Hyperbolic Tangent (tanh) Calculator

This hyperbolic tangent calculator returns tanh(x) for any real number x, with sinh(x) and cosh(x) shown alongside. The hyperbolic tangent is the ratio tanh(x) = sinh(x) / cosh(x), which also equals (e to the x, minus e to the minus x) over (e to the x, plus e to the minus x). It is an odd, S shaped function that always stays between -1 and 1, approaching those limits as x heads to large negative or positive values. Because of that bounded S shape, tanh is widely used as an activation function in neural networks, as well as in physics and engineering. Enter a value of x and read the result, rounded for display. The definition, a worked example and the assumptions are set out below.

Value of x

sinh(x)

cosh(x)

The formula

The hyperbolic tangent is tanh(x) = sinh(x) / cosh(x) = (e^x - e^-x) / (e^x + e^-x). It is odd and bounded strictly between -1 and 1.

Worked example

tanh(1) = sinh(1) / cosh(1), about 1.175201 / 1.543081 = 0.761594. Enter 1 above to confirm.

Frequently asked questions

What is the formula for tanh?

tanh(x) = sinh(x) / cosh(x), or equivalently (e^x - e^-x) / (e^x + e^-x).

What range does tanh take?

It always lies strictly between -1 and 1, approaching -1 for large negative x and 1 for large positive x.

Why is tanh used in machine learning?

Its smooth, bounded S shape maps any input to a value between -1 and 1, which is useful as a neuron activation function.

Who this calculator is for

This calculator is for students, engineers and machine-learning practitioners working with tanh.

What this calculator assumes

You enter a real number x.
tanh is computed from the exponential definition.
Results are rounded for display.

Formula and sources

Related calculators

Hyperbolic Sine Calculator: sinh(x).
Hyperbolic Cosine Calculator: cosh(x).
Inverse Hyperbolic Sine Calculator: arcsinh(x).

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