--- title: Math.atanh() short-title: atanh() slug: Web/JavaScript/Reference/Global_Objects/Math/atanh page-type: javascript-static-method browser-compat: javascript.builtins.Math.atanh sidebar: jsref --- The **`Math.atanh()`** static method returns the inverse hyperbolic tangent of a number. That is,

\begin{aligned}\forall x \in ({-1}, 1),\;\mathtt{\operatorname{Math.atanh}(x)} &= \operatorname{artanh}(x) = \text{the unique } y \text{ such that } \tanh(y) = x \\&= \frac{1}{2}\,\ln\left(\frac{1+x}{1-x}\right)\end{aligned}

{{InteractiveExample("JavaScript Demo: Math.atanh()")}} ```js interactive-example console.log(Math.atanh(-1)); // Expected output: -Infinity console.log(Math.atanh(0)); // Expected output: 0 console.log(Math.atanh(0.5)); // Expected output: 0.549306144334055 (approximately) console.log(Math.atanh(1)); // Expected output: Infinity ``` ## Syntax ```js-nolint Math.atanh(x) ``` ### Parameters - `x` - : A number between -1 and 1, inclusive. ### Return value The inverse hyperbolic tangent of `x`. If `x` is 1, returns {{jsxref("Infinity")}}. If `x` is -1, returns `-Infinity`. If `x` is less than -1 or greater than 1, returns {{jsxref("NaN")}}. ## Description Because `atanh()` is a static method of `Math`, you always use it as `Math.atanh()`, rather than as a method of a `Math` object you created (`Math` is not a constructor). ## Examples ### Using Math.atanh() ```js Math.atanh(-2); // NaN Math.atanh(-1); // -Infinity Math.atanh(-0); // -0 Math.atanh(0); // 0 Math.atanh(0.5); // 0.5493061443340548 Math.atanh(1); // Infinity Math.atanh(2); // NaN ``` ## Specifications {{Specifications}} ## Browser compatibility {{Compat}} ## See also - [Polyfill of `Math.atanh` in `core-js`](https://github.com/zloirock/core-js#ecmascript-math) - [es-shims polyfill of `Math.atanh`](https://www.npmjs.com/package/math.atanh) - {{jsxref("Math.acosh()")}} - {{jsxref("Math.asinh()")}} - {{jsxref("Math.cosh()")}} - {{jsxref("Math.sinh()")}} - {{jsxref("Math.tanh()")}}