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TANH Function

Excel 2007+

Summary

The Excel TANH function calculates the hyperbolic tangent of a given number, a key mathematical operation used in advanced calculations, engineering applications, and statistical modeling.

Syntax

TANH(number)

Parameters

Parameter	Type	Required	Description
number	`Number`	Yes	The real number value to compute the hyperbolic tangent for

Using the TANH Function

TANH computes the hyperbolic tangent using the formula (e^x - e^-x) / (e^x + e^-x), producing results between -1 and 1. It's commonly used in physics, engineering, and financial modeling where hyperbolic functions appear naturally.

Common TANH Examples

Basic TANH Examples

=TANH(-2)

Hyperbolic tangent of -2 returns approximately -0.964028

Zero Input

=TANH(0)

Hyperbolic tangent of 0 returns exactly 0

Positive Value

=TANH(0.5)

Hyperbolic tangent of 0.5 returns approximately 0.462117

Cell Reference

=TANH(A1)

Calculates hyperbolic tangent of value in cell A1

Frequently Asked Questions

TANH returns values between -1 and 1 for all real number inputs.

Yes, TANH works with negative numbers and returns negative results approaching -1.

TAN is the circular tangent (periodic), while TANH is the hyperbolic tangent (bounded between -1 and 1).

Common Errors and Solutions

#VALUE!

Cause: Non-numeric argument provided

Solution: Ensure the input is a valid number

#NUM!

Cause: Input is not a real number (in some cases)

Solution: Verify input contains only numeric values

Notes

TANH approaches 1 as input goes to positive infinity
TANH approaches -1 as input goes to negative infinity
TANH(0) = 0 exactly
Related hyperbolic functions: SINH, COSH

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 11, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+