Math.log1p()

Baseline Widely available

This feature is well established and works across many devices and browser versions. It’s been available across browsers since July 2015.

The Math.log1p() static method returns the natural logarithm (base e) of 1 + x, where x is the argument. That is:

\forall x > -1,\;\mathtt{\operatorname{Math.log1p}(x)} = \ln(1 + x)

Try it

console.log(Math.log1p(1));
// Expected output: 0.6931471805599453

console.log(Math.log1p(0));
// Expected output: 0

console.log(Math.log1p(-1));
// Expected output: -Infinity

console.log(Math.log1p(-2));
// Expected output: NaN

Syntax

Math.log1p(x)

Parameters

x: A number greater than or equal to -1.

Return value

The natural logarithm (base e) of x + 1. If x is -1, returns -Infinity. If x < -1, returns NaN.

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 log(1 + x), where x is a small positive number, you should get an answer very close to x because: $\lim_{x \to 0} \frac{\log(1+x)}{x} = 1$ . If you calculate Math.log(1 + 1.1111111111e-15), you should get an answer close to 1.1111111111e-15. Instead, you will end up taking the logarithm of 1.00000000000000111022 (the roundoff is in binary, so sometimes it gets ugly), and get the answer 1.11022…e-15, with only 3 correct digits. If you calculate Math.log1p(1.1111111111e-15) instead, you will get a much more accurate answer, 1.1111111110999995e-15, with 15 correct digits of precision (actually 16 in this case).

If the value of x is less than -1, the return value is always NaN.

Because log1p() is a static method of Math, you always use it as Math.log1p(), rather than as a method of a Math object you created (Math is not a constructor).

Examples

Using Math.log1p()

Math.log1p(-2); // NaN
Math.log1p(-1); // -Infinity
Math.log1p(-0); // -0
Math.log1p(0); // 0
Math.log1p(1); // 0.6931471805599453
Math.log1p(Infinity); // Infinity

Specifications

Specification
ECMAScript® 2026 Language Specification # sec-math.log1p

Browser compatibility

	Desktop					Mobile						Server
	Chrome	Edge	Firefox	Opera	Safari	Chrome Android	Firefox for Android	Opera Android	Safari on IOS	Samsung Internet	WebView Android	Deno	Node.js
`log1p`	38	12	25	25	8	38	25	25	8	3.0	38	1.0	0.12.0