diff --git a/src/js/position.js b/src/js/position.js
new file mode 100644
index 0000000..8799702
--- /dev/null
+++ b/src/js/position.js
@@ -0,0 +1,32 @@
+import { FPS, gravity } from './constants.js'
+import { add, scale, Vec2 } from './vector.js'
+
+/** @typedef {import('./shape').Shape} Shape */
+/** @typedef {import('./vector').Vector2D} Vector2D */
+
+/**
+ * Update the position of the shape.
+ *
+ * @param {Shape} shape
+ * @param {Vector2D} [g=gravity]
+ */
+export function updatePosition (shape, g = gravity) {
+  // Apply gravity to all shapes with mass
+  const acceleration = shape.M > 0 ? g : Vec2(0, 0)
+  shape.V = add(shape.V, scale(acceleration, 1 / FPS))
+  moveShape(shape, scale(shape.V, 1 / FPS))
+}
+
+/**
+ * Move a shape along a vector.
+ *
+ * @param {Shape} shape
+ * @param {Vector2D} v
+ */
+function moveShape (shape, v) {
+  shape.C = add(shape.C, v)
+
+  shape.X.forEach(function (vertex, index) {
+    shape.X[index] = add(vertex, v)
+  })
+}
diff --git a/test/js/position.test.js b/test/js/position.test.js
new file mode 100644
index 0000000..a5323e1
--- /dev/null
+++ b/test/js/position.test.js
@@ -0,0 +1,47 @@
+import { expect } from 'chai'
+
+import { updatePosition } from '../../src/js/position.js'
+import { RigidShape } from '../../src/js/shape.js'
+import { Vec2 } from '../../src/js/vector.js'
+
+describe('Position', function () {
+  describe('when passed no gravity', function () {
+    it('should update the position using a default value', function () {
+      // Arrange
+      const shape = makeShape()
+      const c = {...shape.C}
+      const v = {...shape.V}
+      const x = [...shape.X]
+
+      // Act
+      updatePosition(shape)
+
+      // Assert
+      expect(shape.C).not.to.equal(c)
+      expect(shape.V).not.to.equal(v)
+      shape.X.forEach((vertex, i) => expect(vertex).not.to.equal(x[i]))
+    })
+  })
+})
+
+function makeShape () {
+  const center = Vec2(500, 200)
+  const friction = 20
+  const restitution = 0
+  const mass = 400
+  const bounds = 1
+  const width = 5
+  const height = 5
+
+  const shape = RigidShape({
+    center,
+    mass,
+    friction,
+    restitution,
+    bounds,
+    width,
+    height
+  })
+
+  return shape
+}
diff --git a/types/position.d.ts b/types/position.d.ts
new file mode 100644
index 0000000..9fe838e
--- /dev/null
+++ b/types/position.d.ts
@@ -0,0 +1,11 @@
+/** @typedef {import('./shape').Shape} Shape */
+/** @typedef {import('./vector').Vector2D} Vector2D */
+/**
+ * Update the position of the shape.
+ *
+ * @param {Shape} shape
+ * @param {Vector2D} [g=gravity]
+ */
+export function updatePosition(shape: Shape, g?: import("./vector.js").Vector2D | undefined): void;
+export type Shape = import('./shape').Shape;
+export type Vector2D = import('./vector').Vector2D;