diff --git a/package.json b/package.json
index 1f008be..7bcf1b1 100644
--- a/package.json
+++ b/package.json
@@ -57,7 +57,8 @@
     "node": ">=14"
   },
   "dependencies": {
-    "@mapbox/tile-cover": "3.0.1"
+    "@mapbox/tile-cover": "3.0.1",
+    "@math.gl/web-mercator": "^4.1.0"
   },
   "packageManager": "yarn@1.22.22",
   "volta": {
diff --git a/src/index.ts b/src/index.ts
index 8cdfd42..73a637e 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -1,4 +1,5 @@
 import {tiles} from '@mapbox/tile-cover';
+import {worldToLngLat} from '@math.gl/web-mercator';
 import type {Polygon} from 'geojson';
 
 const B = [
@@ -14,25 +15,27 @@ const S = [0n, 1n, 2n, 4n, 8n, 16n];
 type Quadbin = bigint;
 type Tile = {x: number; y: number; z: number};
 
-function tileToLongitude(tile: ReturnType<typeof cellToTile>, offset: number) {
-  const {x, z} = tile;
-  return 180 * ((2.0 * (x + offset)) / (1 << z) - 1.0);
-}
+const TILE_SIZE = 512;
 
-function tileToLatitude(tile: ReturnType<typeof cellToTile>, offset: number) {
-  const {y, z} = tile;
-  const expy = Math.exp(-((2.0 * (y + offset)) / (1 << z) - 1) * Math.PI);
-  return 360 * (Math.atan(expy) / Math.PI - 0.25);
+function quadbinToOffset(quadbin: bigint): [number, number, number] {
+  const {x, y, z} = cellToTile(quadbin);
+  const scale = TILE_SIZE / (1 << z);
+  return [x * scale, TILE_SIZE - y * scale, scale];
 }
 
-function cellToBoundingBox(cell: bigint) {
-  const tile = cellToTile(cell);
-  const xmin = tileToLongitude(tile, 0);
-  const xmax = tileToLongitude(tile, 1);
-  const ymin = tileToLatitude(tile, 1);
-  const ymax = tileToLatitude(tile, 0);
+function quadbinToWorldBounds(quadbin: bigint, coverage: number): [number[], number[]] {
+  const [xOffset, yOffset, scale] = quadbinToOffset(quadbin);
+  return [
+    [xOffset, yOffset],
+    [xOffset + coverage * scale, yOffset - coverage * scale]
+  ];
+}
 
-  return [xmin, ymin, xmax, ymax];
+function getQuadbinPolygon(quadbin: bigint, coverage = 1): number[] {
+  const [topLeft, bottomRight] = quadbinToWorldBounds(quadbin, coverage);
+  const [w, n] = worldToLngLat(topLeft);
+  const [e, s] = worldToLngLat(bottomRight);
+  return [e, n, e, s, w, s, w, n, e, n];
 }
 
 export function hexToBigInt(hex: string): bigint {
@@ -113,13 +116,13 @@ export function geometryToCells(geometry, resolution: bigint): Quadbin[] {
 }
 
 export function cellToBoundary(cell: bigint): Polygon {
-  const bbox = cellToBoundingBox(cell);
+  const bbox = getQuadbinPolygon(cell);
   const boundary = [
-    [bbox[0], bbox[3]],
     [bbox[0], bbox[1]],
-    [bbox[2], bbox[1]],
     [bbox[2], bbox[3]],
-    [bbox[0], bbox[3]]
+    [bbox[4], bbox[5]],
+    [bbox[6], bbox[7]],
+    [bbox[0], bbox[1]]
   ];
 
   return {type: 'Polygon', coordinates: [boundary]};
diff --git a/test/index.spec.js b/test/index.spec.js
index d634d32..68d9a55 100644
--- a/test/index.spec.js
+++ b/test/index.spec.js
@@ -80,30 +80,56 @@ test('Quadbin geometryToCells', async t => {
   t.end();
 });
 
-test('cellToBoundary works with quadbins', t => {
-  const result = cellToBoundary(ANY_QUADBIN);
-
-  t.equal(result.type, 'Polygon', 'Should return a Polygon');
-  t.ok(Array.isArray(result.coordinates), 'Coordinates should be an array');
-  t.equal(result.coordinates.length, 1, 'Should have one boundary array');
-
-  t.ok(result.coordinates[0].length === 5, 'Boundary should have 5 points');
-
-  t.end();
-});
-
-test('cellToBoundary works with Quadbins near the antimeridian', t => {
-  for (const quadbin of [
-    BigInt(536903670), // Longitude near +180°
-    BigInt(536870921) // Longitude near -180°
+test('Quadbin cellToBoundary', t => {
+  for (const {quadbin, expectedPolygon} of [
+    {
+      quadbin: BigInt(524800),
+      expectedPolygon: {
+        type: 'Polygon',
+        coordinates: [
+          [
+            [180, 85.0511287798066],
+            [180, -85.05112877980659],
+            [-180, -85.05112877980659],
+            [-180, 85.0511287798066],
+            [180, 85.0511287798066]
+          ]
+        ]
+      }
+    },
+    {
+      quadbin: BigInt(536903670), // Longitude near +180°
+      expectedPolygon: {
+        type: 'Polygon',
+        coordinates: [
+          [
+            [180, 85.0511287798066],
+            [180, -85.05112877980659],
+            [-180, -85.05112877980659],
+            [-180, 85.0511287798066],
+            [180, 85.0511287798066]
+          ]
+        ]
+      }
+    },
+    {
+      quadbin: BigInt(536870921), // Longitude near -180°
+      expectedPolygon: {
+        type: 'Polygon',
+        coordinates: [
+          [
+            [180, 85.0511287798066],
+            [180, -85.05112877980659],
+            [-180, -85.05112877980659],
+            [-180, 85.0511287798066],
+            [180, 85.0511287798066]
+          ]
+        ]
+      }
+    }
   ]) {
     const result = cellToBoundary(quadbin);
-
-    t.equal(result.type, 'Polygon', 'Should return a Polygon');
-    t.ok(
-      result.coordinates[0][0][0] > 170 || result.coordinates[0][0][0] < -170,
-      'Longitude should be near the antimeridian'
-    );
+    t.deepEquals(result, expectedPolygon);
   }
 
   t.end();
diff --git a/yarn.lock b/yarn.lock
index 5e75014..98fa8e5 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -94,6 +94,25 @@
   dependencies:
     tilebelt "^1.0.1"
 
+"@math.gl/core@4.1.0":
+  version "4.1.0"
+  resolved "https://registry.yarnpkg.com/@math.gl/core/-/core-4.1.0.tgz#2f4a1644c6f8fb50aacae57a02f1297f933aefbd"
+  integrity sha512-FrdHBCVG3QdrworwrUSzXIaK+/9OCRLscxI2OUy6sLOHyHgBMyfnEGs99/m3KNvs+95BsnQLWklVfpKfQzfwKA==
+  dependencies:
+    "@math.gl/types" "4.1.0"
+
+"@math.gl/types@4.1.0":
+  version "4.1.0"
+  resolved "https://registry.yarnpkg.com/@math.gl/types/-/types-4.1.0.tgz#ce28c06bcfe07d21311e00aeb25de82fecf7f393"
+  integrity sha512-clYZdHcmRvMzVK5fjeDkQlHUzXQSNdZ7s4xOqC3nJPgz4C/TZkUecTo9YS4PruZqtDda/ag4erndP0MIn40dGA==
+
+"@math.gl/web-mercator@^4.1.0":
+  version "4.1.0"
+  resolved "https://registry.yarnpkg.com/@math.gl/web-mercator/-/web-mercator-4.1.0.tgz#b244112b2805ba68cdecc76f3d12578d05271a1d"
+  integrity sha512-HZo3vO5GCMkXJThxRJ5/QYUYRr3XumfT8CzNNCwoJfinxy5NtKUd7dusNTXn7yJ40UoB8FMIwkVwNlqaiRZZAw==
+  dependencies:
+    "@math.gl/core" "4.1.0"
+
 "@tsconfig/node10@^1.0.7":
   version "1.0.11"
   resolved "https://registry.yarnpkg.com/@tsconfig/node10/-/node10-1.0.11.tgz#6ee46400685f130e278128c7b38b7e031ff5b2f2"