The Excel SECH function returns the hyperbolic secant of a number — the reciprocal of the hyperbolic cosine, 1/COSH. The argument is a plain number, not an angle.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | Any real number. SECH is the reciprocal of COSH, so its result always falls between 0 (exclusive) and 1 (inclusive). |
How to use it
SECH is simply 1/COSH(number), introduced in Excel 2013. There is no degree-vs-radian issue — you pass a plain number:
Because COSH is never less than 1, SECH never exceeds 1 and never errors out — it peaks at 1 when x = 0 and tapers smoothly toward 0 either side. Use =1/COSH(x) in versions before Excel 2013.
The soliton bump. The SECH curve is a smooth, symmetric bell-like pulse that appears in soliton waves and signal processing.
Try it: interactive demo
Pick a SECH example to see the formula and its result.
Practice workbook
Frequently asked questions
What is the hyperbolic secant?
SECH(x) = 1/COSH(x). Its maximum value is 1 (at x = 0) and it never goes below 0.Which Excel versions have SECH?
=1/COSH(x) instead.Does SECH use degrees or radians?
Can SECH ever return an error?
1/COSH(x) is always defined, so SECH never divides by zero or errors.Master functions like this in one day
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