Sample Size Calculator

A sample size calculator tells you how many people or observations you need to survey so that your estimate of a population proportion is precise enough. Instead of guessing, it works backwards from the margin of error and confidence level you want and returns the smallest sample that meets them. Enter a confidence level, a target margin of error, and an estimated proportion, and the tool returns the required sample size.

How to use this calculator

1. Pick a confidence level (90%, 95%, or 99%) — how sure you want to be that the true proportion falls within your margin.
2. Enter the margin of error as a decimal — for example 0.05 for ±5%.
3. Enter an estimated proportion (p). If you have no prior estimate, use 0.5, which is the most conservative choice and gives the largest sample.
4. Read the required sample size, always rounded up to a whole person.

A smaller margin of error or a higher confidence level both push the required sample size up, because tighter, more certain estimates need more data.

Worked example

Suppose you want 95% confidence, a margin of error of 0.05, and you use the conservative proportion p = 0.5. The critical z value for 95% confidence is about 1.96.

n = z² × p × (1 − p) / margin²
n = 1.96² × 0.5 × 0.5 / 0.05²
n = 3.8415 × 0.25 / 0.0025
n = 0.9604 / 0.0025 ≈ 384.15

Because you can’t survey a fraction of a person, always round up:

required sample size = 385

So you need 385 respondents to estimate the proportion within ±5% at 95% confidence. For the formula and the assumptions behind it, see the NIST/SEMATECH e-Handbook section on sample sizes required for a proportion.

Frequently asked questions

Why does the survey sample size use a proportion of 0.5?

The product p × (1 − p) is largest when p = 0.5, so using 0.5 yields the most conservative (largest) sample size. If you have a credible prior estimate — say a proportion near 0.2 — plugging it in lowers the required sample.

How does the margin of error change the sample size?

Halving the margin of error roughly quadruples the required sample, because the margin appears squared in the denominator. Tighter precision is expensive in data.

Does this account for a finite population?

No — this formula assumes a large population. For a small, finite population you can apply a finite population correction, which reduces the required sample when your group is only a few times larger than the sample itself.