What it does
Too few subjects and a real effect is missed. Too many wastes money and, in animal or patient studies, is unethical. Ethics boards and grant reviewers ask for a power calculation. This tool works out the sample size for the common designs and draws the power curve, so you can show how the answer changes if the effect is smaller or larger than you hoped.
- Two group means: an unpaired t test, for example treatment against control.
- Paired means: the same subjects before and after, or matched pairs.
- One mean against a fixed value.
- Two proportions: percentages such as cure rates.
- Survey: how many responses give a percentage within a chosen margin of error.
How to use it
- Choose what you are comparing.
- For means, type the smallest difference worth detecting and the standard deviation, from a pilot study or published data. Their ratio is the effect size d. Cohen’s rough guide: 0.2 is small, 0.5 medium and 0.8 large.
- For proportions, type the expected percentage in each group.
- Choose the significance level α (usually 0.05) and the power, the chance of detecting the effect if it is real (0.8 or 0.9).
- Add the expected dropout, so the number recruited still leaves enough at the end.
The power curves show power against sample size for your effect, and for effects 25 % smaller and larger.
The methods
Means use the exact noncentral t distribution for a two-sided test, the same method as R’s power.t.test and G*Power. Proportions use the normal approximation of R’s power.prop.test. Surveys use n = z²p(1 − p)/E², with the finite population correction when you give a population size. Results are rounded up to whole subjects.
Worked example
To detect a difference of 5 units when the SD is 10 (d = 0.5), at α = 0.05 with 80 % power, you need 64 per group (63.77 before rounding), as R’s power.t.test gives. Comparing 50 % with 75 % at 90 % power needs 77 per group (R: 76.7). A survey with a ±5 % margin at 95 % confidence needs 385 responses. If only 1000 people could answer, 278 are enough.
Frequently asked questions
Where do I get the standard deviation? From a pilot study, earlier work, or published papers in your field. If unsure, use a larger value: it is safer.
Is my data stored? No. Nothing is stored or sent anywhere.
Draw your results with the publication plot maker.
Where the numbers come from
- Methods: as in R's power.t.test and power.prop.test.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.