How this instrument works
Cohen's d is the standard way to express how large a difference between two groups is, in standardized units comparable across studies, rather than in whatever original units the data happened to be measured in. Most commonly, d is computed directly from each group's raw mean, standard deviation, and sample size — the approach this site's separate cohens-d calculator takes. This page solves the same problem from a different starting point: when you already have a reported independent-samples t-statistic (from a paper, a stats package's output, or your own prior analysis) but not the raw group means and standard deviations behind it.
The conversion works because the t-statistic and Cohen's d are mathematically related through the two sample sizes: d = t × √(1/n1 + 1/n2). This relationship, documented by Robert Rosenthal among others, lets you recover the standardized effect size from summary statistics alone, without needing to go back to raw data that may not be available — useful when reading a published study that reports significance tests but not means and standard deviations directly, or when combining results across studies for a meta-analysis.
This is a distinct input framing from this site's cohens-d calculator, not a re-skin of the same tool: cohens-d takes two groups' raw means, standard deviations, and sizes and computes the pooled standard deviation itself before dividing; this page instead starts from an already-computed t-statistic and skips straight to the standardized effect size using only the two sample sizes. Both produce the same underlying quantity, Cohen's d, but from different available inputs — use whichever one matches the data you actually have on hand.
- Enter the reported independent two-sample t-statistic into t-statistic (independent two-sample test).
- Enter the size of the first sample into Sample 1 size (n1), and the second sample's size into Sample 2 size (n2).
- Both sample sizes must be at least 1.
- Read Cohen's d (effect size) for the standardized effect size — its magnitude reflects how large the underlying difference was, using the same 0.2/0.5/0.8 small/medium/large benchmarks as this site's cohens-d calculator.
Worked example — converting a reported t = 2.5 with two groups of 25
A published study reports an independent two-sample t-statistic of 2.5 from comparing two groups of 25 participants each, without listing the raw means and standard deviations directly. Entering t = 2.5, n1 = 25, and n2 = 25, Cohen's d (effect size) reads 0.707107, computed as 2.5 × √(1/25 + 1/25) = 2.5 × √0.08.
By Cohen's own benchmarks (0.2 small, 0.5 medium, 0.8 large), a d of about 0.71 lands solidly between medium and large — a substantial, practically meaningful difference between the two groups, recovered entirely from the reported t-statistic and sample sizes alone, without ever needing the original raw data.
Questions
How is this different from the site's cohens-d calculator?
They compute the same underlying quantity, Cohen's d, but from different starting inputs. This page takes an already-reported t-statistic plus the two sample sizes and converts directly, useful when you're reading someone else's published results and don't have the raw means and standard deviations. This site's separate cohens-d calculator instead takes each group's raw mean, standard deviation, and size directly and computes the pooled standard deviation itself before dividing — the right tool when you have the original data on hand rather than just a reported test statistic.
Why does this conversion only need the two sample sizes, not the means or standard deviations?
Because the t-statistic itself already encodes the standardized difference between the two group means, scaled by the sample sizes used to compute it — the mean difference and pooled standard deviation are effectively baked into t already. The conversion formula, d = t × √(1/n1+1/n2), simply undoes the specific way sample size affects a t-statistic's magnitude, recovering the sample-size-independent effect size without needing to see the raw means and standard deviations that originally went into computing t.
Will this give exactly the same d as computing it from raw means and standard deviations?
Yes, assuming the t-statistic was itself computed from a standard independent two-sample (pooled-variance) t-test — the two formulas are mathematically equivalent, just rearranged to start from different known quantities. Small differences can appear if the original t-statistic came from a Welch's t-test (which doesn't pool variances) or was rounded before being reported, since this conversion assumes the standard pooled-variance form.
Can Cohen's d come out negative here?
Yes — the sign of d simply follows the sign of the t-statistic you enter. A negative t (meaning the first group's mean was lower than the second's, in whatever order the original test used) produces a negative d of the same magnitude. As with the raw-data cohens-d calculator, the magnitude of d indicates the size of the effect, and the sign only indicates direction.
What if I only have a p-value, not a t-statistic?
This calculator specifically needs the t-statistic itself, not just the p-value it corresponds to — a p-value alone doesn't uniquely determine the effect size without also knowing the test's degrees of freedom and being able to work backward through the t-distribution, a separate calculation this page doesn't perform. If your source reports both the t-statistic and the sample sizes (common in most published results), those are exactly the inputs this instrument needs.