The calculation, without hidden assumptions
“How many responses do I need?” is not one formula until the study target is defined. A proportion uses p(1−p); a mean uses an estimated standard deviation. This calculator supports both modes, applies an optional finite-population correction, exposes an optional design effect, and converts completed-response targets into invitations when you enter an expected response rate. The raw and rounded values are shown separately because required samples should be rounded up.
How to use this calculator
Choose whether you are estimating a proportion or a mean and select a confidence level.
Enter the desired margin of error in the unit shown for that mode, plus expected proportion or estimated population SD.
Optionally add population size, design effect and expected response rate, then use the rounded-up response target for planning.
Where people use it
- •Survey response planning
- •Early research-design arithmetic
- •Checking sample-size assumptions in a report or proposal
Example: 95% confidence, ±5 points, p = 0.5
For a large population, z = 1.96, p = 0.5 and E = 0.05 produce n₀ ≈ 384.15, so the completed-response target rounds up to 385 before any design-effect adjustment.
What the result does not assume
- •The formulas assume the sampling model represented by the inputs; clustering, weighting, nonresponse bias, power analysis and complex experimental designs can require a different method.
- •A larger nominal sample does not correct biased recruitment, measurement error or poor questionnaire design.
Frequently asked questions
Why use 50% for an unknown proportion?+
For the basic proportion formula, p = 0.5 maximizes p(1−p) and therefore gives the largest sample under the same confidence and margin assumptions.
What does finite-population correction do?+
When the target population is known and the planned sample is a meaningful share of it, the correction reduces the required sample compared with the infinite-population formula.
Why include response rate?+
The statistical target is completed responses. If only a fraction of invited people are expected to respond, the invitation count must be larger than the completed-response target.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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