Sample Size Calculator
Survey sample size from the confidence level, margin of error and expected proportion, or the margin of error for a sample you have: 95% and ±5% need 385. How it works
Use the Sample Size Calculator
About the Sample Size Calculator
A survey needs 385 completed responses for a ±5% margin of error at 95% confidence when the population is large and you expect a 50% split. The sample size calculator applies Cochran’s formula to your confidence level, margin and expected proportion, then reduces the figure with the finite population correction if you enter a population size. Set Solve for to Margin of error and it works the other way: 1,013 responses at 95% confidence give ±3.08%.
Sample size by confidence level and margin of error
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±10% | 68 | 97 | 166 |
| ±5% | 271 | 385 | 664 |
| ±3% | 752 | 1,068 | 1,844 |
| ±2% | 1,692 | 2,401 | 4,148 |
| ±1% | 6,766 | 9,604 | 16,590 |
For a large population and an expected proportion of 50%, which gives the largest sample.
Sample size for a known population (95% confidence)
| Population | ±5% margin | ±3% margin |
|---|---|---|
| 100 | 80 | 92 |
| 500 | 218 | 341 |
| 1,000 | 279 | 517 |
| 2,000 | 323 | 697 |
| 5,000 | 358 | 881 |
| 10,000 | 371 | 966 |
| 100,000 | 384 | 1,057 |
Expected proportion 50%. The tool rounds n₀ up before the correction, so a figure can be one above a calculator that corrects the unrounded value.
Margin of error by sample size
| Completed responses | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| 100 | ±8.22% | ±9.8% | ±12.88% |
| 200 | ±5.82% | ±6.93% | ±9.11% |
| 400 | ±4.11% | ±4.9% | ±6.44% |
| 500 | ±3.68% | ±4.38% | ±5.76% |
| 1,000 | ±2.6% | ±3.1% | ±4.07% |
| 1,500 | ±2.12% | ±2.53% | ±3.33% |
| 2,000 | ±1.84% | ±2.19% | ±2.88% |
| 5,000 | ±1.16% | ±1.39% | ±1.82% |
Solve for: Margin of error, expected proportion 50%, large population. E = z × √(p × (1 − p) ÷ n), shown to two decimals as the tool does.
How to use this tool
- Leave Population Size empty for a large or unknown population, or enter the number of people you could survey.
- Choose 90%, 95% or 99% confidence and type the margin of error in percent.
- Keep the expected proportion at 50% unless an earlier survey gives a better estimate. The sample size updates as you type.
- To find the margin of error for a sample you already have, set Solve for to Margin of error and type the sample size instead of the margin.
Frequently asked questions
- What sample size do I need for a population of 1,000?
- 279 completed responses for ±5% at 95% confidence, and 517 for ±3%. Without the population size the figures would be 385 and 1,068, so for a group this small the correction cuts the work by more than a quarter.
- What expected proportion should I use if I have no idea?
- Use 50%. The term p × (1 − p) is largest at 0.5, so 50% gives the biggest sample and covers any answer. If an earlier survey found about 20%, entering 20 lowers the 95%, ±5% figure from 385 to 246.
- Does population size matter for a large population?
- Very little once it is large. At 95% and ±5% a population of 10,000 needs 371 and one of 100,000 needs 384, against 385 for an unlimited one. It matters most when the sample would be a sizeable share of everyone, as with 500 people, who need 218.
- Is the sample size the number of people to invite?
- No, it is the number of completed responses. Divide it by the response rate you expect: 385 responses at a 20% response rate means inviting about 1,925 people. The formula also assumes those who answer are a random sample of the population.
- Why does a smaller margin of error need so many more responses?
- The margin is squared in the formula, so halving it multiplies the sample by four. At 95% confidence ±10% needs 97, ±5% needs 385 and ±2% needs 2,401.
- What is the margin of error for a sample of 1,000?
- ±3.1% at 95% confidence with a 50% proportion and a large population; ±2.6% at 90% and ±4.07% at 99%. The formula is E = z × √(p × (1 − p) ÷ n). From a population of 300,000, 72,000 responses give ±0.32%, because the finite population correction √((N − n) ÷ (N − 1)) shrinks the margin when the sample is a large share of everyone.
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