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About this tool
Estimate the sample size a study needs from your target effect size and statistical power.
The Sample Size & Power Calculator returns the number of observations needed to detect a standardised mean difference, using the normal approximation n = k × ((z_α/2 + z_β) ÷ d)², where k is 2 for two equal independent groups and 1 for a one-sample or paired design. You choose Cohen's d, a target power of 80%, 90% or 95%, and a two-sided alpha of 0.10, 0.05 or 0.01, and it reports the per-group figure, the total, the z-values it used, and a padded number that survives 15% attrition. It is for anyone sizing a study, an A/B test or a survey before collecting a single data point.
Open Sample Size & Power Calculator on AltFTool — it loads instantly in your browser.
Enter the Standardized effect size (Cohen d), where 0.2 is small, 0.5 medium and 0.8 large, or tap the d=0.5, 80% power example.
Pick a target power of 80, 90 or 95%, a two-sided alpha of 0.10, 0.05 or 0.01, and whether the design is a paired difference or two equal independent groups.
The result gives the per-group n and the study total, with the z alpha and z power values used and a recruitment figure padded for 15% attrition.
Reports z_α/2 and z_β alongside the result, so the calculation can be reproduced and defended in a methods section.
Gives the per-arm figure, the study total, and the number inflated for 15% dropout — the three numbers a protocol actually needs.
Switches the multiplier between 1 and 2 so a paired design is not accidentally sized as if it were two independent samples.
For a medium effect of d = 0.5 with two-sided alpha of 0.05 and 80% power, this normal approximation gives 63 per group, or 126 in total. The familiar textbook figure of 64 per group comes from a t-distribution refinement that adds a couple of observations; the difference is negligible at these sizes.
Cohen's d is the difference between two means divided by the pooled standard deviation, so it expresses an effect in standard-deviation units. Cohen's conventions put 0.2 as small, 0.5 as medium and 0.8 as large — and because sample size scales with 1/d², halving the effect you want to detect quadruples the sample you need.
Power is the probability of detecting an effect that is genuinely there — 80% power means a 1-in-5 chance of missing it. Raising the target from 80% to 90% at d = 0.5 and alpha 0.05 moves the requirement from 63 to 85 per group, which is the cost of that extra certainty.
Yes — power calculations give the number you need at analysis, not the number you recruit. Dividing by the expected completion rate is the standard adjustment; at 15% attrition the calculator shows 63 per group becoming 75. This is a large-sample approximation for a standardised mean effect, so clustered, unequal-arm, repeated-measures or multiple-outcome designs need a tailored power analysis from a statistician.
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