Sample Size Calculator

How it is calculated

The tool uses Cochran's formula for estimating a proportion: n₀ = z² × p × (1 − p) / e², where z is the normal-distribution value for the confidence level, p the expected proportion (as a fraction) and e the margin of error (as a fraction). The supported confidence levels are 80, 85, 90, 95 and 99%, using z = 1.282, 1.440, 1.645, 1.960 and 2.576; any other level shows no result. If you give a population size above zero, a finite-population correction is applied: n = n₀ / (1 + (n₀ − 1) / N); without one, the adjusted and unadjusted figures are equal. Both results are rounded up to a whole person. Proportion defaults to 50%, the most cautious choice because it makes p(1 − p) largest, and must be between 0 and 100. Margin must be above zero.

Common mistakes

• Counting people you contacted instead of people who answered. The result is the number of completed responses, so divide by your expected response rate to find how many invitations to send.
• Typing the margin as 0.05. The field is a percentage, so ±5% is 5.
• Choosing a proportion other than 50 without evidence. If you have no earlier estimate, leave it at 50, which gives the largest and safest sample. A proportion of 0 or 100 produces a size of 0, which is not a usable plan.
• Entering a confidence level such as 97 and expecting an answer. Only 80, 85, 90, 95 and 99 are recognised; other levels show no result.
• Giving a huge population and expecting a change. For large populations the correction is negligible, so the adjusted and unadjusted sizes are almost the same.