Use this free online sample size calculator to determine how many survey or study respondents you need for statistically reliable results. Enter your desired confidence level, margin of error, and estimated proportion, and optionally correct for a finite population size to get an accurate sample size instantly.
How to Use the Sample Size Calculator
Select your desired "Confidence Level" (90%, 95%, or 99%) from the dropdown.
Enter your acceptable "Margin of Error (%)" - smaller values require larger samples.
Enter the "Estimated proportion" - use 0.5 if you don't know it, which gives the most conservative (largest) sample size.
Optionally enter your "Population Size" if you know the total population and want a finite-population-corrected sample size.
Click "Calculate" to see the required sample size.
Worked Example: Surveying a Residential Township
A residents' association wants to know what share of its 2,000 households support installing solar panels, to within ±5 percentage points at 95% confidence. With no earlier survey to go on, use p = 0.5. The base sample is 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16, which the calculator rounds up to 385. Because 385 is a sizeable fraction of 2,000 households, the finite population correction brings the requirement down to 323 completed responses.
That figure is the number of usable replies, not the number of people to approach. If you expect only 40% of households to respond, plan to contact about 323 ÷ 0.4 ≈ 808 households.
Required Sample Size at p = 0.5 (Large Population)
Margin of error
90%
95%
99%
±10%
68
97
166
±5%
271
385
664
±3%
752
1,068
1,844
±2%
1,692
2,401
4,148
±1%
6,766
9,604
16,590
Halving the margin of error roughly quadruples the sample, because the margin sits squared in the denominator. Going from ±5% to ±1% at 95% confidence takes you from 385 to 9,604 responses, which is why most opinion surveys settle for around ±3%.
Does Population Size Matter?
Less than people expect. At ±5% and 95% confidence, a population of 200 needs 132 responses, 500 needs 218, 2,000 needs 323, 10,000 needs 371 and 1,00,000 needs 384. Beyond a few tens of thousands the answer barely changes, so a survey of a city and a survey of the whole country need about the same number of responses for the same precision.
Assumptions Behind the Number
The formula is for estimating a proportion (a percentage of yes/no answers), not an average such as income or height. Means need a different formula based on the expected standard deviation.
It assumes a simple random sample. Convenience samples, such as asking only those who visit the society office, can be biased whatever their size.
The margin of error applies to the whole sample. If you plan to compare subgroups, for example tenants versus owners, each subgroup needs enough responses on its own.
If you have a reliable earlier estimate of p, such as 0.2, using it gives a smaller sample (246 instead of 385 at ±5%, 95%). If the guess turns out wrong, though, your margin of error will be wider than planned.
Frequently Asked Questions
It uses the standard formula for estimating a proportion: n0 = (Z² x p x (1-p)) / e², where Z is the z-score for your confidence level (1.645, 1.96, or 2.576), p is the estimated proportion, and e is the margin of error expressed as a decimal.
If you enter a known population size N, the calculator applies the finite population correction n = n0 / (1 + (n0 - 1)/N), which reduces the required sample size when your population is small relative to n0. Leave it blank for an infinite or very large population.
Use 0.5 (50%). This is the most conservative estimate because p x (1-p) is maximized at p = 0.5, so it produces the largest possible required sample size, guaranteeing your result is not underpowered.
A sample size has to be a whole number of people, and rounding down would leave you slightly short of the precision you asked for. The calculator therefore rounds both the base and the corrected figures up to the next whole number.
No, it is the number of completed, usable responses you need. Divide it by your expected response rate to find how many people to approach; at a 25% response rate, 385 responses means inviting about 1,540 people.