Sample size & power calculator
for bench experiments
How many replicates you need to see the effect you care about - and, when the run budget is already fixed, the smallest effect that budget can actually detect. No signup, no email required.
Standardised effect size d = 1.25. Anything below about 0.3 is a large study; above 1.0 is comfortably detectable.
How many runs does the design itself cost?
Sample size tells you about replication. This tells you how many distinct conditions a multifactorial design needs - and where fractioning buys you runs back.
| Full factorial 2^4 | 16 runs |
|---|---|
| Half fraction res IV | 8 runs |
| Quarter fraction | 4 runs |
| Plackett-Burman (screening) | 8 runs |
| Central composite (optimisation) | 27 runs |
| Your plan, with replicates + centre points | 19 runs |
With more than about 5 factors, screen first - a Plackett-Burman or resolution IV fraction ranks the effects for a fraction of the runs, and only the survivors go on to a response surface.
The maths, stated plainly
For a two-sample comparison of means, the samples required per group are:
n = 2 (t[1-α/2, df] + t[power, df])² σ² / δ²
where δ is the difference you want to detect and σ the standard deviation of the response. The calculator starts from the normal approximation and then iterates using Student-t quantiles, because once σ is estimated from your own data the t requirement is the one that actually applies - which is why small studies need a few more replicates than the z formula suggests.
Results reproduce R's power.t.test on the standard benchmarks: at 80% power and α = 0.05 two-sided, effect sizes of d = 0.2, 0.5 and 0.8 return 394, 64 and 26 per group.
What it assumes. Two independent groups, roughly normal residuals, equal variance, and equal group sizes. Paired designs, proportions, survival endpoints, and unequal allocation need different formulas. For a multifactorial design, use the factorial planner above for the run count and treat this figure as the replication per condition.
The free 8-day DOE course
Power is lesson 6. The rest covers screening designs, response surfaces, blocking and randomisation - one short lesson a day, written for bench scientists.
Knowing the run count is the easy half
Shadow AI turns a plain-language research question into the whole design - hypotheses, factors and ranges, the DOE itself, controls, materials and a statistical plan. Free to start.