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SECH Function

Excel 2013+

Summary

The Excel SECH function calculates the hyperbolic secant of an angle provided in radians. This mathematical function returns 1 divided by the hyperbolic cosine (COSH) of the specified angle, useful for advanced engineering and scientific calculations.

Syntax

SECH(number)

Parameters

Parameter	Type	Required	Description
number	`Number`	Yes	Angle value in radians (absolute value must be less than 2^27)

Using the SECH Function

SECH is valuable in fields like physics, engineering, and mathematics where hyperbolic functions model real-world phenomena such as catenary curves, transmission lines, and special relativity calculations. Convert degrees to radians using RADIANS or PI()/180 multiplication for degree inputs.

Common SECH Examples

Basic SECH Calculation

=SECH(45)

Hyperbolic secant of 45 radians (very small result due to large angle) - returns approximately 5.73E-20

Degree Angle Conversion

=SECH(30*PI()/180)

Hyperbolic secant of 30 degrees (converted to radians) - returns approximately 1.87E-13

Practical Application

=SECH(RADIANS(45))

Hyperbolic secant of 45 degrees using RADIANS function for proper conversion

Frequently Asked Questions

SECH requires angles in radians. Convert degrees using RADIANS() or multiply by PI()/180.

SECH returns #NUM! error when the absolute value of number is 2^27 or greater.

Non-numeric inputs return #VALUE! error.

Common Errors and Solutions

#NUM!

Cause: Absolute value of number is 2^27 or greater

Solution: Ensure |number| < 2^27 and use appropriate angle values

#VALUE!

Cause: Non-numeric input provided

Solution: Verify the number argument contains a valid numeric value

Unexpected small results

Cause: Large angle values produce very small SECH results

Solution: Check if radians/degrees conversion is needed

Notes

Hyperbolic secant: SECH(x) = 1/COSH(x)
Absolute value constraint: |number| < 2^27 ≈ 134,217,728
For degree angles: SECH(degrees*PI()/180) or SECH(RADIANS(degrees))
Very large angles produce results approaching 0
Excel 2013+ including Microsoft 365
Related to complex number function IMSECH()

Compatibility

Available in: Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2010 and earlier versions

Content last reviewed: December 11, 2025
Update frequency: As needed
Excel versions tested: Excel 2013+