabilities in every discrete mode
- ✓ Mean, variance, and standard deviation returned automatically
- ✓ Runs entirely in your browser, nothing is stored or sent to a server
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Content Researcher · AceCalculator
Amanda Reeds researches and builds AceCalculator's math and statistics tools, with a focus on matching each calculator's output to standard classroom notation and formulas. She has written and verified the working behind AceCalculator's algebra, graphing, and probability calculators.
Frequently Asked Questions
Yes. Calculating probabilities for the bernoulli, binomial, poisson, hypergeometric, normal, and exponential distributions, along with the mean, variance, and standard deviation, is free, with no account, signup, or download required.
Six distributions are supported: Bernoulli, Binomial, Poisson, Hypergeometric, Normal, and Exponential. Each mode has its own inputs, so you don't need a separate binomial probability calculator, poisson distribution calculator, and normal distribution calculator.
Switch to Binomial mode, enter the number of trials (n) and the probability of success (p), enter k (and a second value for a "between" range), choose P(X = k), P(X ≤ k), P(X ≥ k), or P(a ≤ X ≤ b), then press Calculate. The result, mean, and standard deviation appear instantly.
The calculator uses the standard Poisson probability mass function, P(X = k) = (e^−λ λ^k) / k!, where λ is the average number of events in the interval, computed internally with a log-gamma function so it stays accurate for larger λ and k.
Yes. Set the mean to 0 and the standard deviation to 1 in Normal mode to work directly with z-scores, or enter any mean and standard deviation and the calculator reports the equivalent z-score alongside the probability.
Yes. Every mode reports the mean, variance, and standard deviation for the distribution and parameters entered, alongside the requested probability.
Binomial mode assumes each trial is independent with a fixed probability of success, which fits sampling with replacement. Hypergeometric mode is for sampling without replacement from a fixed population, so pick it when successes are drawn from a finite population size that shrinks as you sample.
Yes. Choosing P(X ≤ k) or P(X ≥ k) in Binomial, Poisson, or Hypergeometric mode returns the cumulative probability across every outcome up to or beyond k, the same result a binomial cdf calculator or cumulative distribution calculator provides.
Yes. Every mode, input field, and the probability graph work the same way on a phone or tablet browser as they do on desktop, with no app to install.
Important Disclaimer
AceCalculator's probability distribution calculator is provided for informational and educational purposes only. Results are computed using standard statistical formulas for reference and homework-checking purposes and are not a substitute for verification by a qualified instructor or statistician where accuracy is critical. See our full Disclaimer and Terms and Conditions.