The short answer
For most surveys you need about 385 completed responses. That gives you 95% confidence with a 5% margin of error, no matter how large your population is.
If your population is small, you need fewer. A group of 500 people needs 218 responses; a group of 1,000 needs 278. Want a tighter 3% margin of error? Then plan for roughly 1,068 responses.
The tables below show the exact numbers for every common population size. For your own numbers, use our free Raosoft sample size calculator.
Sample size table by population size
Find your population size in the first column. Each other column is the minimum number of completed responses for that confidence level and margin of error. All values assume a 50% response distribution, the safest choice when you don’t know how people will answer.
| Population size | 95% conf., ±5% | 95% conf., ±3% | 90% conf., ±5% | 99% conf., ±5% | 95% conf., ±10% |
|---|---|---|---|---|---|
| 100 | 80 | 92 | 74 | 88 | 50 |
| 200 | 132 | 169 | 116 | 154 | 66 |
| 300 | 169 | 235 | 143 | 207 | 73 |
| 500 | 218 | 341 | 176 | 286 | 81 |
| 1,000 | 278 | 517 | 214 | 400 | 88 |
| 2,000 | 323 | 697 | 239 | 499 | 92 |
| 5,000 | 357 | 880 | 257 | 586 | 95 |
| 10,000 | 370 | 965 | 264 | 623 | 96 |
| 20,000 | 377 | 1,014 | 267 | 643 | 96 |
| 100,000 | 383 | 1,056 | 270 | 660 | 96 |
| 1,000,000+ | 385 | 1,068 | 271 | 664 | 97 |
Three things the table shows
- Population size stops mattering above about 20,000. Surveying a city of 100,000 or a country of 17 million takes almost the same sample.
- The margin of error drives the cost. Going from ±5% to ±3% nearly triples the sample (385 to 1,068).
- Small groups need a large share. With 100 people you must reach 80 of them, so a census is often easier.
How the sample size is calculated
The numbers come from Cochran’s formula, the same method the Raosoft calculator uses. First you calculate the sample for an unlimited population:
n_0 = \frac{Z^2 \cdot p(1-p)}{E^2}Here Z is the z-score for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the response distribution (0.5 if unknown) and E is the margin of error as a decimal (0.05 for 5%).
Then you apply the finite population correction, where N is your population size:
n = \frac{n_0}{1 + \frac{n_0 - 1}{N}}Worked example. At 95% confidence and ±5%, n0 = 1.96² × 0.25 / 0.05² = 384.16. For a population of 1,000, n = 384.16 / (1 + 383.16 / 1,000) = 277.8. Always round up, so you need 278 responses.
How many people should you invite?
The sample size is the number of completed responses, not invitations. Divide it by your expected response rate to know how many people to contact.
| Expected response rate | Invitations needed for 385 responses |
|---|---|
| 50% (internal staff survey) | 770 |
| 30% (customer email survey) | 1,284 |
| 20% (newsletter or online panel) | 1,925 |
| 10% (cold outreach) | 3,850 |
Add a 10–20% buffer for incomplete or unusable answers.
Common sample size mistakes
- Counting invitations instead of responses. 385 emails sent is not 385 answers.
- Ignoring subgroups. If you want to compare men and women, each group needs its own sample size.
- Using a convenience sample. The formula assumes random sampling. A large but biased sample is still wrong.
- Picking 10% margin of error to save money. Results within ±10 points rarely support a decision.
- Applying it to qualitative research. Interviews and focus groups work with data saturation, not this formula.
Frequently asked questions
Is 100 responses enough for a survey?
Only for a small population. For a group of up to about 130 people, 100 responses can reach ±5% at 95% confidence. For a large population, 100 responses gives a margin of error of about ±9.8%.
Is 385 always the right sample size?
It is the standard minimum for a large population at 95% confidence and ±5%. Smaller populations need fewer; tighter margins or higher confidence need more.
What is the minimum sample size for a student research project?
Use the table with your actual population, such as the number of students in your faculty. Most supervisors accept 95% confidence and ±5%.
What if I don’t know my population size?
Use the 1,000,000+ row or leave the field empty in the calculator. Above 20,000 the result barely changes.
Does a bigger sample always mean better results?
No. Beyond the required size, extra responses add little precision. Sampling quality and question design matter more.
Calculate your exact sample size
The table covers the common cases. For your own population, confidence level and margin of error, use the free Raosoft sample size calculator. It also works in reverse: enter the responses you collected and see your achieved margin of error.
