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Poisson Distribution Calculator

Math Calculators

P(X=k) · cumulative · full table

Quick Answer

Poisson Distribution Calculator: P(X=k) · cumulative · full table. Poisson Distribution Calculator uses standard math formulas to compute accurate results instantly.

P(X = 3)
21.38%
Exactly 3 events when the average is 2.5
P(X = 3)21.38%
P(X ≤ 3)75.76%
P(X > 3)24.24%
Mean = Varianceλ = 2.5
Poisson models RARE, INDEPENDENT events at a constant average rate: goals, calls, defects, accidents. When λ > 20 it approaches the normal distribution N(λ, λ). For football, modelling each team's goals as Poisson is the classic Dixon–Coles baseline.

Distribution table

kP(X=k)P(X≤k)
08.208%8.208%
120.521%28.730%
225.652%54.381%
321.376%75.758%
413.360%89.118%
56.680%95.798%
62.783%98.581%
70.994%99.575%
80.311%99.886%
90.086%99.972%
100.022%99.994%
110.005%99.999%
120.001%100.000%
130.000%100.000%

Calculation steps

  1. 1P(X=3) = λ^k·e^(−λ)/k! = 2.5^3·e^(−2.5)/3!
  2. 2= 2.1376e-1 ≈ 21.38%
  3. 3P(X≤3) = 75.76% · P(X>3) = 24.24%

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How to Use

  1. Enter values or expressions: type directly into the Poisson Distribution Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Poisson Distribution Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: P(X=k) · cumulative · full table.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Poisson Distribution Calculator formula

Poisson Distribution Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Poisson Distribution Calculator?
Open the page and fill in the input fields — results update automatically. P(X=k) · cumulative · full table.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

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Results provided by this tool are for reference only and do not constitute professional advice.