Hyperbolic Functions Calculator

Calculate All Six Hyperbolic Functions with Step-by-Step Solutions

Compute sinh(x), cosh(x), tanh(x), coth(x), sech(x), and csch(x) for any real number x.
Hyperbolic Function Definitions
\( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)
\( \cosh(x) = \dfrac{e^x + e^{-x}}{2} \)
\( \tanh(x) = \dfrac{e^x - e^{-x}}{e^x + e^{-x}} \)
\( \coth(x) = \dfrac{e^x + e^{-x}}{e^x - e^{-x}} \)
\( \text{sech}(x) = \dfrac{2}{e^x + e^{-x}} \)
\( \text{csch}(x) = \dfrac{2}{e^x - e^{-x}} \)
Enter any real number for x.
\( \sinh(x) \)
\( \cosh(x) \)
\( \tanh(x) \)
\( \coth(x) \)
\( \text{sech}(x) \)
\( \text{csch}(x) \)
Enter x and click "Calculate All Functions"
Step-by-step solution will appear here after calculation.
Hyperbolic Identities (verify with your results):
\( \cosh^2(x) - \sinh^2(x) = 1 \)  |  \( 1 - \tanh^2(x) = \text{sech}^2(x) \)  |  \( \tanh(x) = \dfrac{\sinh(x)}{\cosh(x)} \)  |  \( \coth(x) = \dfrac{1}{\tanh(x)} \)  |  \( \text{sech}(x) = \dfrac{1}{\cosh(x)} \)  |  \( \text{csch}(x) = \dfrac{1}{\sinh(x)} \)

More References and Links

  • Graphs of Hyperbolic Functions
  • Trigonometry Calculators and Solvers
  • Maths Calculators and Solvers
  • Geometry Calculators and Solvers
  • 3D Geometry Calculators and Solvers