Statistical Power Calculator — Free Sample-Size Math Tool

This tool answers the question every study should answer before collecting data: how many participants do you need? You enter the effect size you expect (Cohen’s d for mean differences, or a difference in proportions), your alpha level (usually 0.05), and your desired power (usually 0.80, meaning an 80 percent chance of detecting a real effect). The tool returns the sample size per group using standard normal-approximation formulas for one-sample t-tests, two-sample t-tests, and two-proportion tests. Planning sample size before data collection is not bureaucracy. An underpowered study wastes participants’ time and usually finds nothing, even when the effect is real.

How to use it

Choose your test type.
Enter the smallest effect size that would matter in practice.
Keep alpha at 0.05 and power at 0.80 unless you have a reason to change them.
Click Calculate sample size.
Add 10 to 15 percent for expected dropout, and round up.

Worked example

You plan a two-group experiment and expect a medium effect, d = 0.5. With alpha 0.05 and power 0.80, the tool returns 63 participants per group, or 126 in total. Expecting 10 percent dropout, you recruit 139. Compare that with guessing: recruiting 30 per group would give you only about a 50 percent chance of detecting the same effect — a coin flip after all the work of running the study. If you instead expect a small effect of d = 0.2, the required sample jumps above 390 per group, which may tell you to redesign the study rather than run an underpowered version of it.

Honest limits

These are normal approximations, not exact power calculations from a statistics package. For small samples, non-normal data, clustered designs, or repeated measures, use dedicated software such as G*Power and report its output instead. The hardest input is also the most important: the effect size. Guessing an optimistic effect size to justify a small sample is the most common abuse of power analysis. Base your effect size on pilot data or published studies, and run a sensitivity check: what happens to the sample size if the true effect is half what you hoped?

Who it is for

This tool is for students writing a methods section, researchers planning a grant proposal, and thesis supervisors checking a student’s design. It gives defensible planning numbers in seconds. For the final registered protocol, confirm the numbers in a full power-analysis package and cite that output alongside this planning check.

Going further

Run a sensitivity table, not a single calculation. Compute the required sample for a pessimistic effect, a realistic effect, and an optimistic effect, and show all three to your supervisor or funder: the table makes the gamble explicit and protects you if the true effect lands at the low end. Pilot data helps, but pilot effect sizes are noisy and usually inflated, so shrink a pilot estimate before using it — halving it is a common, defensible rule of thumb. Also budget for the realities the formula ignores: unequal group sizes cost power, missing outcomes cost power, and subgroup analyses multiply the required sample. If the honest sample size exceeds what you can recruit, redesign rather than pretend: narrow the question, choose a more sensitive outcome, use a within-subject design where each participant serves as their own control, or collaborate across sites. A smaller, well-powered study of a sharp question beats a large, underpowered study of a vague one every time. Report the power analysis in your methods with all four numbers: the effect size and its source, alpha, power, and the resulting sample size per group, plus the dropout allowance. A reviewer who sees only the final sample size cannot judge whether the study was planned or merely sized by convenience, and funders increasingly treat a missing power justification as a missing design element. If recruitment falls short of the target, say so plainly and report the achieved power for the planned effect: an honest shortfall, disclosed, damages a paper far less than a silent one discovered by a reader recomputing your numbers.

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