When to use it
Use this when planning any survey or poll that estimates a percentage — customer satisfaction, an election poll, a yes/no product question. It tells you the number of completed responses needed so your result is accurate to within your stated margin of error.
The inputs explained
- Confidence level — how often the true value falls within the margin over repeated sampling; 95% is standard.
- Margin of error — the ± precision you want (e.g. ±5%). Tighter margins cost far more responses.
- Estimated proportion — your prior guess for the result. Use 50% when unsure; it maximizes the sample and is therefore conservative.
- Population size — optional. For a small, finite group (e.g. 400 employees) the required sample shrinks; leave it blank for large populations.
Worked example
You want 95% confidence and a ±5% margin, with no prior estimate (p = 50%). The calculator returns 385 responses. Tighten the margin to ±3% and it jumps to about 1,068. If your whole population is only 2,000 people, the finite-population correction brings the ±5% requirement down to about 323.
The formula
The base sample size for a proportion is
n₀ = z² × p(1−p) / e²
where z is the standard-normal quantile for your confidence level and e is the margin of error. With a known population N, apply the finite-population correction n = n₀ / (1 + (n₀−1)/N). Round up. See the methodology page.
Common mistakes
- Forgetting non-response — this is the number of completed responses; inflate your invitations to cover the response rate.
- Subgroup precision — a sample sized for the whole survey is too small to analyze small subgroups at the same margin.
- Over-precise margins — going from ±5% to ±1% multiplies the cost 25-fold for often-unneeded precision.
- Confusing margin of error with confidence level — they are different knobs.