What drives the number
The formula balances three choices. A higher confidence level uses a larger Z value, which pushes the required sample up. A smaller margin of error demands more responses, and because the margin appears squared in the denominator, halving it roughly quadruples the sample. The expected proportion enters through p·(1−p), which is largest at 50% — that is why an even split is the most demanding and therefore the safest assumption when you have no prior estimate.
Together these mean precision is expensive: each extra bit of tightness in your estimate costs disproportionately more data.
Setting realistic inputs
Pick values that reflect the decision you are making rather than defaults.
- Confidence level: 95% is the common standard; use 99% only when the stakes justify a larger sample.
- Margin of error: a typical political poll targets about ±3%, but ±5% is often acceptable for general surveys.
- Expected proportion: use a prior study or pilot if you have one; otherwise 50% is the conservative default.
What the figure does and does not cover
This result is the number of completed, usable responses needed. Because real surveys suffer non-response, you should invite more people than the number shown — divide by your expected response rate to estimate how many to contact.
The formula assumes simple random sampling from a large population and ignores design effects from clustering or stratification. For a small, finite population you can apply a finite-population correction to reduce the required sample. Treat the output as a planning estimate, not an exact guarantee of precision.
Formula
n = Z²·p·(1−p) / E²Frequently asked questions
- What proportion should I use if I have no estimate?
- Use 50%. It maximises p·(1−p) and therefore the required sample size, giving you a conservative figure that works regardless of the true proportion.