👥 Sample Size Calculator
Find the sample size you need for a given confidence level and margin of error, for estimating a proportion (survey) or a mean.
Required sample size
385
respondents
Critical value (z)
1.95996
for this confidence level
n = z²·p(1−p) / E². Use 50% for the expected proportion if unknown. It gives the most conservative (largest) sample. 🔒 Computed in your browser.
How the sample size calculator works
For a proportion, the required sample size is n = z²·p(1−p) / E², where z is the critical value for your confidence level, p the expected proportion (0.5 is the safe, most-conservative choice), and E the margin of error. For a mean, n = (z·σ / E)². An optional finite-population correction reduces n when you are sampling a large fraction of a small population.
The go-to tool before running a survey: it tells you how many responses you need for the precision you want. Uses the exact normal critical value for your confidence level.
Frequently asked questions
How do I calculate sample size for a survey?
Use n = z²·p(1−p) / E². For 95% confidence (z ≈ 1.96), a 5% margin of error (E = 0.05), and the conservative p = 0.5, you need about 385 responses. Enter your values to get the exact figure.
What value should I use for the expected proportion?
If you have no prior estimate, use 0.5. It maximises the required sample size, so your margin of error is guaranteed to be no worse than planned. If you expect a proportion far from 0.5 (say 0.1), the required sample is smaller.
What is the margin of error?
The precision you want, the ± range around your estimate. A 3% margin needs a larger sample than a 5% margin; halving the margin roughly quadruples the required sample.
What is the finite-population correction?
When your sample is a large fraction of a small population, you need fewer respondents than the basic formula suggests. The correction adjusts n downward using the total population size.
Why does higher confidence need a bigger sample?
A higher confidence level (99% vs 95%) uses a larger critical value z, which increases the required sample size. More confidence in a narrower margin costs more data.
Does the population size matter?
Surprisingly little for large populations, a 95%/5% survey needs about 385 responses whether the population is 20,000 or 20 million. It only matters (via the finite-population correction) when the sample is a large share of a small population.