Why does the calculator assume a 50% response distribution?

Cochran's formula uses p(1−p) in the numerator, which is largest (most conservative) when p = 0.5. Using 50% as the assumed proportion gives the largest, safest sample size when you don't know the true proportion in advance.

What is the finite population correction, and when is it applied?

If you enter a population size, the calculator shrinks the initial sample-size estimate using the finite population correction, since surveying a large fraction of a small population needs proportionally fewer respondents than Cochran's base formula assumes.

Sample Size Calculator

Calculate the survey sample size needed for a given confidence level and margin of error.

How this is calculated

Cochran's formula: n = Z² × p × (1−p) ÷ E², adjusted for finite population when given

Assumptions used in this calculation

Worst-case proportion: Assumes the most conservative response distribution (p = 0.5) unless a different expected proportion is provided, which maximizes the required sample size.

About this calculator

Calculates the minimum survey sample size needed for a target confidence level and margin of error, using Cochran's formula with a finite-population correction when a population size is given.

Worked example

95% confidence, 5% margin of error, unlimited population

Result: Required sample size = 385

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Frequently asked questions

Why does the calculator assume a 50% response distribution?

What is the finite population correction, and when is it applied?

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