What is the syntax for ATANH in Excel?

The syntax for ATANH is: =ATANH(number)

What is ATANH in Excel and how does it work?

ATANH returns the inverse hyperbolic tangent of a number. The syntax is =ATANH(number) where number must be between -1 and 1 (exclusive). For example, =ATANH(0.5) returns approximately 0.549. ATANH is the inverse of TANH, meaning TANH(ATANH(x)) = x for |x| < 1.

Why does ATANH return #NUM! error?

ATANH returns #NUM! when the input number is = 1. The inverse hyperbolic tangent is only defined for values strictly between -1 and 1. To avoid errors, use =IF(AND(number > -1, number < 1), ATANH(number), "Invalid") or validate your input before using ATANH.

What is the difference between ATANH and ATAN?

ATANH is the inverse hyperbolic tangent (works with hyperbolic functions), while ATAN is the inverse trigonometric tangent (works with regular trigonometry). ATANH accepts values between -1 and 1 and returns any real number, while ATAN accepts any real number and returns values between -π/2 and π/2.

How is ATANH used in statistics?

ATANH is used in statistics for the Fisher transformation, which converts correlation coefficients to a normally distributed variable. The formula is =ATANH(correlation). This transformation is useful for hypothesis testing and confidence intervals for correlation coefficients.

Can ATANH return negative values?

Yes, ATANH can return negative values. For positive inputs between 0 and 1, ATANH returns positive values. For negative inputs between -1 and 0, ATANH returns negative values. ATANH is an odd function: ATANH(-x) = -ATANH(x) for |x| < 1.

Math & Trig

ATANH Function in Excel

Q: What is the ATANH function in Excel?

Returns the inverse hyperbolic tangent of a number.

Q: Why does ATANH return #NUM! error?

ATANH returns #NUM! when the input number is = 1. The inverse hyperbolic tangent is only defined for values strictly between -1 and 1. To avoid errors, use =IF(AND(number > -1, number < 1), ATANH(number), "Invalid") or validate your input before using ATANH.

Q: What is the difference between ATANH and ATAN?

ATANH is the inverse hyperbolic tangent (works with hyperbolic functions), while ATAN is the inverse trigonometric tangent (works with regular trigonometry). ATANH accepts values between -1 and 1 and returns any real number, while ATAN accepts any real number and returns values between -π/2 and π/2.

Q: How is ATANH used in statistics?

ATANH is used in statistics for the Fisher transformation, which converts correlation coefficients to a normally distributed variable. The formula is =ATANH(correlation). This transformation is useful for hypothesis testing and confidence intervals for correlation coefficients.

Q: Can ATANH return negative values?

Yes, ATANH can return negative values. For positive inputs between 0 and 1, ATANH returns positive values. For negative inputs between -1 and 0, ATANH returns negative values. ATANH is an odd function: ATANH(-x) = -ATANH(x) for |x| < 1.

Returns the inverse hyperbolic tangent of a number.

Syntax

=ATANH(number)

Arguments

number (required): Number between -1 and 1

Examples

=ATANH(0.5) - Inverse hyperbolic tangent - Result: 0.549

ATANH in reporting workflows

Use absolute references when copying formulas across rows.
For conditional totals see [SUMIF](/functions/sumif/) and [SUMIFS](/functions/sumifs/).
Filtered lists may need [SUBTOTAL](/functions/subtotal/) instead of SUM on visible cells only.

Common errors

#NUM! if number <= -1 or >= 1

Use cases

Hyperbolic functions
Engineering
Statistics

Frequently asked questions

What is ATANH in Excel and how does it work? ATANH returns the inverse hyperbolic tangent of a number. The syntax is =ATANH(number) where number must be between -1 and 1 (exclusive). For example, =ATANH(0.5) returns approximately 0.549. ATANH is the inverse of TANH, meaning TANH(ATANH(x)) = x for |x| < 1.
Why does ATANH return #NUM! error? ATANH returns #NUM! when the input number is <= -1 or >= 1. The inverse hyperbolic tangent is only defined for values strictly between -1 and 1. To avoid errors, use =IF(AND(number > -1, number < 1), ATANH(number), "Invalid") or validate your input before using ATANH.
What is the difference between ATANH and ATAN? ATANH is the inverse hyperbolic tangent (works with hyperbolic functions), while ATAN is the inverse trigonometric tangent (works with regular trigonometry). ATANH accepts values between -1 and 1 and returns any real number, while ATAN accepts any real number and returns values between -π/2 and π/2.
How is ATANH used in statistics? ATANH is used in statistics for the Fisher transformation, which converts correlation coefficients to a normally distributed variable. The formula is =ATANH(correlation). This transformation is useful for hypothesis testing and confidence intervals for correlation coefficients.
Can ATANH return negative values? Yes, ATANH can return negative values. For positive inputs between 0 and 1, ATANH returns positive values. For negative inputs between -1 and 0, ATANH returns negative values. ATANH is an odd function: ATANH(-x) = -ATANH(x) for |x| < 1.

Editorial review

Reviewed by Excel.Directory Editorial Team. Updated May 2026.