In JavaScript, the Math object is a built-in object that lets us do various mathematical operations.
It’s a non-function object with mathematical constants and functions to calculate various quantities. It only works with variables with the number type, and it doesn’t work with BigInt data.
The Math object isn’t a constructor. All the methods are static. We can refer to the members with the dot notation like Math.PI to get the value of Pi, or call the cosine function with Math.cos(x).
Constants are defined with full precision allowing for real numbers in JavaScript.
Constants
The Math object has the following constants:
Math.E
Euler’s constant and the base of natural logarithms, approximately 2.718281828459045.
Math.LN2
Natural logarithm of 2, approximately 0.6931471805599453.
Math.LN10
Natural logarithm of 10, approximately 2.302585092994046.
Math.LOG2E
Base 2 logarithm of E, approximately 1.4426950408889634.
Math.LOG10E
Base 10 logarithm of E, approximately 0.4342944819032518.
Math.PI
The ratio of the circumference of a circle to its diameter, approximately 3.141592653589793.
Math.SQRT1_2
The square root of 1/2, approximately 0.7071067811865476.
Math.SQRT2
The square root of 2, approximately 1.4142135623730951.
Methods
The Math object has many methods, like trigonometric functions, power functions, and logarithmic functions.
The trigonometric functions like sin(), cos(), tan(), asin(), acos(), atan(), atan2() expect angles in radians as arguments and also return angles in radians.
To convert radians to degrees, divide by (Math.PI / 180), and multiply by this to convert the other way.
The precision of the results are browser-dependent because each browser engine implements floating-point calculations differently. This means that different browsers may return different results for the same function.
Math.abs(x)
Returns the absolute value of a number. For example, we can use it as follows:
Math.abs(2) // returns 2
Math.abs(-2) // returns 2
Math.acos(x)
Returns the inverse cosine of a number. For example, we can use it as follows:
Math.acos(1) // returns 0
Math.acos(-1) // returns Math.PI
Math.acosh(x)
Returns the inverse hyperbolic cosine of a number. For example, we can use it as follows:
Math.acosh(1) // returns 0
Math.asin(x)
Returns the inverse sine of a number. For example, we can use it as follows:
Math.asin(1) // returns 1.5707963267948966
Math.asin(0) // returns 0
Math.asinh(x)
Returns the inverse hyperbolic sine of a number. For example, we can use it as follows:
Math.asin(1) // returns 0.881373587019543
Math.asin(0) // returns 0
Math.atan(x)
Returns the inverse tangent of a number. For example, we can use it as follows:
Math.atan(1) // returns 0.7853981633974483
Math.atan(0) // returns 0
Math.atanh(x)
Returns the inverse hyperbolic tangent of a number. For example, we can use it as follows:
Math.atanh(1) // returns Infinity
Math.atanh(0) // returns 0
Math.atan2(y, x)
Returns the inverse tangent of the quotient of its arguments. For example, we can use it as follows:
Math.atan2(1, 1) // returns 0.7853981633974483
Math.atan2(1, Math.SQRT2) // returns 0.9553166181245093
Math.cbrt(x)
Returns the cube root of a number. For example, we can use it as follows:
Math.cbrt(3) // returns 1.4422495703074083
Math.ceil(x)
Returns the smallest integer greater than or equal to a number. For example, we can use it as follows:
Math.ceil(1.5) // returns 2
Math.clz32(x)
Returns the number of leading zeroes of a 32-bit integer when x is converted to binary. For example, if we write:
Math.clz32(1)
We get 31 because the 1s digit is 1 and the other 31 digits before it are all 0. And if we write:
Math.clz32(2)
We get 30 because the 1s digit is 0, the 2s digit is 1, and the other 30 digits before it are all 0.
Math.cos(x)
Returns the cosine of a number. For example, we can use it as follows:
Math.cos(0) // returns 1
Math.cosh(x)
Returns the hyperbolic cosine of a number. For example, we can use it as follows:
Math.cosh(0) // returns 1
Math.exp(x)
Returns e to the power of x, where x is the argument, and e is Euler’s constant which is approximately 2.718281828459045, and it’s the base of the natural logarithm. We can use it as in the following code:
Math.exp(10) // returns 22026.465794806718
Math.expm1(x)
Returns Math.exp(x) with 1 subtracted from it. For example, we can use it as in the following code:
Math.expm1(1) // returns 1.718281828459045
Math.floor(x)
Returns the largest integer less than or equal to a number. For example, we can use it as in the following code:
Math.floor(1.1) // returns 1
Math.fround(x)
Returns the nearest single-precision float representation of a number.
A single-precision number has 32 bits, with the first bit used for the sign, the next 8 bits used for the exponent, and the remaining 23 bits are the fractional parts of the logarithm, also called the mantissa.
For example, we can use it as in the following code:
Math.fround(1.2) // returns 1.2000000476837158
Math.hypot(a,b,c,…)
Returns the square root of the sum of squares of its arguments. It takes an infinite number of arguments. For example, we can use it as follows:
Math.hypot(1,2) // returns 2.23606797749979
Math.hypot(1,2,3,4,5) // returns 7.416198487095663
Math.imul(x, y)
Returns the result of 32-bit integer multiplication. It rounds off decimals to the nearest integer before performing the multiplication. For example, we can use it as follows:
Math.imul(1,2) // returns 2
Math.imul(3,4.1) // returns 12
Math.log(x)
Returns the natural logarithm (log with base e, also ln) of a number. For example, we can use it as the following code:
Math.log(Math.E) // returns 1
Math.log(1) // returns 0
Math.log1p(x)
Returns the natural logarithm (log with base e, also ln) of 1 + x for a number x. For example, we can use it like the following code:
Math.log1p(Math.E - 1) // returns 1
Math.log1p(1) // returns 0.6931471805599453
Math.log10(x)
Returns the base 10 logarithm of a number. For example, we can use it like the following code:
Math.log10(1) // returns 0
Math.log10(10) // returns 1
Math.log2(x)
Returns the base 2 logarithm of a number. For example, we can use it like the following code:
Math.log2(2) // returns 0
Math.log2(10) // returns 3.321928094887362
Math.max(a,b,…)
Returns the largest of zero or more numbers. If nothing is passed in, -Infinity is returned. For example, we can use it like the following code:
Math.max(1, 2) // returns 2
Math.max(1,2,3,4,5) // returns 5
Math.max() // returns -Infinity
Math.min(a,b,…)
Returns the smallest of zero or more numbers. If nothing is passed in, Infinity is returned. For example, we can use it like the following code:
Math.min(1,2) // returns 1
Math.min(1,2,3,4,5) // returns 1
Math.min() // returns Infinity
Math.pow(x, y)
Returns base to the exponent power. For example, we can use it like the following code:
Math.pow(1,2) // returns 1
Math.min(2,3) // returns 8
Math.random()
Returns a pseudo-random number between 0 and 1. For example, we can use it as the following code:
Math.random() // returns 0.5275086314071882 or any other number between 0 and 1
Math.round(x)
Returns the value of a number rounded to the nearest integer. For example, we can use it as the following code:
Math.round(1.2) // returns 1
Math.sign(x)
Returns the sign of the x, indicating whether x is positive, negative, or zero. If x is positive, 1 is returned. If an x is negative, then -1 is returned. If x is 0 then 0 is returned. For example, we can use it like in the following code:
Math.sign(1) // returns 1
Math.sign(3) // returns 1
Math.sign(-1) // returns -1
Math.sign(-3) // returns -1
Math.sign(0) // returns 0
Math.sin(x)
Returns the sine of a number. For example, we can use it as in the following code:
Math.sin(1) // returns 0.8414709848078965
Math.sinh(x)
Returns the hyperbolic sine of a number. For example, we can use it as in the following code:
Math.sinh(1) // returns 1.1752011936438014
Math.sqrt(x)
Returns the positive square root of a number. For example, we can use it like in the following code:
Math.sqrt(1) // returns 1
Math.sqrt(2) // returns 1.4142135623730951
Math.tan(x)
Returns the tangent of a number. For example, we can use it as in the following code:
Math.tan(1) // returns 1.5574077246549023
Math.tanh(x)
Returns the hyperbolic tangent of a number. For example, we can use it as in the following code:
Math.tanh(2) // returns 0.9640275800758169
Math.trunc(x)
Returns the integer part of the number x, removing any fractional digits. For example, we can use it as in the following code:
Math.trunc(2.2223) // returns 2
Extending the Math Object
We can extend the Math object by adding custom properties and methods to it since it’s not a constructor. For instance, we can add the following function to the Math object to calculate the fifth root of a number:
Math.fifthRoot = (x) => Math.pow(x, 1/5);
The Math object is handy for making calculations in JavaScript. It has some useful constants and methods for calculations of common math operations like taking the logarithm and trigonometric functions.
We can extend the Math object easily by attaching methods and properties to it directly.
