Effect Size Converter

Seven conversions are available:

• Cohen's d to Pearson's r, and back
• Cohen's d to odds ratio, and back
• t statistic to Pearson's r (with degrees of freedom)
• Pearson's r to Fisher's z, and back

Pick a conversion, enter your value, and you get the result with the exact formula and its assumptions printed underneath. The convert-all panel also shows Cohen's d, Pearson's r, the odds ratio, and Fisher's z together from a single input, and the d and r conversions accept optional group sizes for extra accuracy when your groups are unequal.

Mostly for meta-analysis and for comparing studies. One paper reports an odds ratio, another reports Cohen's d, a third reports only a t statistic, and none of them can be averaged or compared directly. Converting everything to one metric puts them on the same scale. It also helps when a journal or a meta-analyst asks for your result in a metric your software did not report, or when you want to see how a reported statistic translates into something more intuitive like a correlation.

An effect size is a number that describes how strong a finding is, independent of sample size. A p-value only tells you whether a result is unlikely if there were truly no effect; a large study can produce a tiny p-value for a trivial effect. The effect size answers the question readers actually care about: how big is the difference or the relationship? Common examples are Cohen's d for differences between groups, Pearson's r for correlations, and odds ratios for events.

Cohen's d expresses the difference between two group means in standard deviation units. A d of 0.5 means the groups differ by half a standard deviation. The usual benchmarks (Cohen, 1988):

• d of about 0.2: Small effect.
• d of about 0.5: Medium effect.
• d of about 0.8: Large effect.

Treat these as rough guides rather than rules: in some fields even a small effect matters a lot, and in others only large effects are practical.

Pearson's r measures the strength and direction of a straight-line relationship between two variables, from -1 to 1. The usual benchmarks:

• r of about 0.1: Small relationship.
• r of about 0.3: Medium relationship.
• r of about 0.5: Large relationship.

Converting between d and r is common because correlations are easy for readers to picture, and r squared tells you the share of variance the relationship explains.

Fisher's z is a transformed version of a correlation, computed as the inverse hyperbolic tangent of r. The transformation makes the sampling distribution of correlations approximately normal, which correlations on their own are not, especially near -1 and 1. That is why meta-analyses average and compare correlations on the z scale, where the standard error is 1 divided by the square root of n minus 3, and convert back to r at the end. If you are pooling correlations, convert each r to z, average the z values, then convert the average back.

Select "t statistic to Pearson's r", enter your t value and its degrees of freedom, and the tool applies the formula r = the square root of t squared divided by (t squared plus df). The result expresses the tested effect as the share of variance it explains. One note: the tool shows the result as a magnitude; the sign of r follows the sign of t, which you know from the direction of your effect.

You do not have to; group sizes are optional for the d and r conversions. When the two groups are the same size, a simple formula applies. When they differ, the exact formula applies a correction based on n1 and n2, and the result becomes noticeably more accurate when the imbalance is large. If you leave both boxes blank, the tool assumes equal group sizes and says so under the result.

Yes. The convert-all panel takes your single input and shows Cohen's d, Pearson's r, the odds ratio, and Fisher's z together, with the group-size assumption noted underneath. It appears for every conversion except t statistic to r, because a t statistic on its own does not give the tool enough to derive the other metrics without extra assumptions.

The d and r conversions and the t to r conversion are exact given their assumptions. The odds ratio conversion is the soft one: it uses a logistic approximation (Chinn, 2000), which assumes the continuous outcome follows a logistic distribution, and it is least reliable when the outcome is rare or very common. Every result prints its formula and assumptions underneath, so you can check what you are standing on before you report the number.

No. Both express a difference between two group means in standard deviation units, but Hedges' g applies a small-sample correction to the pooled standard deviation, so g comes out slightly smaller than d in small samples. The difference shrinks as sample sizes grow, and for typical studies the two are nearly identical. This converter works with Cohen's d; if a paper reports g, treating it as d introduces only a small error.

No. The converter takes a statistic you already have, from your own analysis output or from a published paper, and translates it between metrics. To get an effect size from raw data, run the analysis in your statistics software first. To plan how many participants a future study needs for an effect size you have in mind, use the sample size and power calculator, which pairs with this tool.

Yes, this effect size converter is completely free. There is no sign-up, no account, no credit card, and no limit on how many conversions you can run. It works as a free effect size calculator for students, researchers, and anyone writing a paper or running a meta-analysis who needs to move between Cohen's d, Pearson's r, odds ratios, t statistics, and Fisher's z. Enter a value and see the result, formula, and assumptions in seconds.

No. Every conversion runs in your browser as plain math. Nothing you type is sent to a server, nothing is stored, and there is no file to upload in the first place. Close the tab and it is gone.