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COSH Function
Summary
The Excel COSH function calculates the hyperbolic cosine of a given number, a fundamental mathematical operation used in engineering, physics, and advanced statistical analysis.
Syntax
COSH(number)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| number | Number |
Yes | The real number input for hyperbolic cosine calculation |
Using the COSH Function
COSH is a key hyperbolic trigonometry function that returns the hyperbolic cosine value. It's widely used in mathematical modeling, electrical engineering for transmission line calculations, physics for relativity equations, and statistical analysis involving hyperbolic distributions.
Common COSH Examples
Basic COSH Calculation
=COSH(4)Calculates hyperbolic cosine of 4, returning approximately 27.308233.
COSH with Natural Exponential
=COSH(EXP(1))Hyperbolic cosine using base of natural logarithm (e ≈ 2.718), returns approximately 7.6101251.
Frequently Asked Questions
Common Errors and Solutions
#VALUE!
Cause: Non-numeric input provided
Solution: Ensure the number argument contains valid numeric data
#NUM!
Cause: Input outside acceptable range (rare for COSH)
Solution: Use numbers within Excel's numeric limits
Notes
- Hyperbolic cosine is always ≥ 1 for real numbers
- COSH(0) = 1
- The function grows exponentially for large |x| values
- Minimum value occurs at x = 0
- Useful in catenary curve calculations and hyperbolic geometry
Compatibility
Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365
Not available in: Excel 2003 and earlier
Content last reviewed: December 11, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+