P-Hat Calculator

Created by Mariamy Chrdileli
Reviewed by Anna Szczepanek, PhD and Adena Benn
Last updated: Jun 05, 2023

Welcome to the Omni p-hat calculator, a simple and convenient tool to help you determine the sample proportion.

If you're trying to calculate the ratio of the number of occurrences of an event to the sample size, you're in the right place. Come along to get answers to some of the p-hat related questions, such as:

  • What is p-hat in statistics?
  • How do I calculate p-hat?
  • What is the symbol for the p-hat? And more.

What is p-hat in statistics?

The sample proportion or p-hat, denoted by the symbol p̂, is an essential value in inferential statistics that represents the ratio of the number of occurrences of a particular event to the sample size. In other words, p-hat indicates the proportion of individuals in a sample who share a specific characteristic or interest. The p-hat value varies between 0 and 1 and is often utilized in polls; however, it is subject to sampling variability (variation of estimates between samples) and may not equal population proportion (the proportion of individuals in a population who possess a particular trait).

Keep reading to learn how to find p-hat. While you're here, you can also learn more about other related statistical concepts, such as the sample size and sampling distribution of the sample proportion with the Omni sample size calculator and standard deviation of mean sample calculator.

How to calculate p-hat

The p-hat formula is quite simple:

p^=xn{\displaystyle {\hat {p}}={\frac {x}{n}}}


  • p^\hat p – Sample proportion aka p-hat;
  • xx – Number of occurrences; and
  • nn – Sample size.

💡 As you may know, determining sampling error is essential for the credibility of your study. Learn more about the concept, and calculate the error of your sample using the sampling error calculator.

P-hat calculation example

Suppose you were conducting a poll to explore whether adding carrot pumpkin soup to the school menu is a good idea. Out of your sample of 700 students, the poll determined that 450 favored this addition and 250 did not. To calculate the sample proportion of yes responses (the number of occurrences) to the size of the sample, you would have to:

  1. Take the number of yes responses, in this case, 450.
  2. Divide it by the sample size, which is 700.
  3. That's all! Your sample proportion (p̂) is 0.64.


What is the meaning of p-hat?

P-hat coveys the sample proportion, the ratio of certain events or characteristics occurring in a sample to the sample size. It can equal or differ from population proportion, which conveys a proportion of a particular feature associated with a population.

How do I find p-hat?

To find p-hat (i.e., sample proportion), you need to follow the next steps:

  1. Take the number of occurrences of an event or the number of successful outcomes.
  2. Divide it by the sample size.
  3. That's all! You have calculated p-hat.

What is the difference between sample proportion and population proportion?

Population proportion describes the ratio of certain events occurring or shared characteristics to the population size. On the other hand, the sample proportion represents the ratio of certain events happening to the sample size.

What does it mean if p-hat equals 0.6 in a political poll?

If p-hat equals 0.6 in a political poll, 60% of voters from the sample support a particular event or a candidate. P-hat is the ratio of the number of occurrences of a particular event to the sample size and is often reported as a percentage in polls.

What is p-hat if there are 25 successes in 60 trials?

If there are 25 successful outcomes in 60 trials, then p-hat (i.e., the sample proportion) equals approximately 0.4. You can calculate the p-hat by dividing the sample size by the number of successful outcomes.

Mariamy Chrdileli
Sample size
Number of occurrences
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