Sample Size Calculator
Find how many responses your survey or study needs for reliable results.
Calculate your sample size
This free tool is for survey makers, students, researchers and small businesses planning a poll or study. It needs no sign-up, and it runs entirely in your browser.
Your required sample size
Sample size for every margin of error
Same confidence level, same proportion and same population, with the margin of error running from 1% to 10%. Your selected margin is highlighted.
How sample size works
Sample size is the number of completed responses you need before your survey result is precise enough to trust. A larger sample gives a smaller margin of error, but the benefit shrinks as the sample grows, because the margin falls with the square root of the sample size. This calculator uses the standard proportion formula, with the finite population correction when you enter a population size.
How many responses does a survey need?
It depends on the confidence level, the margin of error you will accept, and the size of the population. For a typical survey at 95 percent confidence with a 5 percent margin of error and no known population size, the answer is 385 responses. Smaller margins and higher confidence levels need many more responses.
The formula behind that answer traces back to Jerzy Neyman, who introduced confidence intervals in a 1937 paper in the Philosophical Transactions of the Royal Society. The same mathematics still underpins modern survey design.
What is the sample size formula?
For a proportion, the starting sample size is the squared critical value times the proportion times one minus the proportion, divided by the squared margin of error. If the population is small and known, apply the finite population correction, which divides that figure by one plus the starting size minus one over the population size.
Worked example: at 95% confidence the critical value is 1.96, the proportion is 50% and the margin is 5%. The starting size is 1.96 squared times 0.25, divided by 0.05 squared, which is 384.16, rounded up to 385.
Why is 50 percent the safest proportion to use?
A proportion of 50 percent gives the largest possible sample size, because the product of the proportion and one minus the proportion is at its maximum there. If you have no idea what share of people will answer a certain way, planning for 50 percent guarantees your sample is large enough for any other result.
If you already know the share is near 10% or 90%, you can enter that figure instead and the required sample will be smaller. Only do that when you have solid evidence from earlier research.
How does population size change the sample size?
For very large populations, the population size hardly matters, and the sample size stays near the figure for an unlimited population. For small populations, the correction matters a lot. A population of 1,000 needs only 278 responses at 95 percent confidence and a 5 percent margin, instead of 385 for an unlimited population.
That is why a survey of a small company, school or club needs far fewer replies than a national poll, even at the same confidence level and margin of error.
What happens if fewer people respond than planned?
Your margin of error grows, because it depends on the number of completed responses, not the number of invitations sent. If you need 385 completed surveys, you should invite more people than that to allow for non response. As a rule, invite at least a third more people than the number of replies you need.
Sample sizes at 95% confidence, 50% proportion
| Margin of error | Sample size needed | Typical use |
|---|---|---|
| 1% | 9,604 | National polls with very high precision |
| 3% | 1,068 | Detailed market research |
| 5% | 385 | Most surveys and polls |
| 10% | 97 | Quick checks and pilot studies |
Frequently asked questions
What is a good sample size for a survey?
For most surveys, 385 completed responses at 95% confidence and a 5% margin of error is a solid target. Smaller studies can use fewer responses if a wider margin is acceptable.
Does the population size matter for a national survey?
Almost never. Once the population passes about 20,000, the required sample is practically the same as for an unlimited population. Population size only matters for small, known groups.
What if I do not know the proportion in advance?
Use 50%, which is the default in this calculator. It gives the largest sample size, so your survey stays precise whatever the true result turns out to be.
Why is the answer rounded up?
Sample size must be a whole number of people, and rounding down would give a margin slightly larger than the one you asked for. Rounding up guarantees the margin you chose.
How do I handle people who do not reply?
Send more invitations than the sample size shown. If you expect a 50% response rate and need 385 replies, invite about 770 people. Check the response rate as replies arrive.
Is this calculator for means as well as proportions?
This calculator is proportion based, which covers most surveys and polls. For a mean, you need the standard deviation as well. Find the interval for a mean with our Confidence Interval Calculator.
Does this calculator store my data?
No. The calculator runs entirely in your browser. Nothing you type is uploaded, stored or shared.
More tools you may need
Once you know the sample size, check the result with the Confidence Interval Calculator and the Margin of Error Calculator. For single values, use the Z-Score Calculator, the Standard Deviation Calculator and the P-Value Calculator.
