Statistics
Sample Size Calculator
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How to use it
Using the sample size calculator
- 01
Choose your precision
±5% suits informal research; ±3% is common for published polls.
- 02
Set the confidence level
95% is standard; keep it unless stakeholders specify otherwise.
- 03
Optionally add the population size
Known, modest populations earn a meaningful discount via the correction factor.
Good to know
Why p = 0.5 is the safe default
Required n peaks when opinions split evenly. Planning with 50/50 guarantees your margin holds no matter the actual result; a 70/30 question would need fewer responses than calculated, never more.
Sample size does not scale with population
Counterintuitively, a national poll and a city poll need nearly the same n (~385–1,067 depending on margin). Precision depends on absolute response count, not the fraction of the population sampled; until populations get small and the correction kicks in.
- ±5% at 95% → 385 responses.
- ±3% at 95% → 1,068 responses.
- Small N: correction can cut requirements substantially.
How it's calculated
The math behind this calculator
n₀ = z² · p(1−p) / e² (p = 0.5) Corrected: n = n₀ / (1 + (n₀ − 1)/N)For proportions, the most conservative assumption is p = 0.5, which maximizes required n regardless of the true split. We combine that with your chosen z multiplier and margin of error to get the baseline requirement n₀.
When you provide the population size N, the finite-population correction shrinks the requirement; polling 385 people out of 400 is nearly a census. Leave N blank for large or unknown populations where the correction is negligible.
Assumptions & limitations
- Proportion-style questions (percentage splits), using the conservative p = 0.5.
- Simple random sampling without replacement.
- Responses are independent; nonresponse bias is not modeled.
Worked example
At 95% confidence and a ±5% margin of error you need 385 responses for a large population; for a town of 10,000 the correction trims it to 371.
FAQ
Frequently asked questions
- What margin of error should I pick?
- ±5% is fine for internal decisions; ±3% for anything public-facing; ±1% gets expensive fast; responses needed grow with 1/e².
- Do these counts include nonresponse?
- No; this is completes needed. Divide by your expected completion rate to find invitations to send.
- What if my population is unknown or huge?
- Leave the population field blank. Beyond roughly 20× the sample size, the correction changes nothing material.
- Why does 99% confidence need more responses?
- Higher confidence demands a bigger z multiplier (2.576 vs 1.96), and n grows with z²; about 663 vs 385 responses at ±5%.
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