Tools/Binomial Distribution Calculator

Binomial Distribution Calculator

Exact P(X=k), P(X≤k), P(X≥k), plus the normal approximation with continuity correction. Compares the two so you can see when approximation is safe.

Setup

Trials n Success probability p k Tail

Result

Distribution (exact vs normal approx)

Table

k	P(X=k)	P(X≤k)	P(X≥k)

When to use exact vs approximation

Use the exact binomial unless n is so large that computing C(n,k) blows up. The normal approximation with continuity correction is typically accurate within ~0.5% when np ≥ 10 and n(1−p) ≥ 10. For small n or extreme p, stick with exact.

Who uses it

A/B testers computing the probability of seeing k conversions out of n trials.
Quality engineers computing lot-defect probabilities.
Students doing probability homework.

Limitations

Assumes independent trials with constant p — fails for "batting averages" (where success probability changes).
For drawing without replacement, use Hypergeometric instead.