Sample Size Calculator

Determine the required sample size for surveys given confidence level, margin of error, and population.

Sample Size Calculator tool

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Example

Input: 95% confidence, 5% margin of error, 50% population proportion, population size 0 (infinite)

Result: Required sample size 385 (unadjusted 384.16, z = 1.96)

n = z^2 x p x (1 - p) / e^2 = 1.96^2 x 0.5 x 0.5 / 0.05^2 = 0.9604 / 0.0025 = 384.16, rounded up to 385.

Sample Size by Margin of Error

Margin of error90% confidence95% confidence99% confidence
1%6,7669,60416,590
2%1,6922,4014,148
3%7521,0681,844
4%4236011,037
5%271385664
10%6897166

Large or unknown population, 50% proportion. A smaller population needs fewer responses.

  1. Select your desired confidence level from the options - 90%, 95%, or 99%.
  2. Set the acceptable margin of error as a percentage, such as 3% or 5%, and keep the population proportion at 50% unless you have a better estimate.
  3. Enter the total population size if known, or leave it at 0 for a large or unknown population.
  4. Review the calculated minimum sample size required to achieve statistically valid results.
  5. Adjust the confidence level and margin of error to see how they trade off against the required sample size.

How Many Survey Responses Do You Need?

For a survey with a 95% confidence level and a 5% margin of error, you need 385 responses from a large population. This calculator works out that minimum for your own settings. Choose the confidence level and the margin of error. Then add the expected proportion and the population size if you know them.

The two main settings set the precision. The margin of error is how far the survey result may sit from the true value. With a result of 60% and a margin of 5%, the true figure is likely between 55% and 65%. The confidence level says how sure you can be of that range. At 95%, about 95 out of 100 surveys run the same way would capture the true value. Tighter margins cost a lot. Halving the margin from 5% to 2.5% raises the sample from 385 to 1,537.

The expected proportion is your best guess at the answer, such as the share of people who will say yes. Leaving it at 50% is the safe choice, because it gives the largest sample. If you expect about 20%, the sample drops to 246. Population size matters only for small groups. The tool applies a finite population correction. A group of 1,000 needs 278 responses and a group of 500 needs 218. Beyond about 20,000 people, the answer barely changes from 385.

The formula assumes a simple random sample, where everyone has an equal chance of being picked. It does not fix bias from who chooses to reply, and it covers yes or no style answers, not averages. Plan for non-response too. If you need 385 replies and expect a quarter of people to answer, invite at least 1,540. The z-scores behind each confidence level come from the Normal Distribution Calculator.

Formula / How It Works

n = (z^2 x p x (1-p)) / e^2 | Finite correction: n_adj = n / (1 + (n-1)/N) | z(95%) = 1.96, z(99%) = 2.576

Frequently Asked Questions

It means that if you ran the same survey many times, about 95% of the results, each with its margin of error, would contain the true value. It does not mean there is a 95% chance your one result is exactly right. Higher confidence needs more responses: 99% needs 664 for a 5% margin, against 385 at 95%.
It is the plus or minus range around a survey result. A result of 60% with a 3% margin means the true value is likely between 57% and 63%. Smaller margins need much bigger samples. At 95% confidence, a 3% margin needs 1,068 responses, while 5% needs 385.
Only for small populations. For a large or unknown population, 385 responses give a 5% margin at 95% confidence. A population of 1,000 needs 278, and 500 needs 218. Above about 20,000 the answer hardly changes, so a national poll and a city poll need similar sample sizes.
It uses n = z^2 x p x (1 - p) / e^2, where z is 1.645, 1.96 or 2.576 for 90%, 95% or 99% confidence. Here p is the expected proportion and e is the margin of error as a decimal. With a population size N, it adjusts to n / (1 + (n - 1) / N) and rounds up.
Because p x (1 - p) is largest when p is 0.5, so 50% gives the biggest, safest sample size. If you have solid data from a past survey, you can use it instead. Expecting 20% cuts the need from 385 to 246 responses at 95% confidence and a 5% margin.

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