`Math` • JavaScript for impatient programmers (ES2022 edition)

17 `Math`

Math is an object with data properties and methods for processing numbers. You can see it as a poor man’s module: It was created long before JavaScript had modules.

17.1 Data properties

Math.E: number ^[ES1]

Euler’s number, base of the natural logarithms, approximately 2.7182818284590452354.
Math.LN10: number ^[ES1]

The natural logarithm of 10, approximately 2.302585092994046.
Math.LN2: number ^[ES1]

The natural logarithm of 2, approximately 0.6931471805599453.
Math.LOG10E: number ^[ES1]

The logarithm of e to base 10, approximately 0.4342944819032518.
Math.LOG2E: number ^[ES1]

The logarithm of e to base 2, approximately 1.4426950408889634.
Math.PI: number ^[ES1]

The mathematical constant π, ratio of a circle’s circumference to its diameter, approximately 3.1415926535897932.
Math.SQRT1_2: number ^[ES1]

The square root of 1/2, approximately 0.7071067811865476.
Math.SQRT2: number ^[ES1]

The square root of 2, approximately 1.4142135623730951.

17.2 Exponents, roots, logarithms

Math.cbrt(x: number): number ^[ES6]

Returns the cube root of x.
```
> Math.cbrt(8)
2
```
Math.exp(x: number): number ^[ES1]

Returns e^x (e being Euler’s number). The inverse of Math.log().
```
> Math.exp(0)
1
> Math.exp(1) === Math.E
true
```
Math.expm1(x: number): number ^[ES6]

Returns Math.exp(x)-1. The inverse of Math.log1p(). Very small numbers (fractions close to 0) are represented with a higher precision. Therefore, this function returns more precise values whenever .exp() returns values close to 1.
Math.log(x: number): number ^[ES1]

Returns the natural logarithm of x (to base e, Euler’s number). The inverse of Math.exp().
```
> Math.log(1)
0
> Math.log(Math.E)
1
> Math.log(Math.E ** 2)
2
```
Math.log1p(x: number): number ^[ES6]

Returns Math.log(1 + x). The inverse of Math.expm1(). Very small numbers (fractions close to 0) are represented with a higher precision. Therefore, you can provide this function with a more precise argument whenever the argument for .log() is close to 1.
Math.log10(x: number): number ^[ES6]

Returns the logarithm of x to base 10. The inverse of 10 ** x.
```
> Math.log10(1)
0
> Math.log10(10)
1
> Math.log10(100)
2
```
Math.log2(x: number): number ^[ES6]

Returns the logarithm of x to base 2. The inverse of 2 ** x.
```
> Math.log2(1)
0
> Math.log2(2)
1
> Math.log2(4)
2
```
Math.pow(x: number, y: number): number ^[ES1]

Returns x^y, x to the power of y. The same as x ** y.
```
> Math.pow(2, 3)
8
> Math.pow(25, 0.5)
5
```
Math.sqrt(x: number): number ^[ES1]

Returns the square root of x. The inverse of x ** 2.
```
> Math.sqrt(9)
3
```

17.3 Rounding

Rounding means converting an arbitrary number to an integer (a number without a decimal fraction). The following functions implement different approaches to rounding.

Math.ceil(x: number): number ^[ES1]

Returns the smallest (closest to −∞) integer i with x ≤ i.
```
> Math.ceil(2.1)
3
> Math.ceil(2.9)
3
```
Math.floor(x: number): number ^[ES1]

Returns the largest (closest to +∞) integer i with i ≤ x.
```
> Math.floor(2.1)
2
> Math.floor(2.9)
2
```
Math.round(x: number): number ^[ES1]

Returns the integer that is closest to x. If the decimal fraction of x is .5 then .round() rounds up (to the integer closer to positive infinity):
```
> Math.round(2.4)
2
> Math.round(2.5)
3
```
Math.trunc(x: number): number ^[ES6]

Removes the decimal fraction of x and returns the resulting integer.
```
> Math.trunc(2.1)
2
> Math.trunc(2.9)
2
```

Tbl. 12 shows the results of the rounding functions for a few representative inputs.

Table 12: Rounding functions of `Math`. Note how things change with negative numbers because “larger” always means “closer to positive infinity”.
	`-2.9`	`-2.5`	`-2.1`	`2.1`	`2.5`	`2.9`
`Math.floor`	`-3`	`-3`	`-3`	`2`	`2`	`2`
`Math.ceil`	`-2`	`-2`	`-2`	`3`	`3`	`3`
`Math.round`	`-3`	`-2`	`-2`	`2`	`3`	`3`
`Math.trunc`	`-2`	`-2`	`-2`	`2`	`2`	`2`

17.4 Trigonometric Functions

All angles are specified in radians. Use the following two functions to convert between degrees and radians.

function degreesToRadians(degrees) {
  return degrees / 180 * Math.PI;
}
assert.equal(degreesToRadians(90), Math.PI/2);

function radiansToDegrees(radians) {
  return radians / Math.PI * 180;
}
assert.equal(radiansToDegrees(Math.PI), 180);

Math.acos(x: number): number ^[ES1]

Returns the arc cosine (inverse cosine) of x.
```
> Math.acos(0)
1.5707963267948966
> Math.acos(1)
0
```
Math.acosh(x: number): number ^[ES6]

Returns the inverse hyperbolic cosine of x.
Math.asin(x: number): number ^[ES1]

Returns the arc sine (inverse sine) of x.
```
> Math.asin(0)
0
> Math.asin(1)
1.5707963267948966
```
Math.asinh(x: number): number ^[ES6]

Returns the inverse hyperbolic sine of x.
Math.atan(x: number): number ^[ES1]

Returns the arc tangent (inverse tangent) of x.
Math.atanh(x: number): number ^[ES6]

Returns the inverse hyperbolic tangent of x.
Math.atan2(y: number, x: number): number ^[ES1]

Returns the arc tangent of the quotient y/x.
Math.cos(x: number): number ^[ES1]

Returns the cosine of x.
```
> Math.cos(0)
1
> Math.cos(Math.PI)
-1
```
Math.cosh(x: number): number ^[ES6]

Returns the hyperbolic cosine of x.
Math.hypot(...values: number[]): number ^[ES6]

Returns the square root of the sum of the squares of values (Pythagoras’ theorem):
```
> Math.hypot(3, 4)
5
```
Math.sin(x: number): number ^[ES1]

Returns the sine of x.
```
> Math.sin(0)
0
> Math.sin(Math.PI / 2)
1
```
Math.sinh(x: number): number ^[ES6]

Returns the hyperbolic sine of x.
Math.tan(x: number): number ^[ES1]

Returns the tangent of x.
```
> Math.tan(0)
0
> Math.tan(1)
1.5574077246549023
```
Math.tanh(x: number): number; ^[ES6]

Returns the hyperbolic tangent of x.

17.5 Various other functions

Math.abs(x: number): number ^[ES1]

Returns the absolute value of x.
```
> Math.abs(3)
3
> Math.abs(-3)
3
> Math.abs(0)
0
```

Math.clz32(x: number): number ^[ES6]

Counts the leading zero bits in the 32-bit integer x. Used in DSP algorithms.

> Math.clz32(0b01000000000000000000000000000000)
1
> Math.clz32(0b00100000000000000000000000000000)
2
> Math.clz32(2)
30
> Math.clz32(1)
31

Math.max(...values: number[]): number ^[ES1]

Converts values to numbers and returns the largest one.
```
> Math.max(3, -5, 24)
24
```
Math.min(...values: number[]): number ^[ES1]

Converts values to numbers and returns the smallest one.
```
> Math.min(3, -5, 24)
-5
```

Math.random(): number ^[ES1]

Returns a pseudo-random number n where 0 ≤ n < 1.

/** Returns a random integer i with 0 <= i < max */
function getRandomInteger(max) {
  return Math.floor(Math.random() * max);
}

Math.sign(x: number): number ^[ES6]

Returns the sign of a number:
```
> Math.sign(-8)
-1
> Math.sign(0)
0
> Math.sign(3)
1
```