TANH Function

Excel Functions › Math & Trig

All versions Math & Trig

The Excel TANH function returns the hyperbolic tangent of a number, equal to SINH(x)/COSH(x). The argument is a plain number, and the result always lies between −1 and 1.


Quick answer:
=TANH(0) hyperbolic tangent of 0 = 0

Syntax

=TANH(number)
ArgumentDescription
numberRequiredAny real number. TANH is bounded: its result always falls strictly between -1 and 1.

How to use it

The hyperbolic tangent is the ratio TANH(x) = SINH(x) / COSH(x). There is no degree-vs-radian issue — you pass a plain number:

=TANH(0) // = 0
=TANH(1) // approx 0.7616
=TANH(-1) // approx -0.7616 (odd function)

TANH is an odd function and is bounded: as x grows it flattens toward 1, and toward -1 for large negative x. Its inverse is ATANH.

The S-curve. TANH's smooth squash from -1 to 1 makes it a classic activation function in neural networks and a handy way to map any number into a fixed range.

Try it: interactive demo

Live demo

Pick a TANH example to see the formula and its result.

Result:

Practice workbook

📊
Download the free TANH practice workbook
Every example on this page, ready to open in Excel — plus practice challenges with answers on a separate tab. No sign-up required.

Frequently asked questions

What is the hyperbolic tangent?
It is the ratio TANH(x) = SINH(x)/COSH(x), equivalent to (e^x - e^-x)/(e^x + e^-x). The result always lies strictly between -1 and 1.
Does TANH use degrees or radians?
Neither — TANH takes a plain real number, not an angle. There is no degree-to-radian conversion for hyperbolic functions.
Why does TANH never quite reach 1?
TANH approaches 1 as x increases and -1 as x decreases, but never actually reaches either — they are horizontal asymptotes. For large x, Excel rounds the result to exactly 1.
What is the inverse of TANH?
ATANH (inverse hyperbolic tangent) returns the number whose hyperbolic tangent is a given value; its argument must be strictly between -1 and 1.

Master functions like this in one day

This page covers one function. Our Excel Formulas and Functions class covers the 30 that matter most — live, hands-on, taught by professionals in Dallas–Fort Worth, Houston, Austin, Oklahoma City, Denver, or online.

See the Formulas & Functions Class

Related functions: SINH · COSH · ATANH · TAN · EXP