If you typed your <em>R</em>² straight into the effect-size box in G*Power, the sample size it gave you is wrong. G*Power wants <strong><em>f</em>²</strong>, which is a different thing, and the conversion is one division.
f² = R² / (1 − R²)
R² is explained variance over the total: it runs from 0 to 1 and reads as a percentage. It is the figure reported in the paper.
f² is explained variance over the UNexplained: signal variance divided by noise variance. It has no ceiling, which is why it is what power analysis uses, where what matters is the ratio of effect to error.
Same information on two scales, just like eta squared and Cohen’s f in an ANOVA. But the benchmarks do not line up: a small R² is .02 and a small f² is also .02, while R² = .26 (large) is f² = .35.
There are two distinct uses and G*Power separates them into two screens:
The whole-model one ("Linear multiple regression: Fixed model, R² deviation from zero"): f² = R²/(1−R²), which is what this page computes. It answers whether the model as a whole explains anything.
The increment one ("R² increase"): f² = (R²full − R²reduced)/(1 − R²full). It answers whether THAT predictor adds anything above the others, which is almost always the real hypothesis.
Using the first when the hypothesis is the second overestimates power and plans a smaller sample than needed. It is the most expensive error on this axis, because it does not surface until the data are already collected.
R² rises whenever a predictor is added, even noise: with as many predictors as cases it reaches 1 while explaining nothing. The adjusted version penalizes the number of predictors and can even come out negative, which is its way of saying the model adds nothing.
For power you use the unadjusted R², because that is what the formula is defined on. For the paper you report both, and if the gap between them is wide, that is information: it means you are paying a lot of degrees of freedom for little explanation.
Checking that your residual degrees of freedom match the sample you report is in degrees of freedom against N — in regression they are N − k − 1, and that −1 for the intercept is the one most often forgotten.
All thirteen effect size conversions, grouped by what each one is for, are in the index.
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). R squared to Cohen's f squared converter [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/convert/r-squared-to-cohens-f2
For your Methods section: R² was converted into Cohen's f², using the Ciudad Science r squared to Cohen's f squared converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026convr2af2decohen,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{R squared to Cohen's f squared converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/convert/r-squared-to-cohens-f2},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}Arithmetically yes, but the resulting f² is no longer the one G*Power expects, which is defined on the unadjusted R². If you do it, say so, because the number you get is more conservative.
f² explodes: at .90 the f² is 9. That is not a formula error, it is the scale — when almost no noise is left, the signal-to-noise ratio becomes enormous. In social science an R² of .90 is more cause for suspicion than celebration.
No. Pseudo-R² measures (Nagelkerke, Cox-Snell, McFadden) are not proportions of variance and do not convert with this formula. G*Power has its own logistic screen, and it asks for odds ratios.
Not directly either: there is variance at each level and you have to decide which is the denominator. Nakagawa’s marginal and conditional R² are the usual reference, and they are interpreted separately.