Calculate the exact number of participants needed for your study. Supports t-tests, ANOVA, correlation, regression, and chi-square with Cohen's effect size conventions.
"Sample size" hides two different questions, and each one has its own formula. The first: how many participants do I need to detect an effect if it exists? That is an a priori power analysis, which the calculator above runs for a t-test, an ANOVA, a correlation, a regression or a chi-square test. The second: how many people do I need to survey to estimate a percentage within a margin of error? That is the formula for estimating a proportion, the usual one in descriptive theses and surveys, and it is in the block below.
n₀ = Z² · p · (1 − p) / e² n = n₀ / [1 + (n₀ − 1) / N]
Z is the normal value for the confidence level (1.96 at 95%), p the proportion you expect (0.5 if you have no prior estimate, because it is the case that needs the most people) and e the margin of error. At 95%, p = 0.5 and a 5% margin: n₀ = 1.96² × 0.25 / 0.05² = 384.2, rounded up to 385 people. If the population is finite and known (N), you correct it: for N = 2,000 students, n = 384.2 / (1 + 383.2 / 2,000) = 322.4, that is, 323 (Cochran, 1977).
A power analysis is reported with the design, the expected effect size and where it comes from, α, power and the result: "To detect an effect of d = 0.50 with α = .05 and power of .80 in a two-tailed independent-samples t-test, 64 participants per group (128 in total) were required." More examples are in how to report a power analysis in APA 7.
The full walkthrough, with examples for each thesis design, is in how to calculate the sample size for a thesis.
For the five designs here, both rely on noncentral distributions and give the same or a very similar N. G*Power (Faul et al., 2007) covers many more designs; this calculator is quicker for the common cases and explains the result in plain language.
Apply the finite population correction in the block below, which lowers the required sample when the population is small. If you still fall short, state it as a limitation and report the real margin of error your sample gives you, rather than presenting the study as if it had the planned precision.
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Sample size and statistical power calculator [Web application]. Ciudad Science. Retrieved October 18, 2026, from https://analisisdedatospsicologia.com/en/sample-size-calculator
For your Methods section: The sample size required for the specified effect size, significance level and power was computed with the Ciudad Science sample size and statistical power calculator (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026tamanomuestral,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Sample size and statistical power calculator}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/sample-size-calculator},
urldate = {2026-10-18},
note = {Accessed 2026-10-18},
}