What is the syntax for ACOSH in Excel?

The syntax for ACOSH is: =ACOSH(number)

What is ACOSH in Excel and how does it work?

ACOSH returns the inverse hyperbolic cosine of a number. The syntax is =ACOSH(number) where number must be >= 1. For example, =ACOSH(1) returns 0, and =ACOSH(2) returns approximately 1.317. ACOSH is the inverse of COSH, meaning COSH(ACOSH(x)) = x for x >= 1.

Why does ACOSH return #NUM! error?

ACOSH returns #NUM! when the input number is less than 1. The inverse hyperbolic cosine is only defined for values >= 1. To avoid errors, use =IF(number >= 1, ACOSH(number), "Invalid") or validate your input before using ACOSH.

What is the difference between ACOSH and ASINH?

ACOSH returns the inverse hyperbolic cosine (defined for x >= 1), while ASINH returns the inverse hyperbolic sine (defined for all real numbers). ACOSH values range from 0 to infinity, while ASINH can be negative, zero, or positive. Use ACOSH for values >= 1, ASINH for any real number.

How do I use ACOSH in engineering calculations?

ACOSH is useful in engineering for calculating catenary curves, transmission line sag, and other hyperbolic geometry problems. For example, to find the angle in a catenary: =ACOSH(sag/span + 1). ACOSH also appears in solutions to certain differential equations and heat transfer problems.

Can I convert ACOSH result to degrees?

ACOSH returns radians. To convert to degrees, multiply by 180/PI: =ACOSH(number) * 180/PI(). However, note that ACOSH typically returns values in radians for mathematical consistency with other trigonometric functions in Excel.

Math & Trig

ACOSH Function in Excel

Returns the inverse hyperbolic cosine of a number.

Syntax

=ACOSH(number)

Arguments

number (required): Number >= 1

Examples

=ACOSH(1) - Inverse hyperbolic cosine - Result: 0

ACOSH 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

Hyperbolic functions
Engineering
Physics

Frequently asked questions

What is ACOSH in Excel and how does it work? ACOSH returns the inverse hyperbolic cosine of a number. The syntax is =ACOSH(number) where number must be >= 1. For example, =ACOSH(1) returns 0, and =ACOSH(2) returns approximately 1.317. ACOSH is the inverse of COSH, meaning COSH(ACOSH(x)) = x for x >= 1.
Why does ACOSH return #NUM! error? ACOSH returns #NUM! when the input number is less than 1. The inverse hyperbolic cosine is only defined for values >= 1. To avoid errors, use =IF(number >= 1, ACOSH(number), "Invalid") or validate your input before using ACOSH.
What is the difference between ACOSH and ASINH? ACOSH returns the inverse hyperbolic cosine (defined for x >= 1), while ASINH returns the inverse hyperbolic sine (defined for all real numbers). ACOSH values range from 0 to infinity, while ASINH can be negative, zero, or positive. Use ACOSH for values >= 1, ASINH for any real number.
How do I use ACOSH in engineering calculations? ACOSH is useful in engineering for calculating catenary curves, transmission line sag, and other hyperbolic geometry problems. For example, to find the angle in a catenary: =ACOSH(sag/span + 1). ACOSH also appears in solutions to certain differential equations and heat transfer problems.
Can I convert ACOSH result to degrees? ACOSH returns radians. To convert to degrees, multiply by 180/PI: =ACOSH(number) * 180/PI(). However, note that ACOSH typically returns values in radians for mathematical consistency with other trigonometric functions in Excel.

Editorial review

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