Given <em>F</em> and its two degrees of freedom, partial eta squared is <strong>determined</strong>. It is not an estimate and it does not depend on the design: it is the definition rearranged. Which is why it recovers the effect size from any paper that only published the ANOVA table.
η²p = (F · df₁) / (F · df₁ + df₂) · Cohen’s f = √(η²p / (1 − η²p))
Partial eta squared is the effect variance over the sum of effect and error variance: η²p = SSeffect/(SSeffect+SSerror). And F is the ratio of mean squares, which are those same sums divided by their degrees of freedom.
Rearranging, the sums of squares cancel out and what remains is η²p = (F·df₁)/(F·df₁+df₂). Nothing is left over and no assumption is needed: given the three numbers, you have partial eta.
That has a practical consequence people underuse: you can recover the effect size from papers that never reported one, which is nearly everything before 2010. It is the standard route for pooling them in a meta-analysis.
To compute ANOVA power, G*Power does not take eta: it wants Cohen’s f, which comes from eta through another identity, f = √(η²/(1−η²)).
So the full route for planning a study from the literature is: take the F from the earlier paper, convert to partial eta, convert that to f, and feed it to G*Power. Without touching the original data, which you do not have.
The benchmarks for f are .10, .25 and .40 for small, medium and large. They are not eta’s, and confusing them is the fastest way to plan a sample that falls short.
Plain eta squared divides by the TOTAL sum of squares, so it comes out smaller with more than one factor and all effects share a pie of size 1. The partial uses only its own error term, so several partials can sum above 1 with nothing wrong.
This page converts to partial, which is what SPSS returns by default and what almost everyone reports. If your paper just says "eta squared", you have to find out which one before comparing it with anything.
Checking that the one you published matches its own F is in effect size against F, and what to do when several sum above one, in eta squared summing above one.
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). F to partial eta squared converter [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/convert/f-to-partial-eta-squared
For your Methods section: Partial eta squared was obtained from the F statistic and its degrees of freedom, using the Ciudad Science f to partial eta squared converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026convfaetacuadradoparcial,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{F to partial eta squared converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/convert/f-to-partial-eta-squared},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}It works whenever the F and both degrees of freedom belong to the same effect and the same error term. Mixed designs have several error terms and each effect must be paired with its own; mixing them produces a number that belongs to nobody.
They come from a sphericity correction (Greenhouse-Geisser, Huynh-Feldt). The formula still works arithmetically, but the resulting eta is no longer directly comparable with an uncorrected design, and that is worth stating.
Yes, by rearranging: F = (η²p·df₂)/(df₁·(1−η²p)). It is how incomplete tables get reconstructed, and this page computes it internally too.
Omega corrects eta’s optimistic bias and always comes out slightly smaller. It is preferable and increasingly requested, but it needs the sums of squares or the error mean square, so it cannot be recovered from F and df alone.