JavaScript Math

The built-in Math object is JavaScript's calculator: rounding, powers, square roots, absolute values, and useful constants like pi. You have used a few of its methods already. This lesson covers the ones you will reach for most, and the rounding traps that catch people out.

// Math Is Not a Constructor

Unlike Date or Map, you never write new Math(). Everything is used directly:

Math.PI               // 3.141592653589793
Math.sqrt(16)         // 4
new Math()             // TypeError: Math is not a constructor

An object like this, used directly and never created with new, is called static. Every Math property is written Math.property, and every method Math.method(number).

// The Four Rounding Methods

One more surprise: halves always round up, toward positive infinity, even for negative numbers:

Math.round(2.5)    // 3
Math.round(-2.5)   // -2  (not -3)

// Rounding to Decimal Places

Math.round only rounds to whole numbers. To round to 2 places, multiply, round, then divide:

Math.round(3.14159 * 100) / 100    // 3.14  (a number)
(3.14159).toFixed(2)              // "3.14" (a string, for display)

Both can be tripped up by the decimal precision issue from the Numbers lesson:

Math.round(1.005 * 100) / 100    // 1     (expected 1.01)
(1.005).toFixed(2)                // "1.00" (same problem)

1.005 is actually stored as 1.00499999... A tiny nudge fixes it:

function roundTo(n, places) {
  const f = 10 ** places;
  return Math.round((n + Number.EPSILON) * f) / f;
}

roundTo(1.005, 2)   // 1.01

// Powers and Roots

Math.pow(2, 10)   // 1024  (same as 2 ** 10)
Math.sqrt(81)     // 9
Math.cbrt(27)     // 3   cube root
Math.sqrt(-1)     // NaN (no real answer)

// Absolute Value and Sign

Math.abs(-7.5)    // 7.5  distance from zero
Math.sign(-5)     // -1   negative
Math.sign(0)      // 0
Math.sign(42)     // 1    positive

// How far apart are two temperatures, regardless of order?
Math.abs(58 - 71)   // 13

// min and max

Math.max(4, 19, 7)          // 19
Math.min(...[4, 19, 7])     // 4  (spread an array)
Math.max()                  // -Infinity  (nothing to compare)

A handy pattern built from both: keep a number inside a range, called clamping:

const clamp = (n, lo, hi) => Math.min(Math.max(n, lo), hi);

clamp(150, 0, 100)   // 100
clamp(-20, 0, 100)   // 0
clamp(42, 0, 100)    // 42

// Sine and Cosine

Math.sin(x) and Math.cos(x) return a value between -1 and 1. The angle x must be in radians, not degrees, so convert first: radians = degrees × Math.PI / 180.

console.log(Math.sin(90 * Math.PI / 180));   // sine of 90 degrees
console.log(Math.cos(0 * Math.PI / 180));    // cosine of 0 degrees
console.log(Math.sin(90));                     // 90 RADIANS: wrong!

JS Math Reference goes further with trig, including why answers are sometimes a hair off.

// Logarithms

A logarithm answers "how many times must I multiply this base to get x?"

console.log(Math.log2(8));       // 2 x 2 x 2 = 8, so 3
console.log(Math.log10(1000));   // 10 x 10 x 10 = 1000, so 3
console.log(Math.log(10));       // base E: E multiplied about 2.3 times
console.log(Math.log(Math.E));     // 1
console.log(Math.log(1));        // any base to the power 0 is 1

Math.log uses base Math.E, so the two are twins: Math.log(Math.E) is exactly 1. The reference lesson shows a practical use (counting digits).

// Math.random()

Math.random() returns a random decimal from 0 (included) up to 1 (never reached). JS Math Random is all about turning that into dice rolls and random picks.

// Constants

JavaScript has 8 math constants, all written in capitals because they never change:

console.log(Math.E);         // Euler's number
console.log(Math.PI);        // pi
console.log(Math.SQRT2);     // square root of 2
console.log(Math.SQRT1_2);   // square root of 1/2
console.log(Math.LN2);       // natural log of 2
console.log(Math.LN10);      // natural log of 10
console.log(Math.LOG2E);     // base-2 log of E
console.log(Math.LOG10E);    // base-10 log of E

// Area and circumference of a circle
const r = 5;
console.log((Math.PI * r ** 2).toFixed(2));
console.log((2 * Math.PI * r).toFixed(2));

// Quick Check

const temps = [58, 71, 64];
console.log(Math.max(temps), Math.max(...temps));

// Try It

▶ Open Playground

1. Click Open Playground. Predict what round, floor, ceil, and trunc give for 4.5 and -4.5, then run it
2. Round 2.675 to two places with toFixed(2), then with roundTo. Which one gives the answer you expect?
3. Use clamp to keep a volume setting between 0 and 11
4. Find the difference between the highest and lowest value in an array with max, min, and spread