Sample Size & Power Calculator
“How many participants do I need?” is one of the first questions every committee, ethics board and grant reviewer asks. Too few, and your study may miss real effects. Too many, and you waste time, money and participants’ goodwill.
This free calculator performs an a priori power analysis for the most common research designs and produces a short, citation-ready justification you can adapt for your methodology chapter, IRB application or grant proposal.
How to Use the Calculator
- Choose your analysis.
- Independent-samples t-test
- Paired-samples t-test
- One-way ANOVA
- Correlation
- Multiple regression
- Chi-square test
- Survey (estimating a proportion with a margin of error)
- Enter the expected effect size. Use a value from prior research or a pilot study whenever possible. The calculator shows Cohen’s conventional benchmarks for reference.
- Set the significance level (α). The default is .05.
- Set the desired power (1 − β). The default is .80; use .90 when missing an effect would be costly.
- Review your result: the required sample size, a power curve and a draft justification statement.
Understanding the Inputs
| Input | What it means | Common default |
|---|---|---|
| Effect size | How large an effect you expect, or the smallest effect worth detecting | Based on prior studies |
| Alpha (α) | The accepted risk of a false positive (Type I error) | .05 |
| Power (1 − β) | The probability of detecting the effect if it is real | .80 |
| Tails | One-tailed only when a directional hypothesis is strongly justified | Two-tailed |
| Allocation ratio | Relative size of the groups | 1:1 |
Cohen’s Effect Size Benchmarks
| Test | Effect size | Small | Medium | Large |
|---|---|---|---|---|
| t-test | d | 0.20 | 0.50 | 0.80 |
| ANOVA | f | 0.10 | 0.25 | 0.40 |
| Correlation | r | 0.10 | 0.30 | 0.50 |
| Multiple regression | f² | 0.02 | 0.15 | 0.35 |
| Chi-square | w | 0.10 | 0.30 | 0.50 |
Benchmarks are a last resort. Effect sizes drawn from published research in your field produce a far more defensible justification.
Worked Examples (α = .05, two-tailed, power = .80)
- Independent t-test, medium effect (d = 0.50): about 64 per group (128 total)
- One-way ANOVA, three groups, medium effect (f = 0.25): about 53 per group (159 total)
- Pearson correlation, medium effect (r = .30): about 85 participants
- Survey proportion, ±5% margin of error, 95% confidence: about 385 respondents (large population, p = .50)
Always plan for attrition and unusable responses: if you expect 20% dropout, divide the required sample by 0.80.
Example Justification Statement
An a priori power analysis was conducted to determine the minimum sample size required for an independent-samples t-test. Assuming a medium effect size (d = 0.50), based on [prior study], with α = .05 (two-tailed) and power of .80, the required sample size was 64 participants per group (N = 128).
When a Calculator Is Not Enough
Standard formulas assume simple designs. Multilevel models, repeated measures with correlated observations, mediation, SEM, cluster-randomized trials and complex survey designs typically require simulation-based power analysis. If your design is one of these, a calculator result may substantially over- or under-estimate the sample you need.
Learn more about the logic of power in Hypothesis Testing, or see how sample size planning fits into Dissertation Statistics Support.
Get a Professional Power Analysis
Need a sample size justification your committee, IRB or funder will accept without question? Book a free 15-minute consultation. Share your design, hypotheses and any prior effect sizes, and I will provide a documented power analysis with citations, usually within 24 hours of scoping.
Prefer email or chat? Write to [email protected] or message me on WhatsApp at +1 (425) 999-3993.