About the Sample Size Calculator
This sample size calculator tells you how many people you need to survey — or how many items you need to test — so that your result is accurate to within a chosen margin of error at a chosen confidence level. Enter the confidence level (95% is the usual choice), the margin of error you can live with, and, if you know it, the size of the population you are sampling from.
It is built for survey designers, students writing a methodology section, market researchers, UX researchers and quality-control teams. The chart shows how quickly the required sample grows as you tighten the margin of error, which helps you balance precision against cost: halving the margin of error roughly quadruples the sample you need.
The calculation assumes a simple random sample and a yes/no (proportion) style question. If you have no prior estimate of the proportion, leave it at 50%, which gives the largest, most conservative sample size. The result is the number of completed responses you need, so invite more people to allow for non-response.
With the default inputs, the required sample size is 385. Change any value above to recalculate instantly.
How to use the sample size calculator
- 1Pick a confidence level — 95% is standard for most surveys.
- 2Enter the margin of error you can accept, such as ±5%.
- 3Leave the expected proportion at 50% unless you have a reliable prior estimate.
- 4Enter the population size if it is small or known; otherwise leave it at 0.
- 5Use the required sample size as your target number of completed responses.
Formula and method
The first formula (Cochran’s formula) gives the sample size for a very large population: z is the critical value of the standard normal distribution for your confidence level (1.96 for 95%), p is the expected proportion and e is the margin of error as a decimal. Because p(1 − p) is largest at p = 0.5, using 50% gives the most conservative answer.
When you know the population size N, the finite population correction shrinks the sample, which matters when the sample would be a noticeable share of the population. The result is always rounded up to the next whole respondent. The method assumes simple random sampling; clustered or stratified designs need a design-effect adjustment.
- n₀
- Sample size for an unlimited population
- n
- Sample size after finite population correction
- z
- Critical z-value for the confidence level (e.g. 1.96 for 95%)
- p
- Expected proportion (0.5 if unknown)
- e
- Margin of error as a decimal (0.05 for ±5%)
- N
- Population size
Worked examples
Standard survey: 95% confidence, ±5%
With z = 1.96, p = 0.5 and e = 0.05, n₀ = 1.96² × 0.25 ÷ 0.0025 ≈ 384.15, which rounds up to 385 responses. This is the familiar “385” figure used for large populations.
Company of 10,000 employees
Starting from n₀ ≈ 384.15, the finite population correction gives 384.15 ÷ (1 + 383.15 ÷ 10,000) ≈ 369.97, so you need 370 completed responses.
High precision: 99% confidence, ±3%
At 99% confidence z ≈ 2.576. n₀ = 2.576² × 0.25 ÷ 0.0009 ≈ 1,843.03, so you need 1,844 responses — almost five times the standard 95%/±5% survey.
Small population of 500 customers
For 500 customers, 384.15 ÷ (1 + 383.15 ÷ 500) ≈ 217.49, so 218 responses are enough — you need to hear from a large share of a small group.
Frequently asked questions
Why is 385 the magic sample size for surveys?+
At 95% confidence, a ±5% margin of error and p = 0.5, Cochran’s formula gives 384.15, which rounds up to 385. For any large population that is the sample size needed, whether the population is 100,000 or 100 million.
Does a bigger population need a much bigger sample?+
Not really. Once a population is more than a few tens of thousands, the required sample barely changes. Population size only matters when your sample would be a noticeable share of it, which is what the finite population correction handles.
What margin of error should I use?+
Most opinion polls and customer surveys use ±3% to ±5%. Use a smaller margin when decisions depend on small differences, but remember halving the margin roughly quadruples the sample size.
Why use 50% as the expected proportion?+
The term p(1 − p) is largest when p = 0.5, so 50% produces the biggest, safest sample size. If earlier research shows the proportion is near 10% or 90%, you can use that value and need fewer responses.
Is the sample size the number of people I should invite?+
No — it is the number of completed, usable responses. Divide it by your expected response rate to find how many people to invite; at a 20% response rate, 385 responses means inviting about 1,925 people.