Statistics
Statistics
Sample Size Calculator
Estimate the sample size you need for a survey, RCT, or observational study, with finite-population correction.
Input
Study parameters
How close your estimate must be to the true population value. 5% is the survey-research default.
Use 50% if you have no prior estimate, gives the largest, most conservative N.
If known, applies the finite-population correction (lower N).
Output
Required sample size
- Minimum n
- 385
- participants for 95% confidence, ±5% margin
- Critical z
- 1.960
- Infinite-pop n
- 385
Formula: n = z²·p·(1-p)/e². With finite-population correction: n' = n / (1 + (n-1)/N).
When to use what
• Standard survey: 95%, ±5%, p=50% → n ≈ 385
• High-stakes survey: 99%, ±3% → n ≈ 1843
• Pilot study: 90%, ±10% → n ≈ 68
• Tight margin: 95%, ±2% → n ≈ 2401
Write up your methods section in Underleaf
Underleaf is an AI-powered LaTeX editor with inline writing help and a citation finder, useful when you're drafting the rationale behind your sample size.
What this calculator does, and doesn't, cover
This is the standard proportion-based sample-size formula. It answers: "How many participants do I need to estimate a single proportion (e.g. a yes/no question, a presence/absence marker) within a given margin of error at a chosen confidence level?" That covers most survey research and many observational studies.
For comparing two groups (RCT, A/B test, between-subjects experiment), you also need an effect size and power target , that's a power analysis, distinct from this calculator. For time-to-event analysis or hierarchical/nested designs, consult a statistician.
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