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COTH Function
Summary
The Excel COTH function calculates the hyperbolic cotangent of a given number, providing essential trigonometric functionality for advanced mathematical and engineering calculations in spreadsheets.
Syntax
COTH(number)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| number | Number |
Yes | Numeric input representing the hyperbolic angle. Absolute value must be less than 2^27 to avoid errors. |
Using the COTH Function
COTH is valuable in fields like engineering, physics, and mathematics where hyperbolic functions model real-world phenomena such as catenary curves, transmission lines, and exponential growth/decay problems. Use it when standard trigonometric functions don't suffice for your analysis.
Common COTH Examples
Basic COTH Calculation
=COTH(2)Returns approximately 1.037, the hyperbolic cotangent of 2 radians.
COTH in Engineering Context
=COTH(A1)Calculates hyperbolic cotangent for angle in cell A1, useful for catenary or transmission line calculations.
Frequently Asked Questions
Common Errors and Solutions
#NUM!
Cause: Absolute value of number is 2^27 or greater
Solution: Use a number within valid range (|number| < 2^27)
#VALUE!
Cause: Non-numeric input provided
Solution: Ensure the input is a valid number
Notes
- Hyperbolic cotangent is the reciprocal of hyperbolic tangent: COTH(x) = 1/TANH(x)
- Mathematical formula: COTH(x) = (e^x + e^-x) / (e^x - e^-x)
- Ideal for modeling hanging cables, electrical transmission lines, and relativity calculations
Compatibility
Available in: Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365
Not available in: Excel 2010, Excel 2007, Excel 2003 and earlier
Content last reviewed: December 11, 2025
Update frequency: As needed
Excel versions tested: Excel 2013+