Hyperbolic Functions Calculator
Evaluate sinh, cosh, tanh and their inverses for any real number input.
About Hyperbolic Functions Calculator
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
Worked example
With the default values below, Hyperbolic Functions Calculator returns Result of 1.1752011936. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Functionone of sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch(x), arcsinh(x), arccosh(x), arctanh(x)
- sinh(x)
- Input (x)
- 1
Results
- Result
- 1.1752011936
Step by step
- 1Evaluate sinh(1)= 1.1752011936
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.