Cochran's Formula

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Tap a term to see what it means, or .

Calculate

Example: a poll wants to estimate the share of voters who approve of a candidate, at 95% confidence with a margin of error of 5 percentage points. With no prior estimate, p̂ = 50% is used, which gives the largest possible sample. Change the values to work out your own case.

Confidence (%) Estimated proportion p̂ (%) Margin of error e (%)

Step by step

What each term means

Sample Size (n₀): The number of people to include in the sample to get statistically meaningful results, assuming a large or infinite population.
Squared Z-Score (Z²): The critical value of the standard normal distribution for the chosen confidence level. For example, at 95% confidence, Z ≈ 1.96.
Estimated Proportion (p̂): The estimated share of the population with a given characteristic. If unknown, p̂ = 0.5 is used, which maximizes the variance and gives the largest possible sample.
Complement of the Proportion (q̂): Computed as (1 - p̂). It is the estimated share of the population without the characteristic.
Squared Margin of Error (e²): The desired precision, also called sampling error. It is the 'window' around the estimate (e.g. ±5%).