Sample Size & Power Calculator
How many participants do you need? Enter your expected effect size, significance level and target power, and this calculator returns the required sample size — computed with the exact noncentral-t distribution, so t-test results match R’s power.t.test to the decimal.
▶ Watch: sample size and power in R — power.t.test, fixing n to get power, and the pwr package for effect sizes and proportions.
Download the R script · ▶ Practice in the playground
The R code from the video, ready to copy:
# Sample size & power for a two-group t-test
# n per group for 80% power (delta = 5, sd = 10)
power.t.test(delta = 5, sd = 10, power = 0.80, sig.level = 0.05)
# Power for a fixed n = 30 per group
power.t.test(n = 30, delta = 5, sd = 10, sig.level = 0.05)
# With the pwr package: effect size d = 0.5
library(pwr)
pwr.t.test(d = 0.5, power = 0.80, sig.level = 0.05)
# Two proportions: 40% vs 60%
pwr.2p.test(h = ES.h(0.6, 0.4), power = 0.80)How to use it
Interpreting the result
Four quantities are locked together in any power analysis — effect size, sample size, significance level (α) and power. Fix any three and the fourth is determined. This tool fixes α, power and effect size to solve for sample size.
- Effect size is how big a difference you expect, in standardised units. For t-tests we use Cohen’s d (0.2 = small, 0.5 = medium, 0.8 = large). Use a value justified by prior studies or the smallest difference that would matter clinically — not a guess that gives you a convenient number.
- Significance level (α) is your tolerated false-positive rate, conventionally 0.05.
- Power is the probability of detecting the effect if it is real; 0.80 is the usual minimum, 0.90 is safer.
The t-test calculation uses the exact noncentral-t distribution, the same method as R’s power.t.test(), so the numbers agree. Proportions use the standard normal approximation and correlation uses Fisher’s z-transformation.
Do it in R
# two-sample t-test, matches this calculator
power.t.test(delta = 0.5, sd = 1, power = 0.80,
sig.level = 0.05, type = "two.sample")See our tutorial, Sample size calculation in R, for the full walkthrough including proportions and correlations.
FAQ
Frequently asked questions
What effect size should I use?
Base it on prior literature or the minimum effect that would be practically meaningful — never reverse-engineer an effect size to hit a feasible sample size. When unsure, run the calculation across a range of plausible effects and report the sensitivity.
Why does my result differ slightly from another calculator?
Many web calculators use a normal approximation for t-tests, which understates the required n. This tool uses the exact noncentral-t distribution, matching R’s power.t.test. Small differences from other tools usually come from that.
Is 80% power enough?
80% is a common convention, meaning a 20% chance of missing a real effect. For confirmatory or high-stakes studies, 90% is a safer target — at the cost of a larger sample.
Planning a study and want the sample size defended in writing for an ethics board or grant? That’s our statistical analysis service.