Math : Object

Contains math related constants and functions.

Math Properties

E : Number readonly

The constant e = 2.718...

Example:

console.log(Math.E);

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LN10 : Number readonly

The value of the natural log of 10. It is the reciprocal of LOG10E. Useful for computing the log base 10 of a number. See also log10().

Example:

console.log(Math.LN10);
console.log(Math.log(10));
console.log(1 / Math.LOG10E);

var log10 = function(x) {
  return Math.log(x) / Math.LN10;
};
console.log(log10(10000));

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LN2 : Number readonly

The value of the natural log of 2. It is the reciprocal of LOG2E. Useful for computing the log base 2 of a number. See also log2().

Example:

console.log(Math.LN2);
console.log(Math.log(2));
console.log(1 / Math.LOG2E);

var log2 = function(x) {
  return Math.log(x) / Math.LN2;
};
console.log(log2(64));

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LOG10E : Number readonly

The value of the log base 10 of e. It is the reciprocal of LN10. Useful for computing the log base 10 of a number. See also log10().

Example:

console.log(Math.LOG10E);
console.log(Math.log(Math.E) / Math.log(10));
console.log(1 / Math.LN10);

var log10 = function(x) {
  return Math.log(x) * Math.LOG10E;
};
console.log(log10(10000));

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LOG2E : Number readonly

The value of the log base 2 of e. It is the reciprocal of LN2. Useful for computing the log base 2 of a number. See also log2().

Example:

console.log(Math.LOG2E);
console.log(Math.log(Math.E) / Math.log(2));
console.log(1 / Math.LN2);

var log2 = function(x) {
  return Math.log(x) * Math.LOG2E;
};
console.log(log2(32));

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PI : Number readonly

The constant pi = 3.14...

Example:

console.log(Math.PI);

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SQRT1_2 : Number readonly

The value of 1 / sqrt(2).

Example:

console.log(Math.SQRT1_2);
console.log(1 / Math.sqrt(2));

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SQRT2 : Number readonly

The value of sqrt(2).

Example:

console.log(Math.SQRT2);
console.log(Math.sqrt(2));

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Math Methods

abs(x : Number) : Number

Returns the absolute value of x.

Example:

console.log(Math.abs(10));
console.log(Math.abs(-10));

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acos(x : Number) : Number

Returns the angle (in radians between 0 and pi) whose cosine is x. See also cos().

Example:

console.log(Math.acos(1));
console.log(Math.acos(0));
console.log(Math.acos(-1));

var acosDegrees = function(x) {
  return Math.acos(x) * 180 / Math.PI;
};
console.log(acosDegrees(0));

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acosh(x : Number) : Number

Returns the hyperbolic angle whose hyperbolic cosine is x. See also cosh().

Example:

console.log(Math.acosh(1));
console.log(Math.acosh(Math.cosh(3)));

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ECMAScript 2015 Spec

asin(x : Number) : Number

Returns the angle (in radians between -pi/2 and pi/2) whose sine is x. See also sin().

Example:

console.log(Math.asin(1));
console.log(Math.asin(0));
console.log(Math.asin(-1));

var asinDegrees = function(x) {
  return Math.asin(x) * 180 / Math.PI;
};
console.log(asinDegrees(1));

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asinh(x : Number) : Number

Returns the hyperbolic angle whose hyperbolic sine is x. See also sinh().

Example:

console.log(Math.sinh(0));
console.log(Math.asinh(Math.sinh(3)));

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ECMAScript 2015 Spec

atan(x : Number) : Number

Returns the angle (in radians between -pi/2 and pi/2) whose tangent is x. See also atan2() and tan().

Example:

console.log(Math.atan(1));
console.log(Math.atan(0));
console.log(Math.atan(-1));

var atanDegrees = function(x) {
  return Math.atan(x) * 180 / Math.PI;
};
console.log(atanDegrees(1));

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atan2(y : Number, x : Number) : Number

Returns the angle (in radians between -pi and pi) between the positive x axis and the line segment from the origin to the point at (x, y). See also atan() and tan().

Example:

console.log(Math.atan2(1, 0));
console.log(Math.atan2(0, 1));
console.log(Math.atan2(-1, 0));
console.log(Math.atan2(0, -1));

var atan2Degrees = function(y, x) {
  return Math.atan2(y, x) * 180 / Math.PI;
};
console.log(atan2Degrees(1, 0));

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atanh(x : Number) : Number

Returns the hyperbolic angle whose hyperbolic tangent is x. See also tanh().

Example:

console.log(Math.atanh(0));
console.log(Math.atanh(Math.tanh(0.5)));

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ECMAScript 2015 Spec

cbrt(x : Number) : Number

Returns cube root of x.

Example:

console.log(Math.cbrt(8));
console.log(Math.cbrt(27));

console.log(Math.cbrt(1234));
console.log(Math.pow(1234, 1 / 3));

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ECMAScript 2015 Spec

ceil(x : Number) : Number

Returns the next integer greater than or equal to x. See also round(), floor(), and trunc().

Example:

console.log(Math.ceil(1.9));
console.log(Math.ceil(2));
console.log(Math.ceil(-1.9));

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clz(x : Number) : Number

Returns the number of leading 0 bits in the 32 bit unsigned integer representation of x.

Example:

console.log(Math.clz32(0x00000000));
console.log(Math.clz32(0x08000000));
console.log(Math.clz32(0xFFFFFFFF));

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ECMAScript 2015 Spec

cos(x : Number) : Number

Returns the cosine of x (in radians). See also acos().

Example:

console.log(Math.cos(0));
console.log(Math.cos(Math.PI / 2));
console.log(Math.cos(Math.PI));

var cosDegrees = function(x) {
  return Math.cos(x * Math.PI / 180);
};
console.log(cosDegrees(45));

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cosh(x : Number) : Number

Returns the hyperbolic cosine of x. See also acosh().

Example:

console.log(Math.cosh(0));
console.log(Math.cosh(3));
console.log((Math.exp(3) + Math.exp(-3)) / 2);

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ECMAScript 2015 Spec

exp(x : Number) : Number

Returns e raised to the x power. See also log() and expm1().

Example:

console.log(Math.exp(2));
console.log(Math.E * Math.E);

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expm1(x : Number) : Number

Returns e raised to the x power minus 1. This is more accurate than using exp(x) - 1 when x is close to 0.

Example:

console.log(Math.expm1(0));
console.log(Math.exp(0) - 1);

console.log(Math.expm1(1));
console.log(Math.exp(1) - 1);

console.log(Math.expm1(1e-9));
console.log(Math.exp(1e-9) - 1);

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ECMAScript 2015 Spec

floor(x : Number) : Number

Returns the previous integer less than or equal to x. See also round(), ceil(), and trunc().

Example:

console.log(Math.floor(1.9));
console.log(Math.floor(2));
console.log(Math.floor(-1.9));

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fround(x : Number) : Number

Returns the closest single precision (32 bit) floating point number to x.

Example:

console.log(Math.fround(1.1));

// Values are automatically rounded when put in a Float32Array
var float32Array = new Float32Array(1);
float32Array[0] = 1.1;
console.log(float32Array[0]);

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ECMAScript 2015 Spec

hypot(x : Number, y : Number, [z : Number, [...]]) : Number

Returns length of a vector with components [x, y, ...]. This is the square root of the sum of the squares of the components.

Example:

console.log(Math.hypot(3, 4));
console.log(Math.sqrt(3 * 3 +  4 * 4));

console.log(Math.hypot(5, 12)); 
console.log(Math.sqrt(5 * 5 +  12 * 12));

var myVector = [3, 2, 8];
console.log(Math.hypot(...myVector));

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ECMAScript 2015 Spec

imul(x : Number, y : Number) : Number

Returns the product of x and y treating both values as 32 bit integer values and truncating the result to a 32 bit integer value.

Example:

console.log(Math.imul(3, 4));
console.log(Math.imul(-2, 9));

// The following overflows 
console.log(Math.imul(0x40000000, 2).toString(16));

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ECMAScript 2015 Spec

log(x : Number) : Number

Returns the natural logarithm (base e) of x. To compute the logarithm with respect to a different base b, use the formula Math.log(x) / Math.log(b). For base 10, you can use Math.log(x) * Math.LOG10E (or log10() with ECMAScript 2015). For base 2, you can use Math.log(x) * Math.LOG2E (or log2() with ECMAScript 2015). See also exp() and log1p().

Example:

var x = Math.exp(2);
console.log(x);
console.log(Math.log(x));

var logb = function(x, b) {
  return Math.log(x) / Math.log(b);
};
var log10 = function(x) {
  return Math.log(x) * Math.LOG10E;
};
console.log(logb(10000, 10));
console.log(log10(10000));

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log10(x : Number) : Number

Returns the base 10 logarithm of x. See also log(), LOG10E, and LN10.

Example:

console.log(Math.log10(1000));
console.log(Math.log(1000) * Math.LOG10E);
console.log(Math.log(1000) / Math.LN10);

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ECMAScript 2015 Spec

log1p(x : Number) : Number

Returns the natural logarithm (base e) of x + 1. This is more accurate than using log(x + 1) when x is close to 0.

Example:

console.log(Math.log(1 + 1));
console.log(Math.log1p(1));

console.log(Math.log(1e-9 + 1));
console.log(Math.log1p(1e-9));

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ECMAScript 2015 Spec

log2(x : Number) : Number

Returns the base 2 logarithm of x. See also log(), LOG2E, and LN2.

Example:

console.log(Math.log2(16));
console.log(Math.log(16) * Math.LOG2E);
console.log(Math.log(16) / Math.LN2);

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ECMAScript 2015 Spec

max(x1 : Number, x2 : Number, [...]) : Number

Returns the largest number among the parameters.

Example:

var x = 3, y = 1, z = 4;
console.log(Math.max(x, y, z));

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min(x1 : Number, x2 : Number, [...]) : Number

Returns the smallest number among the parameters.

Example:

var x = 3, y = 1, z = 4;
console.log(Math.min(x, y, z));

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pow(x : Number, y : Number) : Number

Returns x raised to the y power.

Example:

console.log(Math.pow(2, 3));
console.log(2 ** 3); // Equivalent to above (ECMAScript 2016)

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random() : Number

Returns a random number between 0 (inclusive) and 1 (exclusive). See also crypto.getRandomValues().

Example:

console.log(Math.random());
console.log(Math.random());
console.log(Math.random());
console.log();

// Random integer between min (inclusive) and max (exclusive)
const randomInt = (min, max) => {
  return Math.floor(Math.random() * (max - min)) + min;
};
console.log(randomInt(0, 100));
console.log(randomInt(0, 100));
console.log(randomInt(0, 100));
console.log();

// Shuffle an array
const shuffle = (array) => {
  for (let i = 0; i < array.length; i++) {
    const swapIndex = randomInt(i, array.length);
    [array[i], array[swapIndex]] = [array[swapIndex], array[i]];
  }
  return array;
};
console.dir(shuffle(['a', 'b', 'c', 'd', 'e']));
console.dir(shuffle(['a', 'b', 'c', 'd', 'e']));
console.dir(shuffle(['a', 'b', 'c', 'd', 'e']));
console.log();


// Produce a normally distributed random number using the Box-Muller transform
const randn = () => {
  if (randn.hasValues) {
    randn.hasValues = false;
    return randn.distance * Math.sin(randn.angle);
  }

  const random = Math.max(Math.random(), 1e-100);
  randn.distance = Math.sqrt(-2 * Math.log(random));
  randn.angle = Math.random() * Math.PI * 2;
  randn.hasValues = true;

  return randn.distance * Math.cos(randn.angle);
}

var minIndex = -4, maxIndex = 5;
var buckets = [];
for (let i = 0; i < 100; i++) {
  var index = Math.round(2 * randn());
  minIndex = Math.min(minIndex, index);
  maxIndex = Math.max(maxIndex, index);
  buckets[index] = (buckets[index] ?? 0) + 1;
}

for (let i = minIndex; i <= maxIndex; i++) {
  console.log(`${i / 2}`.padStart(4), ''.padStart(buckets[i], '*'));
}

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round(x : Number) : Number

Returns the closest integer to x. See also floor(), ceil(), and trunc().

Example:

console.log(Math.round(2.2));
console.log(Math.round(2.5));
console.log(Math.round(-2.5));

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sign(x : Number) : Number

Returns -1 if x is less than 0, 0 if x is 0, and 1 if x is greater than 0.

Example:

console.log(Math.sign(-9));
console.log(Math.sign(-0.3));
console.log(Math.sign(0));
console.log(Math.sign(0.8));
console.log(Math.sign(12));

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ECMAScript 2015 Spec

sin(x : Number) : Number

Returns the sine of x (in radians). See also asin().

Example:

console.log(Math.sin(0));
console.log(Math.sin(Math.PI / 2));
console.log(Math.sin(Math.PI));

var sinDegrees = function(x) {
  return Math.sin(x * Math.PI / 180);
};
console.log(sinDegrees(45));

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sinh(x : Number) : Number

Returns the hyperbolic sine of x. See also asinh().

Example:

console.log(Math.sinh(0));
console.log(Math.sinh(3));
console.log((Math.exp(3) - Math.exp(-3)) / 2);

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ECMAScript 2015 Spec

sqrt(x : Number) : Number

Returns the square root of x.

Example:

console.log(Math.sqrt(16));
console.log(Math.sqrt(49));
console.log(Math.sqrt(100));

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tan(x : Number) : Number

Returns the tangent of x (in radians). See also atan().

Example:

console.log(Math.tan(0));
console.log(Math.tan(Math.PI / 4));
console.log(Math.tan(Math.PI));

var tanDegrees = function(x) {
  return Math.tan(x * Math.PI / 180);
};
console.log(tanDegrees(45));

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tanh(x : Number) : Number

Returns the hyperbolic tan of x. See also atanh().

Example:

console.log(Math.tanh(0));
console.log(Math.tanh(3));
console.log((Math.exp(3) - Math.exp(-3)) / (Math.exp(3) + Math.exp(-3)));

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ECMAScript 2015 Spec

trunc(x : Number) : Number

Returns the integer portion of x. This is the same as floor(x) for positive numbers and ceil(x) for negative numbers. See also round().

Example:

[2.2, -2.4, -2.6].forEach(function(x) {
  console.log(x);
  console.log('  trunc ' + Math.trunc(x));
  console.log('  floor ' + Math.floor(x));
  console.log('  ceil  ' + Math.ceil(x));
  console.log('  round ' + Math.round(x));
  console.log();
});

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ECMAScript 2015 Spec

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