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ATANH Function
Summary
The Excel ATANH function calculates the inverse hyperbolic tangent of a number. This mathematical function is essential for advanced calculations involving hyperbolic functions, returning the value whose hyperbolic tangent equals the input number within the valid range.
Syntax
ATANH(number)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| number | Number |
Yes | A real number in the range (-1, 1) for which to calculate the inverse hyperbolic tangent |
Using the ATANH Function
ATANH finds applications in advanced mathematics, physics simulations, statistical analysis, and engineering computations where hyperbolic functions are involved. Use it when you need the inverse operation of TANH to solve for the original angle given its hyperbolic tangent value.
Common ATANH Examples
Basic ATANH Calculation
=ATANH(0.76159416)Returns approximately 1.00000001, the inverse hyperbolic tangent of 0.76159416.
Negative Value Example
=ATANH(-0.1)Returns approximately -0.10033535, demonstrating function works with negative inputs within range.
Frequently Asked Questions
Common Errors and Solutions
#NUM! Error
Cause: Input number is 1, -1, or outside (-1, 1) range
Solution: Ensure input value is strictly between -1 and 1
Notes
- ATANH is available in Excel 2007 and later versions
- Result approaches infinity as input nears 1 or -1
- Use with TANH for inverse operations in modeling
- Precision may vary with extreme values near boundaries
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 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+