How to use the poisson probability calculator
Find the probability of k events with a known average rate. Enter average rate Ξ», events k in the fields above; the p(x = k), mean and variance are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- l β Average rate Ξ»
- k β Events k
Worked example
With average rate Ξ» = 4, events k = 6, the calculator gives p(x = k) β 0.1041956; mean and variance β 4.
Frequently asked questions
What is the formula for the poisson probability calculation?
P(X = k) = exp(-l) Γ l^k / fact(k). Mean and variance = l. Here l is average rate Ξ», k is events k.
What inputs do I need for the poisson probability calculator?
You need average rate Ξ», events k. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.