Statistics & Probability

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p̂ (p-hat) Calculator.

Calculate a sample proportion from successes and trials.

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Set your values

Results update as you type.

pHat: 0.42

pHat

0.420000
pHatPercent: 42

pHatPercent

42.000000
failures: 58

failures

58.000000

Results update automatically as you type.

Use Cases

Estimate population proportion

Use p-hat to estimate the proportion of a characteristic in a population based on sample data, such as survey responses or quality control results.

Example: If 45 out of 100 surveyed prefer product A, p-hat = 0.45.

Check assumptions for hypothesis tests

Before conducting a one-proportion z-test, verify that the sample size and p-hat meet the normal approximation conditions (np ≥ 10 and n(1-p) ≥ 10).

Example: With 30 successes in 50 trials, p-hat = 0.6, np = 30, n(1-p) = 20, so conditions are met.

Frequently Asked Questions

What is p-hat in statistics?
P-hat (p̂) is the sample proportion, calculated as the number of successes divided by the total number of trials. It estimates the population proportion from sample data.
How do I calculate p-hat?
Enter the number of successes and the total number of trials into the calculator. The p-hat value is computed as successes divided by trials, giving you the sample proportion.
Can p-hat be greater than 1?
No, p-hat ranges from 0 to 1 because it is a proportion. If successes exceed trials, check your inputs for errors.

Tips & Common Mistakes

Tips

  • Ensure successes are a subset of trials; successes cannot exceed trials.
  • Use whole numbers for successes and trials to avoid rounding errors.
  • Double-check your data entry to avoid mistakes in the p-hat calculation.
  • Remember that p-hat is a sample statistic, not the true population proportion.

Common Mistakes to Avoid

  • Entering successes greater than trials, which yields an invalid proportion.
  • Using percentages instead of raw counts for successes and trials.
  • Confusing p-hat with the population proportion (p) when interpreting results.

Last updated: August 13, 2026