Calculate eta squared or partial eta squared from matching ANOVA inputs. A separate generalized mode covers a single within-subject factor without between-subject factors or covariates. Optional F and ordinary omega squared use uncorrected fixed-effects between-subject ANOVA degrees of freedom.

Use the effect and total sums of squares from the same ANOVA.

Partial effect size, F and omega squared

Blank omits partial η², F and omega². Zero is a supplied zero error term.

For ordinary fixed-effects between-subject ANOVA only. Use original ANOVA degrees of freedom, without sphericity corrections.

Related Calculators

Eta Squared Formula

The following formula is used to calculate Eta Squared.

η² = SSeffect / SSₜₒₜₐₗ

Variables:

  • η² is the Eta Squared
  • SS_effect is the sum of squares for the effect
  • SS_total is the total sum of squares

Divide effect SS by total SS to describe the proportion of sample variation associated with the effect. SS error is optional in this mode; supplying it adds partial eta squared. Supplying matching original effect and error degrees of freedom also adds F and the ordinary fixed-effects between-subject omega-squared estimate. Blank optional fields omit those outputs; entered values remain in use when their section is closed.

What is an Eta Squared?

Eta squared describes sample variation associated with an ANOVA effect, not causation or out-of-sample predictive accuracy. It ranges from 0 to 1 when the sums of squares support that ratio. Partial eta squared uses effect / (effect + matching error), or (F × df effect) / (F × df effect + df error) for the corresponding ANOVA test. Fractional corrected degrees of freedom are accepted for this F identity; approximate Welch or mixed-model tests need separate interpretation. The generalized mode uses effect / (effect + error + subjects) only for the stated one-factor repeated-measures design. If total SS is supplied there, it must equal those three components. Cohen’s f is a denominator-specific transformation, not automatically an interchangeable power-analysis input. A zero denominator is undefined; an effect-size ratio of 1 has no finite f. Negative raw omega estimates are retained alongside an explicitly zero-truncated comparison. The .01/.06/.14 ordinary eta-squared heuristic is context-dependent.

How to Calculate Eta Squared?

The following steps outline how to calculate the Eta Squared (η²).

  1. First, determine the sum of squares for the effect (SS_effect).
  2. Next, determine the total sum of squares (SS_total).
  3. Next, gather the formula from above = η² = SS_effect / SS_total.
  4. Finally, calculate the Eta Squared (η²).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

SS_effect = 120

SS_total = 200, so η² = 120 / 200 = 0.6, or 60%. With matching SS_error = 80, partial η² is also 0.6. Optional uncorrected df_effect = 2 and df_error = 27 give F = 20.25 and ordinary omega² ≈ 0.562044.