What is the syntax for ACOTH in Excel?

The syntax for ACOTH is: =ACOTH(number)

What is ACOTH in Excel and how does it work?

ACOTH returns the inverse hyperbolic cotangent of a number. The syntax is =ACOTH(number) where the absolute value of number must be greater than 1. For example, =ACOTH(2) returns approximately 0.549. ACOTH is the inverse of COTH, meaning COTH(ACOTH(x)) = x for |x| > 1.

Why does ACOTH return #NUM! error?

ACOTH returns #NUM! when the absolute value of the input number is less than or equal to 1. The inverse hyperbolic cotangent is only defined for values where |x| > 1. To avoid errors, use =IF(ABS(number) > 1, ACOTH(number), "Invalid") or validate your input before using ACOTH.

What is the difference between ACOTH and ACOT?

ACOTH is the inverse hyperbolic cotangent (works with hyperbolic functions), while ACOT is the inverse trigonometric cotangent (works with regular trigonometry). ACOTH accepts values where |x| > 1 and returns any real number, while ACOT accepts any real number and returns values between 0 and π.

How is ACOTH used in engineering?

ACOTH appears in solutions to certain differential equations, heat transfer problems, and signal processing applications. It's also used in calculations involving transmission lines and wave propagation where hyperbolic functions naturally arise in the mathematical models.

Can ACOTH return negative values?

Yes, ACOTH can return negative values. For positive inputs > 1, ACOTH returns positive values. For negative inputs 1.

Math & Trig

ACOTH Function in Excel

Returns the inverse hyperbolic cotangent of a number.

Syntax

=ACOTH(number)

Arguments

number (required): Number with absolute value > 1

Examples

=ACOTH(2) - Inverse hyperbolic cotangent - Result: 0.549

ACOTH 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

Use cases

Engineering
Physics
Mathematics

Frequently asked questions

What is ACOTH in Excel and how does it work? ACOTH returns the inverse hyperbolic cotangent of a number. The syntax is =ACOTH(number) where the absolute value of number must be greater than 1. For example, =ACOTH(2) returns approximately 0.549. ACOTH is the inverse of COTH, meaning COTH(ACOTH(x)) = x for |x| > 1.
Why does ACOTH return #NUM! error? ACOTH returns #NUM! when the absolute value of the input number is less than or equal to 1. The inverse hyperbolic cotangent is only defined for values where |x| > 1. To avoid errors, use =IF(ABS(number) > 1, ACOTH(number), "Invalid") or validate your input before using ACOTH.
What is the difference between ACOTH and ACOT? ACOTH is the inverse hyperbolic cotangent (works with hyperbolic functions), while ACOT is the inverse trigonometric cotangent (works with regular trigonometry). ACOTH accepts values where |x| > 1 and returns any real number, while ACOT accepts any real number and returns values between 0 and π.
How is ACOTH used in engineering? ACOTH appears in solutions to certain differential equations, heat transfer problems, and signal processing applications. It's also used in calculations involving transmission lines and wave propagation where hyperbolic functions naturally arise in the mathematical models.
Can ACOTH return negative values? Yes, ACOTH can return negative values. For positive inputs > 1, ACOTH returns positive values. For negative inputs < -1, ACOTH returns negative values. The function is odd: ACOTH(-x) = -ACOTH(x) for |x| > 1.

Editorial review

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