Speaking JavaScript (2014)
Part III. JavaScript in Depth
Chapter 21. Math
The Math object is used as a namespace for several math functions. This chapter provides an overview.
Math Properties
The properties of Math are as follows:
Math.E
Euler’s constant (e)
Math.LN2
Natural logarithm of 2
Math.LN10
Natural logarithm of 10
Math.LOG2E
Base 2 logarithm of e
Math.LOG10E
Base 10 logarithm of e
Math.PI
The ratio of the circumference of a circle to its diameter (3.14159 ...), π
Math.SQRT1_2
The square root of one-half, 
Math.SQRT2
The square root of two, 
Numerical Functions
The numerical functions of Math include the following:
Math.abs(x)
Returns the absolute value of x.
Math.ceil(x)
Returns the smallest integer ≥ x:
> Math.ceil(3.999)
4
> Math.ceil(3.001)
4
> Math.ceil(-3.001)
-3
> Math.ceil(3.000)
3
For more on converting floating-point numbers to integers, see Converting to Integer.
Math.exp(x)
Returns ex where e is Euler’s constant (Math.E). This is the inverse of Math.log().
Math.floor(x)
Returns the largest integer ≤ x:
> Math.floor(3.999)
3
> Math.floor(3.001)
3
> Math.floor(-3.001)
-4
> Math.floor(3.000)
3
For more on converting floating-point numbers to integers, see Converting to Integer.
Math.log(x)
Returns the natural (base is Euler’s constant) logarithm ln(x) of x. This is the inverse of Math.exp().
Math.pow(x, y)
Returns xy, x raised to the power of y:
> Math.pow(9, 2)
81
> Math.pow(36, 0.5)
6
Math.round(x)
Returns x rounded to the nearest integer (the greater one if it is between two integers):
> Math.round(3.999)
4
> Math.round(3.001)
3
> Math.round(3.5)
4
> Math.round(-3.5)
-3
For more on converting floating-point numbers to integers, see Converting to Integer.
Math.sqrt(x)
Returns 
, the square root of x:
> Math.sqrt(256)
16
Trigonometric Functions
The trigonometric methods accept and return angles as radians. The following functions show you how you could implement conversions, should you need to:
§ From degrees to radians:
§ function toRadians(degrees) {
§ return degrees / 180 * Math.PI;
}
Here is the interaction:
> toRadians(180)
3.141592653589793
> toRadians(90)
1.5707963267948966
§ From radians to degrees:
§ function toDegrees(radians) {
§ return radians / Math.PI * 180;
}
Here is the interaction:
> toDegrees(Math.PI * 2)
360
> toDegrees(Math.PI)
180
The trigonometric methods are as follows:
Math.acos(x)
Returns the arc cosine of x.
Math.asin(x)
Returns the arc sine of x.
Math.atan(x)
Returns the arc tangent of x.
Math.atan2(y, x)
Returns the arc tangent of the quotient 
.
Math.cos(x)
Returns the cosine of x.
Math.sin(x)
Returns the sine of x.
Math.tan(x)
Returns the tangent of x.
Other Functions
Following are the remaining Math functions:
min(x1?, x2?, ...)
Returns the smallest number among the parameters:
> Math.min()
Infinity
> Math.min(27)
27
> Math.min(27, -38)
-38
> Math.min(27, -38, -43)
-43
Use it on arrays via apply() (see func.apply(thisValue, argArray)):
> Math.min.apply(null, [27, -38, -43])
-43
max(x1?, x2?, ...)
Returns the largest number among the parameters:
> Math.max()
-Infinity
> Math.max(7)
7
> Math.max(7, 10)
10
> Math.max(7, 10, -333)
10
Use it on arrays via apply() (see func.apply(thisValue, argArray)):
> Math.max.apply(null, [7, 10, -333])
10
Math.random()
Returns a pseudorandom number r, 0 ≤ r < 1. The following function uses Math.random() to compute a random integer:
/**
* Compute a random integer within the given range.
*
* @param [lower] Optional lower bound. Default: zero.
* @returns A random integer i, lower ≤ i < upper
*/
function getRandomInteger(lower, upper) {
if (arguments.length === 1) {
upper = lower;
lower = 0;
}
return Math.floor(Math.random() * (upper - lower)) + lower;
}