---
title: "Vector Maths"
package: "@phaser-ae/vector-math"
tier: Free
version: 3.0.0-3
released: 2026-10-14
updated: 2026-10-20
description: "The 2D vector arithmetic every line-art game otherwise rewrites, from add, scale and rotate to lengths, distances, angles and lerps, in one namespace that never mutates its arguments."
url: https://phaser.io/packs/vector-math
site: Phaser - https://phaser.io
---

# Vector Maths

The 2D vector arithmetic every line-art game otherwise writes again: add, scale, rotate, normalise, angles and lerps,
as one namespace of pure functions that never change what you pass them.

## What it does

Every function takes plain `{ x, y }` data and returns a new vector. Nothing mutates its arguments, which matters more
than it sounds: a helper that quietly writes back into the vector you passed is the classic source of a body that
applies one frame's velocity twice, and the bug stays invisible until something moves at the wrong speed. Reached as
`game.vecMath`, generic names such as `add`, `scale` and `dot` cannot collide with anything in your own code.

The squared forms are there for comparisons. `len2` and `dist2` skip the square root, and a comparison never needs
one: `dist2(a, b) < r * r` is the same test as `dist(a, b) < r` and costs less, so reach for it in anything that runs
per pair per frame.

## Features

- **Arithmetic** — `add`, `sub`, `scale` and `dot`.
- **Magnitudes and distances** — `len`, `len2`, `dist` and `dist2`, with and without the root.
- **Safe normalising** — `normalize` leaves a zero vector at zero rather than turning it into `NaN`.
- **Speed limits** — `clampLen` caps a magnitude without changing the direction.
- **Angles and turns** — `fromAngle` and `angleOf` between angles and vectors, and `rotate` about the origin.
- **Blends and steps** — `lerp` between two vectors, and `stepToward`, which moves toward a target by at most a step
  and never overshoots.
- **Steering angles** — `signedAngle` and `turnToward`, the angle helpers of `maths`, available under the same names.

## Good for

- **Thrust-and-coast ships** — thrust along a heading with `fromAngle` and a top speed with `clampLen`.
- **Homing and chasing** — a missile that turns toward its target, an enemy that steps toward the player.
- **Range checks** — `dist2` against a squared radius for every pair of rocks and shots.
- **Any 2D game logic** — positions and velocities in a line-art game or any other 2D game.

## Make it yours

There is nothing to configure: these are functions, used from `game.vecMath` or imported from the package. Two
everyday uses: a ship that adds `fromAngle(heading, thrust * dt)` to its velocity each frame and caps it with
`clampLen`; and a turret that turns its barrel with `turnToward` and checks its range with `dist2` before it fires.

## Works with

- `maths` — the source of `signedAngle` and `turnToward`, bundled with this pack; compose it too for easing, ranges and
  the rest of its game maths.
- `core-vector` — includes this pack with the rest of the vector kit.
- `vector-motion` — integration, gravity and screen wrap over the same plain data.
- `vector-hit` — collision tests over the same points.

## Good to know

- 2D only.
- Plain objects rather than typed arrays: this is for game logic, not for a tight inner loop over ten thousand
  particles, where you work on the arrays directly.
- Every call returns a new object, the price of never mutating; `vector-motion`'s integrator writes in place for that
  reason.

---

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