Unit Converters · Free tool
Sample Size Calculator
Calculate the minimum sample size for any proportion at your chosen confidence level and margin of error. Finite-population correction. Free, no sign-up online.
Required sample size
385
respondents needed for ±5% margin at 95% confidence
The formula and when each input matters
n₀ = z² · p · (1 − p) / E²
z is the critical value from the standard normal distribution for your confidence level. p is the expected proportion (use 0.5 if you don't know — it maximises the variance and gives the most conservative sample size). E is your acceptable margin of error.
When the target population N is small (under ~100,000), the FPC reduces the required sample size: n = n₀ / (1 + (n₀ − 1)/N).
Caveat: this formula assumes simple random sampling. For stratified or cluster designs, adjust by your design effect (typically 1.5–3×).
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What it does
How many respondents do you need to estimate a proportion within a margin of error? This calculator returns the minimum sample size using the standard formula n = z² · p(1−p) / E² with optional finite-population correction for small target groups.
Used in survey design, A/B test planning, clinical trial sizing, and any social-science research where you're estimating a percentage. For follow-up significance testing see the p-value calculator.
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Paste this snippet into any page. Loads on-demand (lazy), no tracking scripts, and sized to most dashboards. Replace the height to fit your layout.
<iframe src="https://freetoolarena.com/embed/sample-size-calculator" width="100%" height="720" frameborder="0" loading="lazy" title="Sample Size Calculator" style="border:1px solid #e2e8f0;border-radius:12px;max-width:720px;"></iframe>How to use it
- Pick a confidence level (95% is the most common).
- Set your acceptable margin of error (e.g. ±5%).
- Set expected proportion — leave at 50% if unknown (conservative).
- Optional: enter the total population for finite-population correction.
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