Calculate the Euclidean distance in JavaScript

Definition

The Euclidean distance between two points is the length of the line segment connecting them. The formula for calculating it in 2D is equal to the hypotenuse of a right triangle, given by the Pythagorean theorem.

d^2 = x^2 + y^2 \\
x = x_2 - x_1\\
y = y_2 - y_1\\
d^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 \\
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Implementation

JavaScript's Math.hypot() method can be used to calculate the Euclidean distance between two points in 2 dimensions.

const distance = (x0, y0, x1, y1) => Math.hypot(x1 - x0, y1 - y0);

distance(1, 1, 2, 3); // ~2.2361

In 3 dimensions, the formula is the same, but with an additional dimension. For readability's sake, we should also use represent each point as an array.

const distance = ([x0, y0, z0], [x1, y1, z1]) =>
  Math.hypot(x1 - x0, y1 - y0, z1 - z0);

distance([1, 1, 1], [2, 3, 2]); // ~2.4495

In fact, for any number of dimensions, we can use the same formula. Using Object.keys() and Array.prototype.map(), we can map each coordinate to its difference between the two points. Then, using the spread operator (...), we can pass the resulting values to Math.hypot().

const euclideanDistance = (a, b) =>
  Math.hypot(...Object.keys(a).map(k => b[k] - a[k]));

euclideanDistance([1, 1], [2, 3]); // ~2.2361
euclideanDistance([1, 1, 1], [2, 3, 2]); // ~2.4495
euclideanDistance([1, 1, 1, 1], [2, 3, 2, 3]); // ~3.1623

Complexity

The time complexity of the algorithmic implementation is O(n), where n is the number of dimensions, due to the complexity of Array.prototype.map().