# JavaScript - how to calculate distance between two points with Pythagorean equation?

Quick solution:

```
// P1 = (x1, y1); P2 = (x2, y2)
var a = x2 - x1;
var b = y2 - y1;
var distance = Math.sqrt(a * a + b * b);
```

Quick example:

```
// ONLINE-RUNNER:browser;
var a = 3 - 1;
var b = 3 - 1;
var distance = Math.sqrt(a * a + b * b);
console.log(distance); // 2.8284271247461903
```

## 1. Overview

Distance calculation between two points is possible with Pythagorean equation. In this article, example how to calculate the distance is presented.

## 2. Mathematical theorem for coordinate system

Distance calculation for points requires to start with transformation of Pythagorean equation to point version.

`a^2 + b^2 = c^2`

=> `c = sqrt(a^2 + b^2)`

`a = |x2 - x1|`

`b = |y2 - y1|`

`c = sqrt(|x2 - x1|^2 + |y2 - y1|^2)`

what can be transformed to:

`c = sqrt((x2 - x1)^2 + (y2 - y1)^2)`

`distance beetwen P1 and P2 is equal to c`

Note:absolute value of`a`

and`b`

can be avoided because of squares inside Pythagorean equation - squares remove minuses.

Example calculations:

`a = |x2 - x1| = |3 - 7| = 4`

`b = |y2 - y1| = |5 - 2| = 3`

`c = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5`

## 3. JavaScript custom distance function example

```
// ONLINE-RUNNER:browser;
function calculateDistance(p1, p2) {
var a = p2.x - p1.x;
var b = p2.y - p1.y;
return Math.sqrt(a * a + b * b);
}
// Example:
var p1 = {x: 7, y: 2};
var p2 = {x: 3, y: 5};
var distance = calculateDistance(p1, p2);
console.log(distance);
```

## 4. Math.hypot method example

Note:

`Math.hypot`

has been introduced inECMAScript 2015.

```
// ONLINE-RUNNER:browser;
function calculateDistance(p1, p2) {
var a = p2.x - p1.x;
var b = p2.y - p1.y;
return Math.hypot(a, b);
}
// Example:
var p1 = {x: 7, y: 2};
var p2 = {x: 3, y: 5};
var distance = calculateDistance(p1, p2);
console.log(distance);
```