Binomial Distribution Calculator

Calculate the probability of a specific number of successes in a sequence of independent trials. Enter your trial parameters below to instantly find the exact or cumulative probability.

How to use this calculator

1. Probability of success ($p$): Enter the likelihood of success on any single trial. This must be a decimal between 0 and 1 (e.g., for a coin flip, enter 0.5).
2. Number of trials ($n$): Enter the total number of times the experiment is repeated.
3. Number of successes ($x$): Enter the target number of successful outcomes you want to calculate the probability for.
4. Choose your calculation: Select whether you want the exact probability (exactly $x$ successes), or a cumulative probability (at most $x$, at least $x$, etc.).

Understanding Your Results

A binomial distribution is used when an experiment has exactly two possible outcomes (often called "success" and "failure"), and the trials are completely independent of one another.

• Probability: The calculated percentage tells you the likelihood of your chosen scenario occurring. For example, if you flip a coin 10 times, the probability of getting exactly 5 heads is about 24.6%.
• Expected Mean ($\mu$): The average number of successes you would expect if you ran this set of trials many times. It is simply the number of trials multiplied by the probability of success ($n \times p$).
• Standard Deviation ($\sigma$): A measure of how much the actual number of successes is likely to vary from the expected mean.