Sample Size Calculator
Find the sample size needed for a target margin of error.
What the Sample Size Calculator does
Sample size is driven by the precision you want, not by how large the population is. Getting from ±5% to ±2.5% requires four times as many responses, which is why survey budgets rise so steeply with precision.
Formula
n = z² × p(1 − p) ÷ E²Finite population: n_adj = n ÷ (1 + (n − 1) ÷ N)Contacts needed = n ÷ Response rate
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Desired margin of error | % | Yes | — |
| Confidence level | one of 6 options | Yes | — |
| Expected proportion | % | Yes | Use 50% if unknown — it is the most conservative. |
| Population size | number | Optional | Optional — leave blank for very large populations. Accepts 0 or more. |
| Expected response rate | % | Optional | — |
How to use it
- Choose Confidence level.
- Enter Desired margin of error and Expected proportion.
- Optionally add Population size and Expected response rate.
- Select Calculate.
Worked example
Targeting ±3% margin at 95% confidence with an unknown proportion.
- Margin
- 3
- Confidence
- 95%
- Proportion
- 50
1.96² × 0.25 ÷ 0.03² = 1,068 respondents needed.
Reading the result
- "Sample as % of population" (when population is entered) shows how small a fraction is actually needed — a reassuring number when justifying a modest sample against an expectation that it should scale with population size.
- The sensitivity table directly answers "what would a tighter margin cost" without separate math for each target.
Assumptions and limitations
- This assumes simple random sampling — the notes state cluster or stratified designs need a design-effect adjustment on top, so the figure here is a floor for those more complex designs, not the final answer.
- Response rate is applied as a single flat percentage — real non-response is rarely random, so correctly inflating "people to contact" does not by itself fix bias if non-responders differ systematically from responders.
Common mistakes
- Assuming a larger population always needs a proportionally larger sample — the FAQ shows the required sample barely moves beyond about 20,000, whatever the true population size.
- Budgeting to contact only as many people as "required sample size" states rather than the higher "people to contact" figure that accounts for non-response.
Frequently asked questions
Why use 50% when I do not know the proportion?
Because p(1 − p) peaks at p = 0.5, giving the largest required sample. Using it guarantees your margin will be no worse than targeted.
Does a bigger population need a bigger sample?
Hardly at all. Beyond about 20,000 the required sample barely moves — 1,067 for 20,000 people and 1,068 for 100 million.