How to work out survey sample size

By Thisys team · Last reviewed 7 October 2026

The number of responses you need depends on three things: how precise the result must be, how sure you want to be, and, for small populations, how many people there are. Here is the standard formula, a table you can use straight away, and the problems that matter more than the maths.

Three terms first

Margin of error: how far the survey's result could be from the true value for the whole population. ±5 percentage points is a common choice.
Confidence level: how sure you want to be that the true value lies within that margin. 95% is the usual choice.
Population: everyone the result should describe, such as all your customers or all your staff.

The formula

For a percentage, such as the share of people who agree with something, the standard formula is:

n₀ = z² × p × (1 − p) ÷ e²

z is 1.96 for 95% confidence (2.576 for 99%). p is the share you expect; use 0.5 if you do not know, which gives the largest and safest number. e is the margin of error as a decimal: 0.05 for ±5 points.

Worked example: 95% confidence, ±5 points, p unknown

1.96² × 0.5 × 0.5 ÷ 0.05²
= 3.8416 × 0.25 ÷ 0.0025
= 384.16, so 385 completed responses. Always round up.

Correcting for a small population

When the population is small, you need fewer responses. The finite population correction is:

n = n₀ ÷ (1 + (n₀ − 1) ÷ N)

N is the population size.

Worked example: A workplace of 1,000 staff, ±5 points

384.16 ÷ (1 + 383.16 ÷ 1,000)
= 384.16 ÷ 1.38316
= 277.7, so 278 completed responses.

For a population in the tens of thousands or more, the correction barely changes the answer, which is why 385 is quoted so often.

Sample size table

Completed responses needed at 95% confidence, with p = 0.5
Population	±10 points	±5 points	±3 points
100	50	80	92
200	66	132	169
500	81	218	341
1,000	88	278	517
2,000	92	323	697
5,000	95	357	880
10,000	96	370	965
100,000	96	383	1,056
Very large (no correction)	97	385	1,068

With a small population a census often makes more sense than a sample. With 100 people you need 80 of them for ±5 points, so invite everyone.

From responses to invitations

People to invite = responses needed ÷ expected response rate

Worked example: 278 responses needed, and you expect 30% of people to answer

278 ÷ 0.30 ≈ 927 invitations.
With a population of 1,000, that means inviting almost everyone anyway.

Use your own past response rates where you have them. They vary a great deal by audience, channel and topic.

Groups need numbers of their own

The margin of error applies to the whole sample. If you will compare groups, each group needs enough responses on its own. A group of 50 has a margin of about ±14 points at 95% confidence, so small differences between groups that size are rarely meaningful.

What the formula cannot fix

Non-response bias: if the people who answer differ from the people who do not, more responses will not correct it.
A sample that is not random: a link shared on social media reaches whoever happens to see it, and the formula assumes a random sample.
Poorly worded questions: a precise measure of the wrong thing is still wrong.
Scores built from two shares, such as NPS, have a wider margin than a single percentage; the NPS guide gives its formula.

Use this template

Each opens its own page, where you can preview every question before you use it.

Use cases: Academic research questionnaires and Panel & longitudinal studies.

Sources and notes

The formula and the finite population correction: William G. Cochran, Sampling Techniques, 3rd edition, Wiley, 1977.

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