Free Tool

Sample Size Calculator

Find out how many participants your study needs. Supports t-tests, ANOVA, correlation, chi-square, and multiple regression — free, instant, no signup required.

Calculate Your Required Sample Size

Choose your statistical test and planning parameters, then click Calculate.

Required sample size

64 per group

Note: this calculator uses normal-approximation formulas, which are accurate for planning purposes. For exact noncentral-distribution calculations, complex designs, or sensitivity analyses, we recommend the free desktop software G*Power.

What Is Sample Size Calculation?

Sample size calculation (also called a priori power analysis) answers one of the most common questions in research planning: how many participants do I need? Collect too few and your study is underpowered — real effects will slip past your statistical tests undetected, and you will wrongly conclude that nothing is going on. Collect far more than necessary and you waste weeks of recruitment on data you never needed. A power analysis, run before data collection starts, finds the point where additional effort stops paying off.

How Power Analysis Works

Every sample size calculation combines four ingredients. You set three of them and solve for the fourth — almost always the sample size:

Significance level (α): the accepted risk of a false positive. The convention across psychology, education, and the health sciences is 0.05.

Statistical power (1 − β): the probability of detecting a real effect if one exists. The standard target is 0.80, meaning you accept a 20% risk of missing a true effect. Clinical trials often require 0.90.

Expected effect size: how large a difference or relationship you expect. Ideally this comes from prior studies in your literature review; when nothing is available, Cohen's small/medium/large conventions offer a defensible starting point.

The statistical test: a paired t-test needs fewer participants than an independent t-test at the same effect size, a correlation uses a different formula altogether, and ANOVA depends on the number of groups.

The calculator above implements the standard normal-approximation formulas for each test, so the numbers match what most methods textbooks report and come very close to G*Power's exact results.

Why Effect Size Is the Hardest Input

Alpha and power are conventions; effect size is a genuine research judgment. The smaller the effect you want to detect, the larger the sample you need — and the relationship is dramatic. Detecting a large difference between two groups (d = 0.8) takes about 26 participants per group, a medium one (d = 0.5) takes about 64, and a small one (d = 0.2) takes roughly 394 per group. Before choosing a value, scan your literature review for reported effect sizes in comparable studies. Our guides on effect size and sample size and power analysis walk through how to pick a realistic estimate and what to do when no prior research exists.

What to Do With the Result

Treat the calculated number as a minimum, not a target. Real studies lose participants to dropout, incomplete questionnaires, and failed attention checks, so most researchers add a 10–20% buffer on top. Report the calculation in your methodology chapter: state the test, alpha, power, the assumed effect size and where it came from, and the resulting minimum N. Thesis committees and journal reviewers increasingly expect exactly this justification — and it takes two sentences once you have the numbers. If you are still unsure which statistical test your design calls for, settle that first, because the test determines the formula.