Find how many responses you need for a reliable survey.
For 95% confidence and a ±5% margin of error you need about 385 responses (using p = 50%), whatever the size of a large population.
Sample size is the number of people you must survey to get results you can trust. Choose a confidence level and margin of error, optionally the expected proportion and the population size, and the calculator gives the required sample size using Cochran's formula with the finite-population correction. A second tool does the same for estimating an average from the standard deviation.
Bigger samples shrink the margin of error, but with diminishing returns — halving it needs four times the sample. After collecting data, use the Confidence Interval Calculator, Z-Score Calculator and P-Value Calculator. To draw a random sample try the Random Number Generator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Confidence level | 95% |
| z-score | 1.959964 |
| Margin of error | 5% |
| Expected proportion | 50% |
| Sample size for a very large population | 385 |
| Setting | Sample size |
|---|---|
| 90% confidence | 271 |
| 95% confidence | 385 |
| 99% confidence | 664 |
| 95%, ±3% margin | 1,068 |
| 95%, population 1,000 | 278 |
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±10% | 68 | 97 | 166 |
| ±5% | 271 | 385 | 664 |
| ±3% | 752 | 1,068 | 1,844 |
| ±2% | 1,691 | 2,401 | 4,147 |
| ±1% | 6,764 | 9,604 | 16,588 |
For a ±5% margin of error at 95% confidence, about 385 for a large population; fewer for small populations.
It maximises p(1 − p), so it gives the largest, safest sample size when you have no estimate.
The maximum expected difference between the survey result and the true population value, at a given confidence level.
An adjustment that reduces the sample size when the sample is a large share of a small population.
Only for small populations. Beyond about 20,000, the required sample barely changes.
Higher confidence needs more responses: 90% needs 271, 95% needs 385 and 99% needs 664 at ±5%.
It uses the standard method: n = z² p(1 − p) ÷ e² corrected n = n₀ ÷ (1 + (n₀ − 1) ÷ N) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
