Free Poisson Distribution Calculator
Probability of k events given an average rate λ.
- Free Forever
- No Registration Required
- Instant Results
- Downloadable Reports
- Mobile Friendly
Inputs
Result
P(X = 6)
10.4196%
Your result is ready.
Download your free detailed report — inputs, result, formula and explanation included.
Estimates only. Verify with a professional for consequential decisions.
- Always Free
- No Hidden Costs
- No Account Required
- Unlimited Calculations
- Instant Reports
Short answer
Probability of k events given an average rate λ.
What is the Poisson Distribution Calculator?
Probability of k events given an average rate λ.
How does the Poisson Distribution Calculator work?
Enter the inputs above and read the result.
Formula
Variables
λAverage number of events per interval
Explanation
The Poisson distribution models rare, independent events occurring at a constant average rate.
Examples
Applications
Advantages
Limitations
Common mistakes
Tips
Related concepts
The Poisson Distribution Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Poisson Distribution
Probability of k events given an average rate λ. Within math calculators, poisson distribution belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.
Learning how poisson distribution is calculated
The Poisson distribution models rare, independent events occurring at a constant average rate. Working through the variables one at a time — λ — makes the result reproducible by hand and easier to sanity-check.
Using poisson distribution to make a decision
Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How poisson distribution compares with related measures
distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
Related calculators
These tools share entities, formulas or user intent with the poisson distribution calculator.
Math
Free Normal Distribution Probability Calculator
Probability that X falls below, above or between values.
Math
Free Average Calculator
Mean of a list of numbers, plus sum and count.
Math
Free Binomial Probability Calculator
Probability of exactly k successes in n trials.
Math
Free Coin Flip Probability Calculator
Chance of getting exactly k heads in n flips.
Math
Free Combination Calculator
nCr combinations and nPr permutations.
Math
Free Confidence Interval Calculator
Confidence interval for a sample mean.
Math
Free Correlation Coefficient Calculator
Pearson's r between two paired data sets.
Math
Free Dice Probability Calculator
Odds of a target sum when rolling multiple dice.
Math
Free Expected Value Calculator
Average outcome of a probabilistic bet or event, over the long run.