Sample Size Calculator
Calculate the minimum sample size required for a statistically valid survey or experiment. Specify confidence level, margin of error, and population size.
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How to use this calculator
n is the infinite-population sample size. n_adj applies a finite population correction when population size N is known.
- 1
Select your target confidence level (95% is the research standard).
- 2
Enter the acceptable margin of error — 5% is typical for surveys.
- 3
Leave response distribution at 50% if unknown (most conservative estimate).
- 4
Enter the population size if finite, or leave 0 for a large/unknown population.
Frequently asked questions
Which formula does the calculator use?
Cochran’s formula for estimating a proportion: n₀ = z² · p(1 − p) ÷ e², rounded up to the next whole number. With the defaults (95%, ±5%, p = 50%) that is 1.96² × 0.25 ÷ 0.0025 = 384.16, shown as 385. The z values are fixed at 1.645, 1.96 and 2.576 for 90%, 95% and 99% confidence; they are rounded versions of the exact normal quantiles.
What does the population size field do?
Leave it at 0 for an unknown or very large population. If you enter N, the finite-population correction n = n₀ ÷ (1 + (n₀ − 1) ÷ N) is applied and rounded up. For 95%, ±5% and 50%, N = 1,000 needs 279 responses, N = 200 needs 132 and N = 100 needs 80, never more than the population itself. At N = 100,000 the answer is 384, almost the same as 385.
Why is 50% the default response distribution?
p(1 − p) is largest at p = 0.5, so 50% gives the biggest, most cautious sample size. If earlier research suggests the share is nearer 10%, entering 10 cuts the 95%/±5% requirement from 385 to 139. Only lower p if you are confident, because if the true share is closer to 50% your margin of error will be wider than planned. The field takes a percentage strictly between 0 and 100.
Is the margin of error in percent or percentage points?
Percentage points on a proportion: ±5 means the estimated share of "yes" answers could be about 5 points either side of the sample value at the chosen confidence. The calculator is built for yes/no or categorical survey questions. It does not size a study for estimating an average, which would need an expected standard deviation.
Does this account for non-response?
No. The result is the number of completed, usable responses required, assuming a simple random sample. If you expect only a fraction to reply, divide the result by that expected response rate to find how many people to contact. Self-selected or convenience samples can be biased no matter how large they are.
Can I use it to plan an A/B test or a clinical trial?
No. It has no power calculation, effect size or baseline-versus-variant comparison. Detecting a difference between two groups usually needs far larger samples than estimating a single proportion to the same margin. Use a dedicated power calculation for experiments.
Does the margin of error apply to subgroups?
Only to the whole sample. If 385 people answer and you look at one segment of 77, the margin for that segment is much wider than ±5%. To report subgroups with the same precision, size each subgroup separately.
What input values are rejected?
Margin of error must be above 0% and below 100%, and the response distribution must be above 0% and below 100%, since p = 0 or 100 would give a sample size of 0. Confidence level is a three-option choice (90%, 95%, 99%).
Sample size calculator for survey proportions
Three inputs drive the answer
For a yes/no question, the required sample depends on how much confidence you want, how narrow a margin you will tolerate, and how evenly split the answers are likely to be. The calculator applies z² · p(1 − p) ÷ e² and rounds up. Halving the margin of error multiplies the requirement by about four, because e is squared in the denominator. Raising confidence from 90% to 99% increases it too, through z.
| Confidence | Margin of error | Sample size |
|---|---|---|
| 90% | ±5% | 271 |
| 95% | ±5% | 385 |
| 95% | ±3% | 1,068 |
| 95% | ±2.5% | 1,537 |
| 95% | ±1% | 9,604 |
| 99% | ±3% | 1,844 |
Worked example: a customer survey
A company with 1,000 customers wants 95% confidence and ±5% on a satisfaction question, with no idea of the split. The infinite-population figure is 385, but the correction for N = 1,000 brings the requirement down to 279. A smaller client list of 200 needs only 132, and a list of 100 needs 80. In each case the calculator never asks for more people than exist, and it still shows the uncorrected 385 beside the adjusted figure.
Worked example: when the population barely matters
Using the same 95% and ±5% settings, a population of 5,000 still needs 358 responses, and a population of 100,000 needs 384. Past a few thousand, only the margin and confidence matter. That is why national polls and city polls often use similar sample sizes. The correction only becomes important when the sample would be a sizeable share of the population.
Choosing the response distribution
Use 50% unless you have good evidence. If a previous wave suggested only about 10% of people hold an opinion, setting p = 10 cuts the 95%/±5% requirement from 385 to 139. The saving is real but risky: if the true share is closer to 50% than you assumed, the realised margin will exceed ±5%. Pilot data are the best justification for lowering p.
What the number does not cover
The figure assumes random selection and complete answers. Non-response, poorly worded questions, and a sampling list that misses part of the population produce errors that more respondents will not fix. Estimating an average, comparing two groups, or detecting a small effect requires different calculations, and this tool does not perform them.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →