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Mathematics

Sample size for a proportion

Plan the valid responses and invitations needed from your margin of error, confidence level and expected response rate.

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01

Your inputs

The starting values are an example.

50% is the conservative assumption when the proportion is unknown.
0 means no finite population correction.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

n₀=z²p(1−p)/e². For a known finite population N: n=Nn₀/(N−1+n₀). Round up to whole people.

Worked example

At 95% confidence, a margin of 5 percentage points and p=50%, 385 valid responses are needed without finite population correction. A 50% response rate requires 770 invitations.

Things to check

  • The formula plans a simple random sample. It does not correct biased selection or systematic non-response.
  • A higher response rate reduces the required invitations, not the required valid responses.

Frequently asked questions

Why not always use the actual target population size?

Finite population correction is appropriate when sampling without replacement from a known finite population. A loosely defined target audience may not meet this assumption.