Enter the sample size and the number of occurrences into the calculator to determine the p-hat.

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## P-Hat Formula

The following formula is used to calculate p-hat (p^).

p^ = X / n

- Where p^ is the probability
- X is the number of occurrences of an event
- n is the sample size

## P-Hat Definition

P hat, is the long form of the term p^. P^ is the probability that a given outcome will occur given a specified sample size. In other words, it’s the probability of the event within the chosen sample, and is often represented of the entire population if the sample was chosen correctly.

P-hat is most often used in the field of statistics, but statistics are used in nearly all STEM fields, so you can say that the p-hat sees important use in many fields. A formula and example of how it’s used are shown below the calculator.

## P-hat Example

How to calculate p-hate?

**First, determine the sample size.**Determine the size of the sample you wish to analyze. For this example we will say this is a sample size of 100.

**Next, determine the number of occurrences in the sample.**Measure how many occurrences of an event or parameter are found in the sample. For this example we will say this is 10.

**Finally, calculate p-hat.**Calculate p^ using the formula. We find, p^=10/100 = .10

## FAQ

**What is p-hat?**

P-hat, also denoted p^, is a term used in statistics to describe the probability of an event occurring base on a sample size. In other words, if p is the probability of the entire population, p^ is the probability of just a subset or sample of that population.