Sample Size Calculator — Two-Group Mean Test (Power & α)

Estimate minimum sample size per group for comparing two independent means. Private by design—everything runs locally in your browser.

Inputs

(e.g., 0.80)
(two-tailed)
(same units as means)
(pooled SD)

Results

Minimum Sample Size
Per group: —   |   Total (both groups): —
Two-tailed test; equal variances and equal group sizes assumed.
Details
Cohen’s d: —
Z1−α/2: —   |   Zpower: —
Formula: \( n = \dfrac{2\,(Z_{1-\alpha/2}+Z_{1-\beta})^2}{d^2} \) where \( d = \Delta/\sigma \).

How This Sample Size Calculator Works

This tool estimates the required sample size per group for a two-sample mean test (independent groups, equal variances, equal group sizes) using a normal approximation to power analysis.

Formula

For minimum sample size per group:

$$ n = \\frac{2\\,(Z_{1-\\alpha/2} + Z_{1-\\beta})^2\\,\\sigma^2}{\\Delta^2} \\quad \\text{where} \\quad d=\\frac{\\Delta}{\\sigma} $$

Equivalently: $$ n = \\frac{2\\,(Z_{1-\\alpha/2} + Z_{1-\\beta})^2}{d^2} $$

Inputs

  • Power (1−β): Probability of detecting a true effect (commonly 0.80 or 0.90).
  • α (Significance): False-positive rate (commonly 0.05 two-tailed).
  • Δ (Difference in means): Minimum effect worth detecting.
  • σ (Standard deviation): Estimated from prior data or a pilot study.

Notes & Limitations

  • Assumes equal variances and equal group sizes; paired/unequal-variance designs are out of scope.
  • Uses standard normal quantiles (accurate for common settings).
  • Rounding up is applied to ensure whole participants per group.

Frequently Asked Questions

Can I use Cohen’s d directly?

Yes. If you know d, set Δ = d × σ or set σ = 1 and enter Δ = d.

Two-tailed vs one-tailed?

This calculator uses a two-tailed test (Z1−α/2). For a one-tailed test, replace Z1−α/2 with Z1−α.

Are inputs and results stored?

No. All computations run locally in your browser.

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