Sample Size Calculator
Choose a confidence level and margin of error to find how many responses a survey needs. Enter the population size if it is small enough to matter.
Result
- Z-score for the confidence level
- 1.96
- Unrounded result
- 384.15
This is the number of completed responses needed. Invite more people to allow for those who do not respond. The formula assumes a simple random sample.
Formula
- n₀ = z² × p × (1 − p) ÷ e²
- Finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
- z = 1.645 for 90%, 1.96 for 95%, 2.576 for 99%
How the Sample Size Calculator works
The sample size for estimating a proportion depends on three things: how confident you want to be, how precise the estimate should be, and how varied the answers are. Cochran's formula combines them.
Using 50 percent for the expected proportion gives the largest sample and is the safe choice when you have no prior estimate. For small populations the finite population correction reduces the sample needed.
Worked example
For 95 percent confidence and a 5 percent margin of error with p = 0.5: n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.1, so 385 responses. For a population of 10,000 the corrected figure is 370.
Frequently asked questions
Why is 385 such a common sample size?
It is the result for 95 percent confidence and a 5 percent margin of error with a large population, the most common survey settings.
Does a bigger population need a much bigger sample?
No. Beyond a few tens of thousands the required sample barely changes. A population of 1 million and one of 100 million both need about 385 for the same settings.
How do I halve the margin of error?
Quadruple the sample. The margin of error shrinks with the square root of the sample size.
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Calculations run in your browser and nothing you enter is sent to a server. Results are provided for general information. Check critical figures independently before relying on them.