---
title: "Game maths"
package: "@phaser-ae/maths"
tier: Free
version: 3.0.0-3
released: 2026-10-14
updated: 2026-10-20
description: "The everyday maths of a game in one place: easing curves, 2D vectors, angles, ranges, smoothing, hit tests and a seed hash."
url: https://phaser.io/packs/maths
site: Phaser - https://phaser.io
---

# Game maths

The maths a game uses every frame: easing curves, vectors, angles, ranges, smoothing and hit tests, as plain functions
on `game.maths`. It saves writing a dot product, a shortest-arc turn or a point-in-polygon test by hand, and getting the
edge cases wrong.

## What it does

Every function takes plain numbers or `{ x, y }` objects and returns a new value. Nothing touches the game's objects,
its clock or its renderer, so the functions are safe to call anywhere, any number of times, from any step or test. It
has no dimension of its own, though its vectors and geometry are 2D.

The easing table has ten families (quad, cubic, quart, quint, sine, expo, circ, back, elastic and bounce), each in `in`,
`out` and `inOut` forms, plus `linear` and `swing`, short aliases such as `'elastic'`, and `bezier` for a CSS-style
cubic bezier. `ease()` resolves a name, a function or a bezier tuple, and throws on an unknown name so a typo shows at
once. The `tween` pack takes its easings from here, so a name that works in one works in the other.

The rest covers the small jobs that come up constantly. `turnToward` turns a turret along the shortest arc at a limited
rate. `approach` smooths a camera zoom the same way at any frame rate. `mapRange` turns hit points into a bar width.
`geom.segmentHitsCircle` checks a shot against an enemy, `geom.lineOfSight` checks a view past circular cover, and
`geom.predictPath` gives the points of a ballistic arc for an aiming preview. `hashCode` turns a level code into a seed.

## Features

- **Thirty-two named easings** — ten families in three shapes each, plus linear and swing, short aliases and cubic
  bezier curves.
- **2D vectors** — add, subtract, scale, dot, cross, length, distance, normalise, clamp length, polar conversion,
  rotate, lerp, step toward, perpendicular and reflect.
- **Angles** — radians throughout, wrapping, the shortest signed turn and a rate-limited turn toward.
- **Scalars and ranges** — lerp, clamp, range mapping, rounding, smoothstep and exponential approach.
- **Hit tests** — points in rectangles, circles and polygons, segment intersection, a segment against a circle and line
  of sight past circles.
- **Shape helpers** — polygon area and centroid, convex hull, closest point on a segment and a ballistic path preview.
- **A seed hash** — FNV-1a from a string to a 32-bit number, for seeding from a level code.

## Good for

- **Any game that tweens**, where one set of easing names serves code and tweens alike.
- **Shooters and top-down action**, with turrets that turn at a set rate and shots tested against enemies.
- **Artillery and throwing games** that preview a ballistic arc before the shot.
- **Smooth cameras and interface motion** that behave the same at 30 or 144 frames a second.
- **Seeded levels and daily challenges** made from a level code.

## Make it yours

There is nothing to configure: it is a library of functions. It arrives with `core-2d`, `core-3d` and `core-vector`, so
most games already have it. Two different uses: a twin-stick shooter that normalises the stick with `vec.normalize`,
turns its turret with `turnToward` and tests bullets with `segmentHitsCircle`; and a puzzle game's interface that uses
nothing but `ease('easeOutBack')` for pops and `approach` for smooth scrolling.

## A quick look

A few everyday calls:

```ts
const { ease, vec, geom, approach, turnToward, hashCode } = game.maths;
ease('easeOutBack')(0.5);
vec.normalize({ x: 3, y: 4 });
h.rot = turnToward(h.rot, vec.angleOf(vec.sub(player, h)), 3 * dt);
cam.zoom = approach(cam.zoom, wanted, 6, dt);
if (geom.segmentHitsCircle(muzzle, muzzleEnd, enemy, enemy.width / 2)) hit(enemy);
hashCode('level-3');
```

## Works with

- `tween` — requires this pack and shares its easing table.
- `core-2d`, `core-3d` and `core-vector` — include it.
- `geometry` — for whole shapes and curves as data: points along, random inside and overlaps.
- `vector-math` — for the maths of vector-line games.

## Good to know

- Vectors and geometry are 2D only.
- `vec` returns a fresh object on every call; in a hot loop over thousands of objects, write the arithmetic inline.
- `pointInPolygon` is undefined exactly on the boundary.
- `hashCode` is a 32-bit hash, so collisions are possible, and it is not cryptographic.

---

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