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
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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.
Frequently asked questions
How do I use Binomial Distribution Calculator step by step without mistakes?
Follow the order given in the usage section: Compute exact binomial probabilities and the normal approximation. Includes P(X=k), P(X≤k), P(X≥k), and a comparison chart. The step-by-step part matters less than the unit check that sits inside it. Confirm every unit matches the thing you are actually trying to measure before you press calculate - that single check catches more wrong answers than any other habit, and it costs about ten seconds.
What are the common mistakes when using Binomial Distribution Calculator?
Most common mistakes come down to four habits: entering 20 when the field expects 0.2 because the field is a percentage; leaving a field blank and accepting the default without checking what it stands for; changing one input and reading a result that was calculated before the change; and quoting the output as an exact figure when the page describes it as a reference estimate. Press calculate again after any edit, and treat the number as a reference point rather than a final answer.
How do I read the result from Binomial Distribution Calculator?
Read the final figure first, then come back to this section for the conditions behind it: Compute exact binomial probabilities and the normal approximation. Includes P(X=k), P(X≤k), P(X≥k), and a comparison chart. Keep two things apart: the number itself, which comes from the values you typed, and the assumptions it depends on, which decide whether that number is meaningful. The page sets out what a higher or lower result means for your case, so check that direction as well as the magnitude.
Can I act on the Binomial Distribution Calculator result directly?
Treat it as one reference sheet before you decide, rather than as the answer itself: Assumes independent trials with constant p — fails for "batting averages" (where success probability changes). For drawing without replacement, use Hypergeometric instead. P ProbLab A free, no-login toolkit for real probability and statistics questions. Tools The output describes a magnitude under the conditions you entered. It does not include what it actually costs to act, what might change while you act, or how the other side behaves. Before you commit, compare the result against reality and note which assumptions do not hold where you are.
What inputs does Binomial Distribution Calculator need?
Binomial Distribution Calculator takes 3 inputs: Trials n、Success probability p、Tail. They are listed in the order they feed the calculation, so an earlier value can change a later one. Do not skip a field you do not recognise - work out what it means first, because a silently guessed value produces a number that looks reasonable and is not. Before typing anything, make sure every figure uses the same unit and the same time period.
What should I check before I run Binomial Distribution Calculator?
Three checks pay for themselves. First, confirm the question you need answered is really inside the scope of this tool rather than a neighbouring one. Second, confirm that the figures you have are drawn from the same source and the same period - mixing monthly and annual numbers, or two different definitions of the same quantity, quietly distorts the result. Third, keep the key inputs written down, so that later you can tell which set of numbers produced a figure you are about to quote.
Who is Binomial Distribution Calculator for, and who should not use it?
It suits people who already have concrete numbers and want a quick sense of scale - drafting a budget, aligning on a figure with a colleague, or sanity-checking an estimate before a meeting. It is not for people who need an exact value they can promise to a third party, and it is not for people who have not yet agreed what each input means. Spending a few minutes settling the definitions first is far cheaper than re-running the numbers afterwards.