How many people are enough for a survey?

For a large population, about 385 responses give 95% confidence with ±5% margin and about 1,068 give ±3%. For a small population the correction reduces the number. If subgroups are reported separately, calculate for each subgroup.

What should I enter if I do not know the expected proportion?

Enter 50%. The product p(1−p) is largest at 50%, so it gives the safest (largest) sample. If you have an estimate from an earlier survey or a pilot, entering it can reduce the sample.

My population is 100,000 or a million; does it change the result?

Hardly at all. Once the population is above a few hundred thousand the required number is very close to the infinite-population value (385 for 95/5/50). Population size only matters for small populations.

What if the response rate is low?

Find invitations as n / response rate, but remember this does not remove non-response bias. Send reminders, shorten the survey and check whether respondents represent the population on known traits (region, sector, size).

Does the same margin of error apply to every question?

No. The margin is calculated for proportion questions at the chosen proportion; it is widest for answers near 50% and narrower at the extremes. For numeric (mean) questions the deviation depends on the variable's standard deviation, which this tool does not calculate.

Does it also apply to quota, stratified or cluster sampling?

No, only to simple random sampling. Stratified sampling reaches the same margin with fewer responses, cluster sampling usually needs more (design effect). For complex designs multiply by the design effect or consult a statistician.

Survey sample size calculator

Find how many people to survey: enter the population size, confidence level, margin of error and expected proportion; the finite-population correction and the number of invitations from your expected response rate are worked out for you. Or see the margin of error of the responses you already have.

Free tool · Data analytics

What should we calculate?

Required sample sizeMargin of error for the responses I have

Population size N

The total number of people who could be surveyed (customer list, headcount…). Leave empty to treat the population as very large or unknown.

Confidence level (%)

How often the result would fall within the margin if we repeated the same survey. Any value from 50 to 99.99 can be entered.

Quick pick:

Margin of error (±%)

The largest deviation you accept in the result, in percentage points. The sample grows quickly as it shrinks.

Expected proportion (%)

The estimated share who will answer "yes". If you do not know it, enter 50%: it gives the largest (safest) sample.

Expected response rate (%)

How many of those invited will answer? Empty counts as 100% (invitations = sample).

The calculation runs in your browser; the values you enter are not sent anywhere.

Results

Required sample size n: 385
People to invite: 385
n₀ for an infinite population: 384.15
z value: 1.960

The population was left empty and is treated as infinite; no correction.

With a 100% response rate you must invite at least 385 people to get 385 responses.

Sensitivity table

With the same population and expected proportion, the sample needed for each margin of error and confidence level (response rate is not applied).

Required sample size by margin of error and confidence level
Margin	Confidence 90%	Confidence 95%	Confidence 99%
±1%	6,764	9,604	16,588
±2%	1,691	2,401	4,147
±3%	752	1,068	1,844
±4%	423	601	1,037
±5%	271	385	664
±7.5%	121	171	295
±10%	68	97	166

z = Φ⁻¹(1 − (1 − confidence)/2) · n₀ = z²·p(1−p) / e² · n = n₀ / (1 + (n₀ − 1)/N) · invitations = n / response rate · e = z·√( p(1−p)/n · (N−n)/(N−1) )

The calculation assumes simple random sampling and no non-response bias. With stratified or cluster sampling, weighting and subgroup analysis (each subgroup has its own margin) the required number changes. Results are rounded up. This tool is a planning aid.

Let us design your survey, the sampling plan and how the results become decisions, together.

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How to use

A
Enter the population size (if you know it), confidence level, margin of error and expected proportion; if unsure start with 95%, 5% and 50%.
B
Read the required sample size and the number of people to invite for your expected response rate.
C
Choose the "margin of error" mode to see the margin for the responses you already have; compare other targets in the sensitivity table.

Margin of error, confidence level and expected proportion

The margin of error says how far a survey result can deviate from the true population value, in percentage points. ±5% at 95% confidence means "if we ran the same survey many times, about 95% of the results would fall within 5 points of the true value"; it does not mean one given survey is 95% likely to be right.

The required sample is proportional to p(1−p) and is largest at p = 50%, so entering 50% is the safe route when you do not know the proportion. Halving the margin of error roughly quadruples the sample; raising the confidence from 95% to 99% needs about 73% more responses.

When does the finite-population correction help?

If the population is small (a few hundred) and the sample is a meaningful part of it, the result is more precise than the infinite-population formula suggests, and the correction reduces the number needed. For example at 95% confidence, ±5% and a 50% proportion an infinite population needs 385 people; a population of 1,000 needs 278.

As the population grows the correction loses its effect: a population of 100,000 still needs about 383. So for large populations the sample is almost independent of the population size.

Response rate and non-response bias

Not everyone invited will answer. If the required sample is n and the response rate is 20%, you must invite at least n / 0.20 = 5n people. But sending more invitations does not remove non-response bias: if respondents differ systematically from non-respondents, the margin of error does not show that deviation.

With low response rates, reminders, a short survey, a suitable channel and, where possible, a small follow-up sample of non-respondents to test for bias are worth more.

FAQ

How many people are enough for a survey?: For a large population, about 385 responses give 95% confidence with ±5% margin and about 1,068 give ±3%. For a small population the correction reduces the number. If subgroups are reported separately, calculate for each subgroup.
What should I enter if I do not know the expected proportion?: Enter 50%. The product p(1−p) is largest at 50%, so it gives the safest (largest) sample. If you have an estimate from an earlier survey or a pilot, entering it can reduce the sample.
My population is 100,000 or a million; does it change the result?: Hardly at all. Once the population is above a few hundred thousand the required number is very close to the infinite-population value (385 for 95/5/50). Population size only matters for small populations.
What if the response rate is low?: Find invitations as n / response rate, but remember this does not remove non-response bias. Send reminders, shorten the survey and check whether respondents represent the population on known traits (region, sector, size).
Does the same margin of error apply to every question?: No. The margin is calculated for proportion questions at the chosen proportion; it is widest for answers near 50% and narrower at the extremes. For numeric (mean) questions the deviation depends on the variable's standard deviation, which this tool does not calculate.
Does it also apply to quota, stratified or cluster sampling?: No, only to simple random sampling. Stratified sampling reaches the same margin with fewer responses, cluster sampling usually needs more (design effect). For complex designs multiply by the design effect or consult a statistician.

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