Hyperbolic Functions Calculator

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Forward mode takes x and returns all six hyperbolic values. Inverse mode takes x and returns all six arc-hyperbolic values.
Any real number for forward mode. For inverse mode, domain restrictions apply: arcosh needs x >= 1, artanh needs |x| < 1, etc.
Number of decimal places shown in each result.
sinh(x)
1.175201

Hyperbolic sine: (e^x - e^-x) / 2

cosh(x)1.543081
tanh(x)0.761594
coth(x)1.313035
sech(x)0.648054
csch(x)0.850918

At x = 1: sinh = 1.175201, cosh = 1.543081, tanh = 0.761594.

  • cosh(x) is always >= 1 (here 1.543081), and sinh(x) can be any real number.
  • The Pythagorean-like identity cosh^2(x) - sinh^2(x) = 1 holds: 1.

Next stepSwitch to Inverse mode to work backwards: enter a hyperbolic function output and recover the original x.

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