SigmaCalc

Sample Size Calculator

Work backward from the precision you want to the number of people you need to survey.

Margin of error (0–1)

Estimated proportion (0–1)

Confidence level (%)

Required sample size

385

respondents needed

What you entered

Margin of error: ±5%Estimated proportion: 50%Confidence: 95%

1
Worst-case variance term
0.5 × (1 − 0.5)= 0.25
2
Apply the sample size formula
n = z² × p(1−p) ÷ E² = 1.96² × 0.25 ÷ 0.05²= 385
3
Round up to a whole number of respondents
⌈385⌉= 385

Result

Required sample size: 385

To estimate a proportion within ±5 percentage points at 95% confidence, you need at least 385 respondents — using 50% as the estimate (as done here by default) gives the most conservative, largest required sample.

Sample size needed at 95% confidence

Each row is the number of responses needed to achieve the margin of error shown, at 95% confidence with a worst-case proportion of 0.5.

Target margin of error	Required sample size
1%	9,604
2%	2,401
3%	1,068
4%	601
5%	385
10%	97

The relationship is inverse-square, and this table is the clearest way to see what that costs: halving the margin from 4% to 2% takes you from 601 responses to 2,401, a fourfold increase. Getting to 1% needs nearly ten thousand. That is why 5% at 385 is such a common target - it is the point where precision and cost balance for most purposes. Using a proportion of 0.5 is deliberately conservative; if you have good reason to expect a lopsided result, say 0.1, the required sample falls substantially. None of this accounts for non-response, so recruit more than the figure suggests.

Why 50% is the safe default

The variance term p(1−p) is largest when p = 0.5, so using 50% as your estimated proportion (when you have no prior information) gives the most conservative, largest required sample size — you'll never be caught short.

Diminishing returns on precision

Cutting your margin of error in half roughly quadruples the required sample size, since sample size scales with the square of the margin of error — going from ±5% to ±1% precision is far more than 5× the work.

Frequently asked questions

I want a ±3% margin of error at 95% confidence. How many people do I need?

Using the worst-case p = 0.50: n = (1.96/0.03)² × 0.25 = 1,067 respondents. If you already have reason to believe the proportion is near 80%: n = (1.96/0.03)² × 0.80 × 0.20 = 683. The closer to 50%, the more people you need.

How is this different from the margin of error calculator?

This calculator works backwards: you specify the precision you want, and it tells you how many people to survey. The margin of error calculator works forwards: you enter results you already have, and it tells you the precision you achieved.

Does population size matter for sample size?

Surprisingly little. For populations above ~10,000, the required sample size is essentially the same whether your population is 50,000 or 50 million. A finite population correction factor helps for very small populations, but it rarely changes the answer by much.