Eta Squared (η²) Effect Size Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
Eta squared (η²) is calculated by dividing the between-groups sum of squares by the total sum of squares: η² = SSbetween ÷ SStotal. A value of 0.3 (45 ÷ 150) means 30% of the total variance in the data is explained by group membership, an effect judged large according to Cohen's conventional thresholds.
Explanation
In an analysis of variance (ANOVA), the total variability of the data breaks into two parts: the variability between the compared groups (SSbetween, due for example to a different treatment or experimental condition) and the variability within each group (the rest, attributable to chance or uncontrolled factors). Eta squared simply expresses the proportion the first part represents in the total variability: the closer η² is to 1, the more the difference between groups explains a large part of the observed variation; the closer it is to 0, the more that variation is mostly explained by within-group variability. Unlike the coefficient of determination R², which measures the share of variance explained by a continuous linear relationship between two variables, eta squared applies to categorical groups (comparing several treatments, several conditions) — both quantities nonetheless share the same variance-decomposition logic and the same 0-to-1 scale. Statistical significance (a low p-value) only indicates that an effect probably exists, without specifying its real magnitude: eta squared fills that gap, just as Cohen's d does for comparing two means, by quantifying the practical size of the effect rather than just its existence.
Example: SSbetween = 45, SStotal = 150
Inputs
Between-groups sum of squares: 45. Total sum of squares: 150.
Calculation
η² = 45 ÷ 150 = 0.3, that is 30% of the total variance explained by the groups.
Result
η² = 0.3, an effect judged large according to Cohen's conventional thresholds (≥ 0.14).
Frequently asked questions
What are the usual thresholds for interpreting eta squared?
The convention established by Jacob Cohen (1988) proposes indicative benchmarks: a small effect from η² = 0.01, medium from 0.06, and large from 0.14. These are general benchmarks, not absolute thresholds — the effect magnitude actually meaningful depends heavily on the field of study and the practical stakes involved.
Can eta squared exceed 1 or be negative?
No: by construction, the between-groups sum of squares can never exceed the total sum of squares (it is a component of it), and both quantities are sums of squares, so always positive or zero. Eta squared is therefore always between 0 and 1 inclusive.
What is the difference between eta squared and partial eta squared?
This calculator gives "classic" eta squared, which relates the between-groups variability to the total variability of the entire study. Partial eta squared, a variant used in multi-factor ANOVAs, instead relates that variability to the sum of the between-groups variability and the residual variability specific to that factor, excluding the study's other factors — a distinction that only matters for analyses with several simultaneous factors.