What is the syntax for COSH in Excel?

The syntax for COSH is: =COSH(number)

What is COSH (hyperbolic cosine)?

COSH calculates the hyperbolic cosine: (e^x + e^-x)/2. It describes the shape of a hanging chain or cable (catenary curve). COSH(0)=1 and the function is always ≥1, symmetric around the y-axis.

What is a catenary curve and how does COSH relate?

A catenary is the curve formed by a hanging chain or cable under gravity. The equation is y = a*COSH(x/a). Power lines, suspension bridge cables, and the Gateway Arch all follow catenary curves described by COSH.

How do I calculate a catenary curve in Excel?

Use y = a*COSH(x/a) where 'a' is a parameter controlling the curve's shape. For x values from -5 to 5: =a*COSH(x/a). Smaller 'a' = tighter curve, larger 'a' = flatter curve. Plot x vs y for the catenary shape.

Math & Trig

COSH Function in Excel

Returns the hyperbolic cosine of a number.

Syntax

=COSH(number)

Arguments

number (required): Any real number

Examples

=COSH(1) - Hyperbolic cosine of 1 - Result: 1.543

COSH 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

Works with any real number

Use cases

Engineering
Physics
Catenary curves

Frequently asked questions

What is COSH (hyperbolic cosine)? COSH calculates the hyperbolic cosine: (e^x + e^-x)/2. It describes the shape of a hanging chain or cable (catenary curve). COSH(0)=1 and the function is always ≥1, symmetric around the y-axis.
What is a catenary curve and how does COSH relate? A catenary is the curve formed by a hanging chain or cable under gravity. The equation is y = a*COSH(x/a). Power lines, suspension bridge cables, and the Gateway Arch all follow catenary curves described by COSH.
How do I calculate a catenary curve in Excel? Use y = a*COSH(x/a) where 'a' is a parameter controlling the curve's shape. For x values from -5 to 5: =a*COSH(x/a). Smaller 'a' = tighter curve, larger 'a' = flatter curve. Plot x vs y for the catenary shape.

Editorial review

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