How this sample size is calculated
For a proportion, the calculator uses Cochran's formula, n₀ = z²·p(1 − p)/e², where z comes from your confidence level (1.645, 1.960 or 2.576), p is the proportion you expect and e is the margin of error as a decimal. For a mean it uses n₀ = (z·σ/e)². If you enter a population size, the finite population correction shrinks n₀; if you enter a response rate, it tells you how many people to invite.
This sizes a study for precision. If your goal is to show that two groups differ, or that a correlation is non-zero, use the power analysis calculator instead: precision and power answer different questions.
Sample size table (95% confidence, p = 50%)
| Margin of error | N = 100 | 500 | 1,000 | 10,000 | Very large |
|---|---|---|---|---|---|
| ±10% | 50 | 81 | 88 | 96 | 97 |
| ±5% | 80 | 218 | 278 | 370 | 385 |
| ±3% | 92 | 341 | 517 | 965 | 1,068 |
| ±2% | 97 | 414 | 707 | 1,937 | 2,401 |
| ±1% | 99 | 476 | 906 | 4,900 | 9,604 |
The table uses the confidence level selected above. Notice the diminishing returns: halving the margin of error needs four times the sample, and beyond a population of about 10,000 the population size barely matters.
Choosing the inputs
- Confidence level. 95% is the convention in most fields. 99% roughly adds 70% to the sample size.
- Margin of error. ±5 points is typical for opinion surveys; ±3 for published polls; ±10 is acceptable for exploratory pilots.
- Expected proportion. 50% is the worst case. Use a prior estimate when you have one.
- Response rate. Online surveys of the general public often return 10–30%. Plan invitations accordingly and report the achieved rate.
For stratified or cluster samples, multiply the result by the design effect (often 1.5–2 for cluster designs) before recruiting.
Frequently asked questions
What sample size do I need for a survey?
For a population proportion at 95% confidence and a ±5% margin of error, the conservative answer (p = 0.5) is 385 completed responses for a large population. For a population of 1,000 the finite population correction brings that down to 278. Divide by your expected response rate to get the number of invitations.
Why use 50% as the expected proportion?
p(1 − p) is largest when p = 0.5, so it gives the biggest (safest) sample size when you have no prior estimate. If earlier data suggest the proportion is near 10% or 90%, using that value gives a smaller n.
When should I apply the finite population correction?
When your sample would be more than about 5% of the population. The correction n = n₀ / (1 + (n₀ − 1)/N) reflects that sampling a large share of a small population leaves less uncertainty.
Is this the same as a power analysis?
No. This calculator sizes a study to estimate a value with a chosen precision. If you plan to test a hypothesis (for example, compare two groups), size the study with a power analysis, which needs an expected effect size and a target power.
How do I estimate the standard deviation for a mean?
Use the SD from a pilot study or from published studies using the same instrument. A rough fallback is range ÷ 4 for approximately normal data. Overestimating the SD is safer than underestimating it.