Compute sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch and their inverses. Enter a number or a function value to solve for x.
This smart calculator computes hyperbolic functions such as sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch(x) as well as their inverse hyperbolic functions instantly with accurate numeric results.
Easily select any function from the dropdown menu.
As soon as you enter a value, the calculator automatically computes the result without needing a submit button.
Fast, smooth, and beginner-friendly.
The calculator uses exponential definitions such as:
Inverse functions are calculated using logarithmic formulas.
The calculator automatically detects undefined or invalid values.
1️⃣ Select a hyperbolic or inverse hyperbolic function from the dropdown menu.
2️⃣ Enter a numeric value in the input field.
3️⃣ The calculator applies the correct mathematical formula:
4️⃣ If the input falls outside the valid domain, the calculator shows “invalid input” or “undefined”.
5️⃣ The result is displayed instantly in the format:
function(value) = result
If you select:
sinh(x)
And enter:
x = 1
The calculator computes:
sinh(1) ≈ 1.1752
Using the formula (e¹ − e⁻¹) / 2.
Clear answers about computing hyperbolic and inverse hyperbolic functions quickly and accurately.
It calculates the values of hyperbolic functions such as sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch(x) and their inverse functions including arsinh(x), arcosh(x), artanh(x), arcoth(x), arsech(x), and arcsch(x).
It uses the exponential definitions: sinh(x) = (eˣ − e⁻ˣ) / 2 and cosh(x) = (eˣ + e⁻ˣ) / 2. Other functions like tanh(x) are derived from these formulas.
Inverse hyperbolic functions are computed using logarithmic formulas. For example, arsinh(x) = ln(x + √(x² + 1)) and artanh(x) = ½ ln((1 + x) / (1 − x)).
Yes. It automatically detects values outside the valid mathematical domain. For example, arcosh(x) is only defined for x ≥ 1, and artanh(x) is only valid when −1 < x < 1. If an invalid value is entered, the calculator displays “invalid input” or “undefined.”
No. The calculator works in real time. As soon as you enter a value or change the selected function, the result updates automatically.
Some functions are undefined at 0. For example, coth(0) and csch(0) are undefined because they involve division by zero. The calculator correctly displays “undefined” in such cases.
Yes. It is ideal for algebra, calculus, and engineering students who need quick and accurate hyperbolic function calculations for homework, quizzes, and exam preparation.
Yes. The calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktop computers.
Yes. It is completely free to use with no sign-up or hidden fees required.
You can click the “Clear” button to remove the current input or use the “Reload Calculator” button to reset the function selection and start fresh.
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