COTH Function

Excel Functions › Math & Trig

Excel 2013+ Math & Trig

The Excel COTH function returns the hyperbolic cotangent of a number — the reciprocal of the hyperbolic tangent, 1/TANH. The argument is a plain number, not an angle.


Quick answer:
=COTH(1) hyperbolic cotangent of 1 = approx 1.3130

Syntax

=COTH(number)
ArgumentDescription
numberRequiredAny non-zero real number. COTH is the reciprocal of TANH, so an argument of 0 returns a #DIV/0! error.

How to use it

COTH is simply 1/TANH(number), introduced in Excel 2013. There is no degree-vs-radian issue — you pass a plain number:

=COTH(1) // approx 1.3130
=COTH(2) // approx 1.0373
=COTH(-1) // approx -1.3130 (odd function)

COTH is an odd function whose magnitude is always greater than 1, approaching 1 as the input grows. Use =1/TANH(x) in versions before Excel 2013.

Undefined at zero. Because TANH(0) is zero, =COTH(0) returns a #DIV/0! error. Use any non-zero argument.

Try it: interactive demo

Live demo

Pick a COTH example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What is the hyperbolic cotangent?
It is the reciprocal of the hyperbolic tangent: COTH(x) = 1/TANH(x). It is an odd function, undefined at x = 0, and its magnitude is always greater than 1.
Which Excel versions have COTH?
COTH was added in Excel 2013. In Excel 2010 and earlier, use =1/TANH(x) instead.
Why does COTH(0) return an error?
The hyperbolic tangent of 0 is zero, and dividing by zero is undefined, so =COTH(0) returns #DIV/0!. Use any non-zero argument.
Does COTH use degrees or radians?
Neither — COTH takes a plain real number, not an angle. There is no degree-to-radian conversion for hyperbolic functions.

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Related functions: TANH · COT · SECH · CSCH · EXP