You get a completed-response target and see how confidence and margin of error affect it.
The calculator estimates the complete responses needed to measure a proportion at the selected confidence level and margin of error. It uses p=0.5, the conservative scenario, with a normal approximation. If population is omitted, it treats the population as large; if a total is provided, it applies finite population correction. The estimate assumes an appropriately selected sample.
For a population of 100,000, 95% confidence, and a ±5 percentage-point margin of error, the target is 383 complete responses. If no population is entered, the conservative estimate is 385 responses.
Add your numbers or start with sample data.
Complete the fields to see the result and interpretation here.
Higher confidence or a smaller margin of error requires a larger sample.
Beyond a certain point, a much larger population changes the sample very little.
The target is completed responses, not merely invitations sent.
For a large population, n = z² × 0.25 ÷ e². When N is provided, we use n = N × z² × 0.25 ÷ [e² × (N − 1) + z² × 0.25].
A large sample reduces random error, but it does not fix selection bias or low-quality responses.
The calculator uses the large-population formula. This is suitable when the total is unknown or large enough that finite population correction would have little effect.
When the expected proportion is unknown, 50% creates the greatest variance and therefore the most conservative sample target for the selected precision.
Higher confidence or a smaller margin of error requires more responses. Lower confidence or a wider margin reduces the target.
No. More responses reduce random error but do not fix poor audience selection, undercoverage, nonresponse, duplicates, or biased questions.
The references support the definitions and assumptions. The formula used is shown on this page and covered by automated tests.
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