Survey Sample Size Calculator

How it is calculated

The tool first computes the sample size for a very large population, then shrinks it if you give a population size: n₀ = z² × p × (1 − p) ÷ e² and n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Here e is the margin of error as a fraction (5 % = 0.05), p the expected proportion as a fraction (50 % = 0.5), and N the population. The z value is 1.645 for 90 %, 1.96 for 95 % and 2.576 for 99 % confidence; any other level falls back to 1.96. A proportion that is empty or outside 0–100 is replaced by 50 %, the most cautious choice. Results are always rounded up to a whole person. Leave the population at 0 for a very large or unknown group. A margin of zero or 100 % or more gives no result.

Common mistakes

• Reading the margin of error as a percentage of the sample rather than percentage points around the result. A 5 % margin on a 50 % result means roughly 45 % to 55 %.
• Counting invitations instead of completed responses. The figure is the number of usable answers you need, so if only 20 % reply, you must contact about five times as many people.
• Entering a made-up expected proportion. If you do not know it, keep 50 %, which gives the largest and safest size. Choosing 10 % with no basis can understate what you need.
• Typing a population that is only a rough guess when it is actually very large. Above a few tens of thousands the correction barely changes anything, so 0 and a large number give almost the same answer.
• Expecting a different confidence level from a box that offers only 90, 95 and 99 %. Another value is treated as 95 %.