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The Math.acosh() function returns the hyperbolic arc-cosine of a number, that is

x1,Math.acosh(x)=arcosh(x)= the unique y0such thatcosh(y)=x\forall x \geq 1, \mathtt{\operatorname{Math.acosh}(x)} = \operatorname{arcosh}(x) = \text{ the unique } \; y \geq 0 \; \text{such that} \; \cosh(y) = x




A number.

Return value

The hyperbolic arc-cosine of the given number. If the number is less than 1, NaN.


Because acosh() is a static method of Math, you always use it as Math.acosh(), rather than as a method of a Math object you created (Math is no constructor).


Using Math.acosh()

Math.acosh(-1);  // NaN
Math.acosh(0);   // NaN
Math.acosh(0.5); // NaN
Math.acosh(1);   // 0
Math.acosh(2);   // 1.3169578969248166

For values less than 1 Math.acosh() returns NaN.


For all x1x \geq 1, we have arcosh(x)=ln(x+x2-1)\operatorname {arcosh} (x) = \ln \left(x + \sqrt{x^{2} - 1} \right) and so this can be emulated with the following function:

Math.acosh = Math.acosh || function(x) {
  return Math.log(x + Math.sqrt(x * x - 1));


Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.acosh' in that specification.
Standard Initial definition.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.acosh' in that specification.

Browser compatibility

Feature Chrome Edge Firefox (Gecko) Internet Explorer Opera Safari
Basic support 38 (Yes) 25 (25) No support 25 7.1
Feature Android Chrome for Android Edge Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support No support No support (Yes) 25.0 (25) No support No support 8

See also

Document Tags and Contributors

 Last updated by: jameshkramer,