Sample Size Calculator
Choose 90%, 95% or 99% confidence and enter the margin of error you can accept, in percent, from 0.1 to 50. Enter 5 for ±5%, because 0.05 would mean ±0.05%. The calculator returns the sample size a survey needs to estimate a proportion within that margin. Set the expected proportion if you have an estimate. It starts at 50%, the value that gives the largest sample and so holds whatever the true share turns out to be. Add the population size to get the smaller sample a finite population needs.
How to use the Sample Size Calculator
- Enter your numbers in the Sample Size Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The sample size formula
n = z² × p(1 − p) ÷ E², rounded up · · · Finite population: n ÷ (1 + (n − 1) ÷ N), rounded up
z is 1.645 for 90% confidence, 1.96 for 95% and 2.576 for 99%. E is the margin of error as a decimal and N is the population size. p is the share you expect, and p(1 − p) is the variability: it peaks at 0.25 when p is 50% and falls toward 0 as p nears 0% or 100%. The formula assumes a random sample and a normal approximation to the binomial distribution.
Worked example
At 95% confidence and a 3% margin, n = 1.96² × 0.25 ÷ 0.03² = 1,067.1, which rounds up to 1,068. A 5% margin needs 385, or 271 at 90% confidence and 664 at 99%. Enter a population of 10,000 and the sample for a 5% margin at 95% confidence drops to 371. Set the expected proportion to 10% and that 5% margin at 95% confidence needs 139 before any population adjustment.
Frequently asked questions
Why is 1,000 a common survey size?
At 95% confidence, 1,000 responses give a margin of 1.96 × √(0.25 ÷ 1,000) = 3.1%. That is close to ±3%, and each extra point of precision costs far more people. A 2% margin needs 2,401.
Does population size matter?
It matters when the sample is a large share of the population. Enter the population size and the calculator applies the finite population correction, n ÷ (1 + (n − 1) ÷ N). At 95% confidence and a 5% margin, a population of 10,000 needs 371 instead of 385, and a population of 1,000 needs 279.
Can I enter my own expected proportion?
Yes, in the Expected Proportion box, in percent. It starts at 50%, which gives the largest sample. If you expect a share near 10% or 90%, you need fewer responses. For 10% at 95% confidence and a 5% margin, n = 1.96² × 0.09 ÷ 0.05² = 138.3, which rounds up to 139. If the true share turns out closer to 50% than your estimate, the real margin is wider than the one you entered.
What does the formula assume?
A random sample, completed responses and a normal approximation to the binomial distribution. Section 7.2.4 of the NIST e-Handbook of Statistical Methods gives one criterion for that approximation, that n × p and n × (1 − p) are both at least 5, which at p = 10% means a sample of at least 50. The calculator adds a note when the result falls short of that.
Is this the sample size for a statistical test?
It sizes an estimate to a margin of error. A hypothesis test also depends on the power you want, and the formula NIST gives for testing a proportion adds a term for it. This calculator has no power input, so use it for surveys and polls.
What does "margin of error" actually mean?
The half-width of the confidence interval at the level you choose. A poll showing 52% support with a ±3% margin at 95% confidence has an interval from 49% to 55%. Repeat the poll with fresh random samples, and about 95 of 100 such intervals contain the true value. The formula assumes a random sample and counts completed responses, not invitations sent.