Binomial & Poisson Probability Calculator
Calculate binomial and Poisson point and cumulative probabilities, expectation and variance with a distribution histogram.
About this binomial & poisson probability calculator
Calculate binomial and Poisson point and cumulative probabilities, expectation and variance with a distribution histogram Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, Binomial trials are independent with a fixed success probability: P(X=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ, E(X)=np, Var(X)=np(1−p). Poisson counts assume independent events at a constant rate: P(X=k)=exp(−λ)λᵏ/k!, E(X)=Var(X)=λ. CDF sums masses from 0 through k. For binomial k>n, PMF=0 and CDF=1.
Worked numerical calculation
Scenario: What should the example produce?
Sample input:
Processing: Choose a distribution and enter its parameters and target count. Calculate PMF, CDF, expectation and variance. Inspect the histogram intervals; editing or switching removes old results.
Illustrative output:
Domain range & precision boundaries
Native Lanczos log-gamma and normalized recurrence avoid factorial overflow. binary64 approximations, not exact symbolic values; tiny probabilities may underflow. n: integer 0–5000; λ: 0–5000 for bounded browser work; k: nonnegative safe integer. Decimal point and optional e notation; no grouping marks. No file or usage quota. Runs locally and works offline after loading. No added calculation dependency, fee or external service. Bars show probability per contiguous integer interval, with at most 100 bars; wide ranges group consecutive counts. The red bar contains k, if displayed. Inspect every bin using the selector. Binomial support is complete. Poisson is displayed through ceil(λ+12√(λ+1)+40); the omitted tail bound is shown separately and is positive when λ>0. Numeric Poisson probabilities use this normalized finite support, except PMFs beyond it use log-gamma directly.
Calculations in Binomial & Poisson Probability Calculator use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Binomial & Poisson Probability Calculator run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
Binomial & Poisson Probability Calculator verification · Audit standards
How to use it
- Enter, paste, or select your input data into the Binomial & Poisson Probability Calculator workspace controls.
- Review parameter fields, units, or options configured for Binomial & Poisson Probability Calculator.
- Click the action button or observe immediate live calculations rendered by Binomial & Poisson Probability Calculator.
Frequently asked questions
How are the results defined?+
Binomial trials are independent with a fixed success probability: P(X=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ, E(X)=np, Var(X)=np(1−p).
What does each histogram bar mean?+
Boundary constraints concerning "What does each histogram bar mean?" prevent invalid parameter state mutations client-side.
What precision and limits apply?+
No file or usage quota.
What should the example produce?+
Security isolation for "What should the example produce?" ensures zero transmission beyond your local workstation.