Survey sample size calculator

How many responses do you need?

A survey of everyone is rarely possible, so you survey a sample and treat its answers as a stand-in for the whole group. The question is how big that sample has to be before its answers are close enough to the truth. That depends on three things:

• Margin of error: how close is close enough. ±5% is the usual choice. ±3% needs far more responses, and ±10% far fewer.
• Confidence level: how sure you want to be that the true answer is within that margin. 95% is standard.
• Population size: how many people you could survey. It matters less than you'd think. Past a few thousand people, the sample you need barely grows.

The calculator also asks for an expected response rate, and uses it to tell you how many people to invite to get the responses you need.

How it's calculated

For a very large population, the sample size is n₀ = z² × p(1 − p) ÷ e², where z is 1.645, 1.96 or 2.576 for 90%, 95% or 99% confidence, e is the margin of error as a fraction, and p is 0.5, the most cautious assumption. For a known population N, it's adjusted down to n = n₀ ÷ (1 + (n₀ − 1) ÷ N).

A worked example

For 95% confidence and a ±5% margin of error, a very large population needs 1.96² × 0.25 ÷ 0.05² ≈ 385 responses. With a population of 10,000, that falls to about 370. If you expect 20% of the people you invite to respond, invite about 1,850.

In Excel or Google Sheets

With the population in B1, the z-score in B2 and the margin of error (as a decimal, such as 0.05) in B3:

=ROUNDUP((B2^2*0.25/B3^2) / (1 + (B2^2*0.25/B3^2 - 1) / B1), 0)