The Excel FISHER function returns the Fisher transformation of a correlation coefficient — turning a skewed correlation into an approximately normal value so you can build confidence intervals and test correlations.
Syntax
| Argument | Description | |
|---|---|---|
x | Required | A value to transform, strictly between −1 and 1 (typically a correlation coefficient). |
How to use it
FISHER applies the transformation z = ½ · ln((1+x)/(1−x)), also written as ATANH(x). Sample correlation coefficients have a skewed, bounded distribution; the Fisher transform stretches them into a roughly normal scale where standard z-based methods apply.
The usual workflow is: transform your correlation with FISHER, build a confidence interval on the transformed (normal) scale using its standard error, then convert the interval endpoints back to correlations with FISHERINV.
Note: x must be strictly inside −1 to 1. At exactly ±1 the transform is infinite and FISHER returns the #NUM! error.
Try it: interactive demo
Enter a correlation between -1 and 1 to see its Fisher transformation.
Practice workbook
Frequently asked questions
What is the Fisher transformation used for?
How do I reverse a FISHER result?
FISHERINV, which applies the inverse transform. FISHERINV(FISHER(x)) returns the original x, so the round trip is exact.What inputs are valid for FISHER?
x must be strictly between −1 and 1. Values of exactly −1 or 1 (or outside that range) produce the #NUM! error because the transform is infinite there.Is FISHER the same as ATANH?
=FISHER(0.75) and =ATANH(0.75) return the same value.Master functions like this in one day
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