Hyperbolic Functions Calculator
Evaluate sinh, cosh, tanh and their inverses for any real number input.
Inputs
Result
1.1752011936
Step by step
Evaluate sinh(1)
(e^1 − e^−1) / 2
= 1.1752011936
How it works
Hyperbolic functions are analogs of trigonometric functions defined using the exponential function: sinh(x) = (eˣ − e⁻ˣ)/2, cosh(x) = (eˣ + e⁻ˣ)/2, tanh(x) = sinh(x)/cosh(x). Their inverses are expressed in terms of logarithms.
Formulas
Hyperbolic definitions
sinh x = (eˣ − e⁻ˣ)/2, cosh x = (eˣ + e⁻ˣ)/2
- x
- Input value
- e
- Euler's number ≈ 2.71828
Inverse hyperbolic
arcsinh(x) = ln(x + √(x² + 1))
- x
- Input value
Frequently Asked Questions
What is the difference between sin and sinh?
sin is circular (relates to the unit circle), while sinh is hyperbolic (relates to the unit hyperbola). sinh(x) = (eˣ − e⁻ˣ)/2 grows exponentially, unlike sin which oscillates between −1 and 1.
What are hyperbolic functions used for?
They appear in catenary curves (hanging cables), special relativity (rapidity), and solutions to differential equations like the heat equation.