Find out how many people you need to survey. Choose a confidence level and margin of error, optionally the size of the population you are sampling from, and get the number of responses required. Switch modes to see the margin of error of a sample you already collected.
n₀ = z² × p(1 − p) ÷ e². Using p = 50 % gives the largest, safest sample; if you know the proportion is near 10 % or 90 % the sample can be much smaller.
📌 For proportions (yes/no answers, conversion rates, defect rates). Assumes a random sample; response rates below 100 % mean you must invite more people than the sample size. For means, use n = (z × σ ÷ e)² with your estimated standard deviation.
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Sample size at 95 % confidence (p = 50 %)
Margin of error
Large population
Population 100,000
Population 10,000
±1 %
9,604
8,763
4,899
±2 %
2,401
2,345
1,936
±3 %
1,068
1,056
965
±5 %
385
383
370
±10 %
97
96
96
Halving the margin of error quadruples the sample. At 99 % confidence multiply by about 1.73; at 90 % by 0.70.
The formula
n₀ = z² × p × (1 − p) ÷ e²
n = n₀ ÷ (1 + (n₀ − 1) ÷ N) (finite population correction)
margin of error = z × √(p(1 − p) ÷ n)
Example: 95 % confidence (z = 1.96), ±5 % margin, p = 0.5: n₀ = 1.96² × 0.25 ÷ 0.05² = 384.16 → 385 responses. For a customer base of 1,000: 384.16 ÷ (1 + 383.16 ÷ 1000) = 277.0 → 278. A finished survey of 400 responses has a margin of ±1.96 × √(0.25 ÷ 400) = ±4.9 %.
For the standard 95 % confidence and ±5 % margin of error, 385 responses from a large population. Tightening to ±3 % needs 1,068; ±2 % needs 2,401. If the population is small the number drops: 370 for a population of 10,000, 278 for 1,000, 80 for 100. Enter your own targets above.
If 52 % of your sample say yes with a ±5 % margin at 95 % confidence, the true share in the population is between 47 % and 57 %, and a survey repeated many times would capture the true value in 95 % of runs. Confidence level sets how sure you want to be; margin of error sets how precise.
The term p(1 − p) is largest at p = 0.5, so 50 % gives the biggest, safest sample size. If you know the answer is lopsided — say 10 % of customers churn — set 10 % and the required sample falls by almost two thirds. Use 50 % when you have no prior information.
Only when the sample is a noticeable fraction of it. For a country, a city or a customer base of a million, the population is effectively infinite and 385 is enough for ±5 %. For a company of 200 employees the finite population correction brings the sample to 132. That is why national polls of 1,000 people work.
The calculator gives the number of completed responses. If you expect 20 % of invitees to answer, invite five times as many: 385 responses needs about 1,925 invitations. Low response rates can also bias results if non-responders differ from responders.