What the Research Sample Size Calculator does
This calculator works out how many completed responses a survey or study needs to estimate a proportion or an average to the precision you choose. Enter a confidence level and a margin of error, add the population size if it is small enough to matter and your expected response rate, and it returns the completes you need, the invitations to send and the arithmetic behind both.
The method is the classic one taught in survey sampling (Cochran's formula with the finite population correction), done in your browser with every step shown, so you can paste the working straight into a methods section or an ethics application.
How to use it
- Choose whether you are estimating a proportion ("what percentage of staff would recommend us?") or a mean ("what is the average wellbeing score?").
- For a proportion, keep the expected proportion at 50% unless an earlier survey gives you a better figure. For a mean, enter the standard deviation from a pilot or a previous study.
- Pick the confidence level and the margin of error you can live with. 95% and plus or minus 5 points is a common default for organisational surveys; national polls usually aim for plus or minus 3.
- If you are sampling from a known, limited group - one company, one school, one membership list - enter its size so the finite population correction can reduce the sample.
- Enter the response rate you honestly expect. The tool divides the completes by it to tell you how many people to invite, and warns when that is more people than exist.
Reading the results
Completes is the number of usable responses you need back. Invitations is how many people you must approach to get them at your expected response rate.
The margin of error is the half-width of the confidence interval. "52% plus or minus 5 points at 95% confidence" means that if you repeated the survey many times, about 95% of the intervals built this way would contain the true value.
The table shows what precision other sample sizes buy. Precision improves with the square root of the sample, so halving the margin needs roughly four times the responses - the reason plus or minus 1 point is rarely affordable.
Worked example: a staff survey in a company of 1,200 people
An HR team wants to estimate the share of employees who would recommend the company as a place to work, to within plus or minus 5 percentage points at 95% confidence. It has no earlier figure, so it uses 50%. Past internal surveys got about a 40% response rate.
Without the population size: n0 = 1.95996 squared x 0.5 x 0.5 / 0.05 squared = 3.84146 x 0.25 / 0.0025 = 384.15.
With the finite population correction for N = 1,200: n = 384.15 x 1,200 / (384.15 + 1,199) = 460,975 / 1,583.15 = 291.18, rounded up to 292 completed responses.
At a 40% response rate the team must invite 292 / 0.40 = 730 employees. Because that is well over half the company, the calculator suggests considering a census: inviting all 1,200 costs little more and removes sampling error, though non-response still needs attention.
Formulas and scoring rules
- Proportion
n0 = z^2 x p x (1 - p) / e^2p is the expected proportion as a decimal, e the margin as a decimal (5 points = 0.05). p = 0.5 gives the largest n0.- Mean
n0 = (z x sigma / e)^2sigma is the expected standard deviation and e the margin, in the same units.- Finite population correction
n = n0 x N / (n0 + N - 1)Applied only when you enter a population size N.- Design effect and response rate
completes = ceil(n x deff); invitations = ceil(completes / response rate)Sample sizes are always rounded up to whole people.- Margin for a given sample
e = z x sqrt(p (1 - p) / n) x sqrt((N - n) / (N - 1)) x sqrt(deff)For a mean, sqrt(p (1 - p) / n) becomes sigma / sqrt(n). z is the two-sided normal quantile: 1.645 at 90%, 1.960 at 95%, 2.576 at 99%.
How this differs from an A/B test sample size
An A/B test calculator answers a different question: how many visitors per variant are needed to detect a given difference between two conversion rates with a chosen power. That is a hypothesis test between two groups, and it uses power as well as significance.
This calculator estimates one quantity - a proportion or a mean - to a stated precision. It adds what survey work needs and an experiment calculator does not: means with a standard deviation, the finite population correction for small populations, the invitations implied by a response rate, a design effect for cluster samples and a margin-of-error table. For comparing two groups, use the A/B Test Sample Size Calculator or the Statistical Power Calculator instead.
Why a bigger population barely changes the answer
For a large population the required sample hardly depends on its size: 384 completes give plus or minus 5 points whether the population is 100,000 or 100 million. The correction only bites when the sample is a noticeable fraction of the population - roughly above 5% - which is why it matters for a staff survey and not for a national poll.
Limitations: what the result does not prove
- The formulas assume a random sample. A convenience sample - whoever clicks a link on social media - has no meaningful margin of error, however many responses it collects.
- The margin covers random sampling error only. Non-response bias, coverage gaps in your list and question wording can all move the result by more than the margin.
- Sub-group results are less precise. If you want plus or minus 5 points for each of four departments, you need roughly the full sample in each department, not a quarter of it.
- For comparing two groups or testing a hypothesis, sample size depends on power and effect size; use a power calculation instead.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- NIST/SEMATECH e-Handbook - sample sizes required - checked 19 Sep 2026
- NIST/SEMATECH e-Handbook - sample sizes for a mean (7.2.2.2)
Frequently asked questions
Why is 385 the magic number for surveys?
At 95% confidence, plus or minus 5 points and an expected proportion of 50%, Cochran's formula gives 384.15, which rounds up to 385 whole people. It is the worst case for a large population; a smaller known population, a different margin or confidence level all change it.
When should I apply the finite population correction?
Whenever you know the population and the sample is more than a few per cent of it - a school, a company, a membership list. For national or very large populations it changes almost nothing, so you can leave the population field blank.
What response rate should I assume?
Use your own past surveys of the same group if you have them; that beats any general figure. Response rates vary widely by channel, audience, incentives and reminders, so plan conservatively and send reminders rather than relying on an optimistic guess.
Can I use this for an online panel or a social media poll?
Only if people were selected at random from a defined population. Self-selected samples are not random, so the margin of error does not describe their error; report them as unweighted opinions of the people who answered.
What standard deviation should I enter for a mean?
Take it from a pilot study or a published study using the same measure. Without one, the range divided by four is a rough stand-in for roughly normal data; for a 1-to-10 scale that is about 2.25. An underestimate gives a sample that is too small.
What is a design effect?
It is the factor by which a complex design, such as sampling whole classes or clinics, inflates the variance compared with a simple random sample. A design effect of 1.5 needs 50% more completes. Estimate it from earlier surveys of the same design or ask a statistician.
Does a 95% confidence level mean the result is 95% likely to be right?
Not quite. It describes the method: 95% of intervals built this way from repeated random samples would contain the true value. Any single interval either contains it or not, and non-sampling errors are not covered at all.
Last reviewed by the A2Z.Tools team against the sources listed above.
