/JavaScript

# Math.expm1()

The Math.expm1() function returns ex - 1, where x is the argument, and e is the base of natural logarithms.

## Syntax

Math.expm1(x)


### Parameters

x

A number.

### Return value

A number representing ex - 1, where e is the base of natural logarithms and x is the argument.

## Description

For very small values of x, adding 1 can reduce or eliminate precision. The double floats used in JS give you about 15 digits of precision. 1 + 1e-15 = 1.000000000000001, but 1 + 1e-16 = 1.000000000000000 and therefore exactly 1.0 in that arithmetic, because digits past 15 are rounded off.

When you calculate $e x \mathrm{e}^x$ where x is a number very close to 0, you should get an answer very close to 1 + x, because $lim x → 0 e x − 1 x = 1 \lim_{x \to 0} \frac{\mathrm{e}^x - 1}{x} = 1$. If you calculate Math.exp(1.1111111111e-15) - 1, you should get an answer close to 1.1111111111e-15. Instead, due to the highest significant figure in the result of Math.exp being the units digit 1, the final value ends up being 1.1102230246251565e-15, with only 3 correct digits. If, instead, you calculate Math.exp1m(1.1111111111e-15), you will get a much more accurate answer 1.1111111111000007e-15, with 11 correct digits of precision.

Because expm1() is a static method of Math, you always use it as Math.expm1(), rather than as a method of a Math object you created (Math is not a constructor).

## Examples

### Using Math.expm1()

Math.expm1(-1); // -0.6321205588285577
Math.expm1(0);  // 0
Math.expm1(1);  // 1.718281828459045


## Browser compatibility

Desktop Mobile Server
Chrome Edge Firefox Internet Explorer Opera Safari WebView Android Chrome Android Firefox for Android Opera Android Safari on IOS Samsung Internet Deno Node.js
expm1
38
12
25
No
25
8
38
38
25
25
8
3.0
1.0
0.12.0