Effect Size Calculator
Significance Is Not the Same As Size
A p-value can tell you a difference between two groups is unlikely to be due to chance, but it says nothing about how large that difference actually is — with a big enough sample, even a trivial difference becomes statistically significant. Effect size fills that gap. Cohen's d expresses the gap between two group means in standard deviation units, making it comparable across studies that used completely different measurement scales.
The Formula
Cohen's d = (Mean1 − Mean2) / Pooled SD
Interpreting the Magnitude
Cohen proposed benchmark thresholds for |d| that remain the standard reference point in behavioral and social science research:
| |d| range | Magnitude | Rough overlap of the two distributions |
|---|---|---|
| < 0.2 | Negligible | ~92% overlap |
| 0.2 – 0.49 | Small | ~85% overlap |
| 0.5 – 0.79 | Medium | ~67% overlap |
| ≥ 0.8 | Large | ~53% overlap or less |
Thresholds as defined in the calculator's own classification logic; overlap figures are the commonly cited approximate distributional overlaps associated with each band.
Where This Calculation Matters
- Study planning — an expected effect size is a required input for sample size and power calculations before a study is even run.
- Meta-analysis — because Cohen's d is scale-free, it is the standard unit for pooling results across studies that measured the same construct with different instruments.
- Practical significance — reporting effect size alongside a p-value lets readers judge whether a statistically significant result is actually large enough to matter in practice.
How to Use This Calculator
- Enter the mean and standard deviation for Sample 1, along with its sample size (n).
- Enter the mean and standard deviation for Sample 2, along with its sample size (n).
- Select Calculate to get Cohen's d and its magnitude classification.
Related Calculations
Use the resulting effect size directly in the Power Calculator to estimate a study's statistical power, or work backward to find a required sample size with the Sample Size for Mean Calculator.