An <em>η</em>² of .14 is a Cohen’s <em>f</em> of <strong>.40</strong>, and the G*Power box wants the second one. Type the .14 in there and it will ask for 495 participants for what takes 66. The conversion is a square root; what actually needs checking is which eta you are entering.
f = √( η² / (1 − η²) ) · back again: η² = f² / (1 + f²)
Cohen’s f is defined as the standard deviation of the group means over the within-group standard deviation. Eta squared is between-group variance over total variance, which is between plus within. Write the second, rearrange, and the first appears: f² = η²/(1 − η²). Nothing is left over, no distributional assumption is added, and the reverse is equally exact.
The delicate part is not the algebra, it is the first box. The identity describes the relation between the effect variance and the variance left outside it. If the eta you enter is the plain one, "left outside" is everything else and the resulting f is exactly what G*Power expects. If it is a partial from a design with more than one factor, the other effects have already been removed from the denominator, and the f inherits that discount without telling you.
That is the assumption you accept when converting a partial: that the study you are planning will have those same factors under control, with the same measurement and the same cleaning. Sometimes it is true, because you are replicating the whole design. When you are planning a one-way experiment using the partial from someone else’s factorial, it is not, and the sample comes out short systematically.
Plain (η²) divides effect variance by total variance. Partial (η²p) divides it by the effect plus its own error, with the other factors already out of the denominator. Generalized (η²G) uses a denominator that changes depending on which variables were manipulated and which were only measured; it does not convert with this formula.
And here is the trap that costs most: SPSS labels it "partial" even in a one-way ANOVA, where the two coincide. As soon as there are two factors they stop coinciding, and the partial is always the larger. Converting a η²p of .14 whose plain eta over the total is .05 plans for 66 participants where 189 were needed.
If the paper you take the figure from does not say which it is, check whether the design had more than one factor. With one it makes no difference; with two or more, it does.
Cohen gave .10, .25 and .40 for f, and .01, .06 and .14 for eta squared. They look like two separate conventions and they are the same one passed through this formula: f = .10 corresponds to η² = .0099; f = .25 to η² = .0588; f = .40 to η² = .1379. Rounded: .01, .06 and .14. The conversion cannot move you across a benchmark, because the function is increasing and the cuts sit in the same places.
What does change with the scale is the sample size, which is computed on f. In a three-group ANOVA with α = .05 and power .80, an f of .10 asks for 969 participants, one of .25 asks for 159 and one of .40 asks for 66. Between a small and a large effect there is a factor of fifteen in fieldwork cost.
The error that does move you across a benchmark is applying plain-eta thresholds to a partial. A η²p of .14 in a three-factor design can correspond to a plain eta of .04 over total variance, and calling it "large" in the discussion is a writing decision, not a finding.
In within-subjects designs, the "Repeated measures, within factors" screen asks for three more things besides f: the number of measurements, the average correlation between them, and the nonsphericity epsilon. Correlation pushes hard: with the same people measured several times, between-person variance leaves the error term and the same effect is detected with far fewer participants.
And that is the problem. By default G*Power assumes your f was computed on the total standard deviation and applies the correlation correction itself. The η²p SPSS prints in a repeated-measures ANOVA is already computed on that analysis’s error term — with the correction inside. If you convert that η²p and do not tick "as in SPSS" under Options, the correction is applied twice and the N you get back is optimistic.
Epsilon counts too, and hardly anyone moves it from 1. If your Greenhouse-Geisser is going to land around .70, leaving it at 1 plans a study with more power than you will have. It is the usual habit — keeping the flattering figure from the previous paper — and in repeated measures you pay for it twice.
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). Eta squared to Cohen's f converter [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/convert/eta-squared-to-cohens-f
For your Methods section: Eta squared was converted into Cohen's f, using the Ciudad Science eta squared to Cohen's f converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026convetacuadradoafdecohen,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Eta squared to Cohen's f converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/convert/eta-squared-to-cohens-f},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}The arithmetic is the same and a number comes out. What changes is what it means: the resulting f compares the effect against an error term the other factors have already been removed from. If you are replicating that same design, it works as is. If you are planning a simpler one, it overestimates power and leaves you short.
It converts the same way, f = √(ω²/(1 − ω²)), and it is usually the better idea. Eta squared is upward biased in small samples and omega corrects that bias, so the f is slightly smaller and the study you plan slightly larger. For power, erring high is the cheap error.
Not with this formula. η²G changes the denominator depending on which variables were manipulated and which were only measured, so its relation to Cohen’s f is no longer the one above. If your source gives η²G, either find the plain eta in the same paper or plan another way.
η² = f²/(1 + f²). It is useful for reading, in variance-explained terms, an effect that a power paper reported as f — which is what sample-size sections usually do.