# 6 Simple JS Math Functions You Can Use Everyday.

By Kelly Milligan

Here at Thinkingbox we often need to break outside of normal browser conventions. HTML and CSS provide a great foundation, but when the goal is to create something a bit more bespoke we must turn to JavaScript.

We love these simple math functions that make things a whole lot easier; they enable us to organize complex systems into simple rules. Once you’re used to using them, you can turn to them increasingly often when solving a math or visual problem. Aces!

**Sign**

A useful tool for discovering the “direction” of a number. Is it positive, negative or zero?

function sign( val ) {

return val === 0 ? 0 : val > 0 ? 1 : -1

}// Example:

const scrollDelta = ( currentScrollY — prevScrollY )

const scrollDirection = sign( scrollDelta )

*Note: There’s a **native browser method** for **sign**, however it is not supported in Internet Explorer (Edge has support though thankfully).*

**Clamp**

Trim a value to be within the **min** and **max** values. Combines a **Math.min()** and **Math.max()** into a single method.

function clamp( val, min, max ) {

return Math.min( Math.max( val, min ), max )

}// Example:

const MAX_VELOCITY = 10

const clampedVelocity = clamp( velocity, -MAX_VELOCITY, MAX_VELOCITY )

**Within Range**

Check whether the supplied number is within the **min** and **max** numbers. Returns a boolean value

function withinRange( val, min, max ) {

return ( val >= min && val <= max )

}// Example:

const isMouseOnLeft = withinRange(mouseX, 0, window.innerWidth / 2)

**Lerp** (Linear intERPolation)

Calculates a value between two different values, based on the **alpha** or **ratio** value. Super useful for animation and tweening.

function lerp( a, b, alpha ) {

return a + alpha * ( b — a )

}// Example:

const alpha = Math.sin( performance.now() ) * 0.5 + 0.5 // cycle between 0 and 1

const positionX = lerp( 0, window.innerWidth, alpha )

*Note: There are also versions of lerp that calculate 2D and 3D point interpolations, which are very useful in canvas or WebGL animation.*

**Degrees to Radians, Radians to Degrees**

When dealing with angles in Javascript (or many other math systems) it’s assumed that they are defined in Radians: where one **360 degree** revolution is equal to **2π radians** (6.283 radians).

It can be much easier to reason about angles in degrees for us, so having a quick way to convert between the different angle units is helpful!

function degToRad( degrees ) {

return degrees * ( Math.PI / 180 )

}function radToDeg( radians ) {

return radians * ( 180 / Math.PI )

}// Example:

const progress = Math.sin( performance.now() ) * 0.5 + 0.5 // cycle between 0 and 1

const progressAroundCircle = degToRad( 360 * progress )

*Note: These conversions become very useful when working with canvas or WebGL contexts, as many of their native functions for angle-based operations use radians.*

**Distance**

Calculate the total distance (the “hypotenuse”) between two points using the Pythagorean Theorem. Particularly useful for mouse coordinate calculations.

function distance( x1, y1, x2, y2 ) {

const dx = x2 — x1

const dy = y2 — y1 return Math.sqrt( dx * dx + dy * dy )

}// Example:

const proximity = distance( 0, 0, mouseX, mouseY )

if ( proximity < 200 ) console.log( ‘mouse is in upper left corner!’ );