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Sample Proportion from Successes & Trials

Calculate the observed success fraction p-hat from counts, or recover a compatible whole-number count.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Forty successes in 100 observations give p-hat = 40/100 = 0.4, equivalent to 40%. Enter 0.4 in the fraction field.

Sample proportion p̂ = success count / total count

Enter these known values and leave the other values blank.

Counts are whole numbers, total count is positive, and successes range from zero to the total.
The proportion field uses a fraction from zero to one, not a percent. Inverse inputs must produce whole counts.
This describes observed data. It does not estimate a confidence interval, correct sampling bias or guarantee the population proportion.

Enter 0.4 in the proportion field. The success and total fields hold counts.

Yes. No successes gives zero; every observation being a success gives one.

Bookify requires whole-number counts and a success count no greater than the total.