How to use this calculator
- Enter or choose design.
- Enter or choose effect size (Cohen’s d).
- Enter or choose sample size (per group, or pairs).
- Enter or choose significance level α.
- Enter or choose test.
- The power at this sample size updates as you type. Use Copy result or Share to keep it.
Method
δ = d√(n/k), k = 2 for two groups, 1 for one sample; two-sided power = Φ(δ − z₁₋α/₂) + Φ(−δ − z₁₋α/₂); n = k(z_α + z_β)² ÷ d²; t-adjusted n = n + z_α² ÷ (2k)
- d
- standardised effect size
- n
- per-group size (or number of pairs)
- z_α
- critical value (z₁₋α/₂ two-sided, z₁₋α one-sided)
- z_β
- normal quantile of the target power
Worked example
- δ = 0.5 × √(64 ÷ 2) = 2.8284; power ≈ Φ(2.8284 − 1.96) = Φ(0.8685) = 80.7%.
- n = 2 × (1.96 + 0.8416)² ÷ 0.25 = 62.8 → 63 per group (z).
- Guenther adjustment: 62.8 + 1.96² ÷ 4 = 63.75 → 64 per group, matching Cohen’s table for a t-test.
Detecting d = 0.5 with 80% power at α = 0.05 (two-sided) needs about 64 people per group, 128 in total.
What the result means
Plan for the smallest effect that would matter in practice, not the effect you hope for. Halving d roughly quadruples the sample needed.
Assumptions and limits
- Normal approximation to the t-test; the exact noncentral-t power is slightly lower for small samples (0.8015 rather than 0.8074 in the example).
- Equal group sizes and a common standard deviation.
- Not for proportions (use the A/B test sample size calculator), ANOVA, regression or clustered designs.
- Power analysis is only as good as the assumed effect size.
Questions
Why 80% power?
It is a common convention balancing cost against a 20% risk of missing a real effect. Many trials now target 90%.
Should I use a one-sided test to save participants?
Only if an effect in the other direction would be treated exactly like no effect, and you decided before collecting data.