Math

Instant, private, and free

Hyperbolic Cosine Calculator.

Calculate the hyperbolic cosine of a real number.

On-device calculationNo signup
01

Set your values

Results update as you type.

Value: 1.543081

Value

0.000000

Results update automatically as you type.

Use Cases

Physics and Engineering Calculations

Hyperbolic cosine appears in the analysis of catenary curves, such as the shape of a hanging cable or chain under its own weight. Use this calculator to quickly evaluate cosh for design or study.

Example: Calculate cosh(2) to find the sag of a cable at a given point.

Mathematics and Education

Students and educators can verify hyperbolic function values, explore the behavior of cosh, and check homework or exam problems without manual computation.

Example: Check that cosh(0) = 1 and cosh(1) ≈ 1.54308.

Frequently Asked Questions

What is the hyperbolic cosine (cosh) of a number?
The hyperbolic cosine, denoted cosh(x), is defined as (e^x + e^-x)/2. It describes the shape of a hanging cable and appears in many areas of mathematics and physics. For real inputs, cosh(x) is always greater than or equal to 1.
How do I use this hyperbolic cosine calculator?
Simply enter a real number in the 'Input' field. The calculator will compute cosh(x) using the formula (e^x + e^-x)/2 and display the result instantly. No additional steps are required.
What is the range of the hyperbolic cosine function?
For any real number x, cosh(x) returns a value in the interval [1, ∞). The minimum value is 1 when x = 0, and it grows exponentially as |x| increases.

Tips & Common Mistakes

Tips

  • Remember that cosh(x) is an even function: cosh(-x) = cosh(x). So you only need to consider the absolute value of your input.
  • For large inputs (|x| > 700), the result may overflow standard floating-point representations; consider using scientific notation or a high-precision tool.
  • Use the identity cosh^2(x) - sinh^2(x) = 1 to cross-check your results if you also compute sinh(x).
  • If you need the inverse, use the arcosh (or inverse hyperbolic cosine) function, which is the inverse of cosh for non-negative inputs.

Common Mistakes to Avoid

  • Confusing hyperbolic cosine (cosh) with ordinary cosine (cos). They are different functions: cosh uses exponential functions, while cos is trigonometric.
  • Forgetting that cosh(x) is always ≥ 1, so a result less than 1 indicates an error in input or calculation.
  • Entering non-numeric values or leaving the input blank, which will cause an error. Ensure you enter a valid real number.

Last updated: August 13, 2026