Effect Size Calculator
Calculate Cohen's d, Pearson r, and eta-squared (η²) with magnitude labels, step-by-step working, and automatic cross-conversions between all three metrics.
Select an effect size type, enter the values, and click Calculate Effect Size.
Use Quick Load to see a worked example instantly.
Effect Size on a Distribution Curve
A larger Cohen's d means less overlap between two groups — the effect is easier to observe in practice.
What Is Effect Size?
Effect size is a standardised measure of the magnitude of a phenomenon — how large an effect is, independent of sample size. Unlike a p-value (which only tells you whether an effect exists), effect size tells you how meaningful or practically important the effect is.
Two studies can both produce p < 0.05 yet have very different effect sizes. A drug trial with 10,000 participants might detect a statistically significant improvement that is clinically meaningless (d = 0.02), while a smaller study might find a large, practically important effect (d = 0.90). Effect size bridges the gap between statistical significance and real-world importance.
The American Psychological Association (APA 7th edition) requires effect sizes to be reported alongside all inferential statistics. Cohen's d, Pearson r, and eta-squared (η²) are the three most widely used metrics across social science, psychology, medicine, and education research.
Cohen's d: Standardised Mean Difference
Cohen's d expresses the difference between two group means in standard deviation units. It is the most common effect size for t-tests and mean comparisons.
For paired samples or one-sample tests, use:
| Magnitude | |d| range | Typical meaning |
|---|---|---|
| Negligible | |d| < 0.2 | No practically meaningful difference |
| Small | 0.2 ≤ |d| < 0.5 | Detectable but modest difference |
| Medium | 0.5 ≤ |d| < 0.8 | Noticeable difference in context |
| Large | |d| ≥ 0.8 | Substantial, easily observable difference |
How to Calculate Pooled Standard Deviation
For independent samples, the pooled SD weights each group's variance by its degrees of freedom:
Example: Group 1 (M=50, SD=10, n=30) vs Group 2 (M=42, SD=12, n=28):
d = (50 − 42) / 11.01 ≈ 0.727 → Medium effect
Pearson r as an Effect Size
When a study reports a correlation, the Pearson r coefficient is itself an effect size. Cohen's benchmarks for r differ from those for d:
| Magnitude | |r| range | Typical meaning |
|---|---|---|
| Negligible | |r| < 0.10 | No meaningful relationship |
| Small | 0.10 ≤ |r| < 0.30 | Weak relationship |
| Medium | 0.30 ≤ |r| < 0.50 | Moderate relationship |
| Large | |r| ≥ 0.50 | Strong relationship |
r² (eta-squared) tells you the proportion of variance in one variable explained by the other — r = 0.35 means 12.25% of variance is shared between the two variables.
Eta-Squared (η²) for ANOVA
Eta-squared (η²) is the proportion of total variance in the outcome that is attributable to the between-groups factor. It is read directly from the ANOVA table:
Cohen's benchmarks for η² are lower than those for d or r because raw proportions of variance are inherently smaller numbers:
| Magnitude | η² range | Typical meaning |
|---|---|---|
| Negligible | η² < 0.01 | Less than 1% variance explained |
| Small | 0.01 ≤ η² < 0.06 | 1–6% variance explained |
| Medium | 0.06 ≤ η² < 0.14 | 6–14% variance explained |
| Large | η² ≥ 0.14 | 14%+ variance explained |
Converting Between Effect Size Metrics
Different journals and disciplines prefer different effect size metrics. The calculator automatically converts between all three. The formulas used are:
d → r
r = d / sqrt(d² + 4)
Cohen (1988) equal-n approximation
r → d
d = 2r / sqrt(1 − r²)
r → η²
η² = r²
Exact when η² is the squared correlation
η² → r → d
r = sqrt(η²) then d = 2r / sqrt(1−r²)
Why Effect Size Matters in Research
A p-value answers "Is this effect real?" — effect size answers "Is this effect worth caring about?" Both questions matter. Large samples can produce tiny p-values for trivial effects; small samples can miss large effects entirely.
Power analysis also requires effect size. Before collecting data, researchers must estimate the expected effect size to determine how large a sample they need. Reporting effect sizes in published studies allows future researchers to use those estimates in their own power calculations — compounding the value of each study.
Meta-analyses aggregate effect sizes across studies to reach more reliable conclusions than any single study can provide. Without standardised effect sizes, meta-analysis is impossible.
Effect Size Calculator FAQ
What is effect size in statistics?
What is a good effect size for Cohen's d?
What is the formula for Cohen's d?
What is the difference between Cohen's d for independent and paired samples?
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What does eta-squared measure?
Is effect size the same as statistical significance?
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