Sample Size Calculator

How many survey responses do you need, or how many participants per group in an experiment? Pick the scenario, enter the confidence level and margin of error or the effect size, and get the required sample size with the formula explained for your methods section.

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Confidence level

Margin of error (%)

Expected proportion (%)

Use 50% if unknown; it gives the largest sample.

Population size

0 = very large or unknown

Responses needed

385

n = z²·p(1−p)/e², with the finite population correction n / (1 + (n−1)/N) when the population size is given. This is the number of completed responses; invite more people to allow for non-response.

How to use

Choose Survey (proportion) or Compare two groups (means).
For surveys, enter the confidence level, margin of error, expected proportion and, if known, the population size. For two groups, enter effect size, α and power.
Read the required sample size.

Options explained

Survey: n = z²·p(1−p)/e². At 95% confidence, ±5% and 50% this is 385; with a population of 1,000 the correction gives 278.
Two groups: n = 2(z₁₋α/₂ + z₁₋β)²/d² plus a small-sample correction. d = 0.5, α = 0.05 and 80% power gives 64 per group, as in G*Power.

Reference tables

Survey sample sizes with an expected proportion of 50% and no population size (a very large population), rounded up to whole responses:

Confidence level	±10%	±5%	±3%	±2%	±1%
90%	68	271	752	1,691	6,764
95%	97	385	1,068	2,401	9,604
99%	166	664	1,844	4,147	16,588

The correction for a finite population is n = n₀ ÷ (1 + (n₀ − 1) ÷ N), where n₀ is the figure above and N is the population size. It matters most when the sample would be a large share of the population: for 95% and ±5%, a population of 1,000 reduces 385 to 278. The page shows the uncorrected figure underneath as “Without the finite population correction”.

Participants per group for comparing two means, two-sided with α = 0.05:

Effect size (Cohen’s d)	80% power	90% power
0.2 (small)	394	527
0.5 (medium)	64	86
0.8 (large)	26	34

Halving the effect size roughly quadruples the sample you need.

Frequently asked questions

What expected proportion should I use?

Use 50% if unsure; it gives the largest, most conservative sample.

Is this the number to invite?

It's the number of completed responses. With an expected 60% response rate, invite sample size ÷ 0.6.

How do I choose the effect size?

Base it on earlier studies or a pilot. Without data, 0.5 (medium) is a common choice.

Privacy

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