Math
Sample Size Calculator
Find the survey sample size you need for any margin of error and confidence level. Supports finite population correction and the conservative p=0.5 default.
Sample Size Calculator
How sure you want to be that the true value falls inside the margin of error. 95% is the polling standard.
Acceptable swing in percentage points. Smaller numbers need bigger samples.
Best guess for the share answering one way (0 to 1). Use 0.5 if you have no prior estimate; it maximizes the sample needed.
Optional. Tick "Known" for small or finite groups; leave unchecked to assume a very large population.
Required sample size
385
Assumes an effectively infinite population.
Uncorrected (infinite N)
385
z-score
1.96
Finite correction
Off
Frequently Asked Questions about the Sample Size Calculator
Why do national polls typically use 1,000 to 1,500 respondents?
That is the sample size needed for a +/-3% margin of error at 95% confidence with the conservative p=0.5 assumption. The formula returns 1,068 for +/-3% and 385 for +/-5%, so most opinion polls land in that 1,000 to 1,500 band, then round up a bit to cover non-response and screening losses.
Why use 0.5 as the default proportion when I have no estimate?
The variance term p(1-p) in the formula peaks at p=0.5, so plugging in 0.5 gives the largest sample size for any chosen margin of error and confidence level. That makes 0.5 the safe, conservative default. If you have prior data showing the true proportion is closer to 0.2 or 0.8, entering it can drop the required sample by a third or more.
When does the finite population correction matter?
The correction n / (1 + (n - 1) / N) shrinks the required sample whenever N is not much larger than the uncorrected count. For a population of 500, the +/-5% at 95% sample drops from 385 to 218. Above roughly N = 100,000 the correction changes the answer by less than 1%, so most public polling treats the population as effectively infinite and skips the correction entirely.
What is the trade-off between sample size and margin of error?
Tighter margins of error cost a lot of extra responses. Going from +/-5% to +/-3% at 95% confidence almost triples the sample (385 to 1,068). Going from +/-5% to +/-1% requires 9,604 respondents. Decide how precise you really need to be: a +/-5% sample is more than enough for most A/B tests, customer surveys, and product research.
Why does doubling accuracy quadruple the sample size?
Sample size scales with 1 / E^2, where E is the margin of error. Halving E (twice the accuracy) divides the denominator by 4, so the required sample multiplies by 4. That is why +/-2.5% needs 1,537 respondents while +/-5% needs only 385 at 95% confidence with p=0.5. The same relationship explains why the last few percentage points of precision are always the most expensive.