Plan the responses needed for a population proportion using confidence, margin of error, population size and response rate.
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0.001 – 50
0.001 – 99.999
0 – 1000000000000
0.01 – 100
Completed responses needed
385
Simple random sampling and a normal-approximation planning model. Nonresponse bias, clustering and design effects are not accounted for. A 50% expected proportion gives the largest required sample.
Initial n = z² × p × (1 − p) ÷ margin², with p and margin expressed as fractions.
For finite population N, correct n to n ÷ (1 + (n − 1) ÷ N), then round up.
Invitations = completed responses ÷ expected response fraction, rounded up.
For expected proportion p and margin e, n₀ = z²p(1 − p)/e². A finite population N adjusts this to n₀/[1 + (n₀ − 1)/N]; round up.
At 95% confidence, 50% expected proportion and a 5 percentage-point margin, an unspecified population needs 385 completed responses. A population of 1,000 needs 278.
No. The calculation assumes simple random sampling. Selection bias, nonresponse bias and clustering can make the stated margin inappropriate.
Last updated . Results are estimates for informational purposes only.