Everyday Tools

Binomial Probability Calculator

Estimate the binomial probability of getting an exact number of successes across a fixed number of trials.

Updated April 14, 2026
Free online tool
Planning and research use

Why this page exists

Fixed-trial probability questions get easier to understand when the binomial formula is handled for you instead of worked out by hand. This calculator helps visitors estimate binomial probability from number of trials, success probability, and target successes.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Binomial probability calculator

Estimate binomial probability from number of trials, success probability, and target successes.

Result

0.237668

Estimated binomial probability for the exact number of successes entered across the fixed number of trials.

Binomial probability0.237668

Probability (percentage)23.7668%

Combination count210

Inputs used4 successes in 10 trials at 35.0% success probability

The calculation uses 210 ways to arrange 4 successes across 10 trials.
At 35.0% success probability per trial, the exact probability of 4 successes is about 0.237668.
Use the result for fixed-trial probability questions where you want the chance of exactly the number of successes entered, not at least or at most that number.

This is a standard binomial-probability estimate for a fixed number of independent trials with the same success probability on each trial. Use it only when those assumptions fit the situation.

Planning note

Last updated April 14, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Enter the number of trials, the probability of success for each trial, and the number of successes you want to evaluate.

The calculator applies the standard binomial probability formula for the exact number of successes entered.

It shows the probability in decimal and percentage form along with a readable summary of the inputs used.

Understanding your result

This is a standard binomial-probability estimate. It assumes independent trials and the same probability of success on each trial.

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Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Estimate the chance of an exact number of successes

A binomial-probability estimate can make repeated yes-or-no trial questions easier to answer without hand calculations.

Compare different success-rate assumptions

Changing the per-trial success probability can show how quickly the exact outcome probability shifts.

Use it with other probability tools

Binomial probability often fits naturally beside simple probability, percentile, and spread tools.

FAQ

Common questions

What does this calculator estimate?

It estimates the probability of getting exactly the number of successes entered across the fixed number of trials entered.

What assumptions does binomial probability use?

It assumes each trial is independent and that the probability of success stays the same on every trial.

Does this calculate at least or at most a number of successes?

No. This version estimates the probability of exactly the number of successes entered, not cumulative probabilities.

Related tools

Keep comparing

Use these related tools to compare nearby scenarios, check a second estimate, or keep narrowing down the right decision.

Everyday ToolsUpdated April 13, 2026