Eta Squared Calculator

StatisticsLast updated: August 22, 2026

Eta squared (η²) tells you how much of the total variability in the dependent variable is explained by the independent variable. The F and p values in an ANOVA table only answer "is there a difference?"; η² answers "how large is that difference?" and is read the same way as R² in regression.

This calculator returns η², partial η², ω², and ε² together, either from the sums of squares in your ANOVA output (SS_effect, SS_error, and optionally SS_total) or from F with its degrees of freedom alone. It explains how the measures differ, tells you which one to report, and shows the share of the effect in the total variability as a bar chart. In factorial designs you also see on the results screen why partial η² can be so much larger than η².

If you have the full ANOVA table, choose sums of squares; if the paper only reports something like "F(2, 27) = 6.28", the second option is enough.
The between-groups sum of squares of the factor you are interested in, as shown in the ANOVA table.
The within-groups (residual, error) sum of squares.
Leave empty for a one-way ANOVA. In a factorial design the other effects also enter the total, so this value must be entered.
In a one-way ANOVA, the number of groups − 1.
In a one-way ANOVA, N − k (total observations − number of groups).
Sets the false positive risk. In the social sciences 5% is the common choice.

ANOVA Effect Size Formulas

Eta squared:         η²  = SS_effect / SS_total
Partial eta squared: η²ₚ = SS_effect / (SS_effect + SS_error)
Omega squared:       ω²  = (SS_effect − df₁·MS_error) / (SS_total + MS_error)
Epsilon squared:     ε²  = (SS_effect − df₁·MS_error) / SS_total
From F:              η²ₚ = (F·df₁) / (F·df₁ + df₂)
Omega from F:        ω²  = df₁·(F − 1) / (df₁·(F − 1) + N),   N = df₁ + df₂ + 1
Cohen f:             f   = √(η² / (1 − η²))
Mean square:         MS  = SS / df,   F = MS_effect / MS_error

In a one-way ANOVA, SS_total = SS_effect + SS_error, so η² and partial η² are equal. In factorial designs the sums of squares of the other factors are also part of SS_total, which pulls the two measures apart.

How to Calculate

  1. Enter the sum of squares of the effect you are interested in (SS_effect) and the error sum of squares (SS_error) from your ANOVA table.
  2. If the design is factorial (two-way ANOVA, interaction terms, and so on), be sure to fill in SS_total; if you leave it empty the calculator assumes a one-way design.
  3. Enter the degrees of freedom of the effect and the error: in a one-way ANOVA, df₁ = k − 1 and df₂ = N − k.
  4. If all you have is a reported line such as "F(2, 27) = 6.28", switch the input format to the F value and enter F, df₁, and df₂.
  5. Read η², partial η², and ω² together in the results, and check how far ω² drops below η² in a small sample.
  6. Use the contribution chart to see the share of the effect in the total variability, and report F, p, and the effect size together.

Worked Examples

η² from one-way ANOVA output

A one-way ANOVA with three groups and 30 observations: MS_error = 7.84 and F(2, 27) = 6.278, so with p = 0.006 the result is significant. η² = 98.4 / 310 = 0.3174, meaning 31.7% of the total variability is explained by the differences between the groups. The bias-corrected ω² = 0.2603 and Cohen f = 0.6819; η² exceeding ω² shows the overestimation caused by the small sample.

Eta squared (η²): 0.3174 · Partial eta squared (η²ₚ): 0.3174 · Omega squared (ω²): 0.2603

η² versus partial η² in a two-way ANOVA

SS_total (360.80) is 135.10 units larger than SS_effect + SS_error, so the design is factorial. For the same effect, η² = 45.20 / 360.80 = 0.1253 while partial η² = 45.20 / 225.70 = 0.2003; the partial value is clearly larger. F(1, 36) = 9.015 with p = 0.005; if you do not state which type of η² you report, the effect size will be badly misread.

Eta squared (η²): 0.1253 · Partial eta squared (η²ₚ): 0.2003 · Omega squared (ω²): 0.1099

From F and degrees of freedom only

If a paper reports nothing but "F(3, 76) = 4.35", the effect size can still be recovered: partial η² = (4.35·3) / (4.35·3 + 76) = 0.1465, ω² = 0.1116, and Cohen f = 0.4144. With p = 0.007 the result is significant and corresponds to an effect on the medium-to-large boundary; the implied total sample size is N = 80.

Eta squared (η²): 0.1465 · Partial eta squared (η²ₚ): 0.1465 · Omega squared (ω²): 0.1116

Frequently Asked Questions

What is the difference between eta squared and partial eta squared?
Both use the same numerator (SS_effect) but different denominators: η² puts the total sum of squares in the denominator, while partial η² uses only the effect plus the error sum of squares. In a one-way ANOVA these two denominators are the same, so the values are equal. In a factorial design partial η² removes the variability of the other factors from the denominator, so it is always larger, and the partial η² values of all effects can add up to more than 1.
Which one should I report: η², partial η², or ω²?
In a one-way design η² (identical to partial η²) is enough. In a factorial design SPSS reports partial η² by default and that is common in the literature, but η² is fairer when you compare effects coming from different designs. If the sample is small (under 20 per group), reporting ω² is the most honest choice; whichever measure you use, state it explicitly in the text.
Why is omega squared smaller than eta squared?
η² is the proportion of variability observed in the sample, and because it credits part of the error variance to the effect it systematically overestimates the population effect. ω² corrects this bias by subtracting the error mean square, giving a nearly unbiased estimate of the population value. The gap grows as the sample shrinks and the effect weakens; for very small effects ω² can even come out negative, in which case it is set to zero.
How large does η² have to be to count as large?
By Cohen's benchmarks, 0.01 is a small, 0.06 a medium, and 0.14 a large effect; these correspond to f = 0.10, 0.25, and 0.40. The limits are not absolute: an effect of 0.06 can be noteworthy in psychology, while 0.14 may be ordinary in a tightly controlled experiment. Compare the value with the typical magnitudes in your own field.
How do I get these values in SPSS and R?
In SPSS, Options → "Estimates of effect size" in the Univariate or One-Way ANOVA dialog adds the partial η² column; SPSS does not report ω², which has to be computed by hand. In R, rstatix::anova_test() returns η²ₚ (ges/pes) by default, while the effectsize package provides eta_squared(), omega_squared(), and epsilon_squared() together with confidence intervals. The formulas used here produce the same results.
Should I report η² if the effect is not significant?
Yes, always. A non-significant result does not mean "no effect"; η² and its confidence interval show whether the study was sensitive enough to detect the effect. A non-significant result with η² = 0.12 points to an underpowered sample and is valuable information for meta-analyses.
Are η² and R² the same thing?
In a one-way ANOVA, yes: η² is numerically identical to the R² of a regression model built with dummy variables for the grouping variable. The difference is that ANOVA works with a categorical factor and η² can also capture non-linear relationships, whereas Pearson r² measures only the linear one. Adjusted R² and ω² share the same bias-correction logic as well.