diff --git a/src/ol/coordinate.js b/src/ol/coordinate.js
index ec9d2a101b..85b31f325c 100644
--- a/src/ol/coordinate.js
+++ b/src/ol/coordinate.js
@@ -406,21 +406,35 @@ export function toStringXY(coordinate, opt_fractionDigits) {
  * exclusive.
  *
  * @param {Coordinate} coordinate Coordinate.
- * @param {import("./proj/Projection.js").default} projection Projection
+ * @param {import("./proj/Projection.js").default} projection Projection.
  * @return {Coordinate} The coordinate within the real world extent.
  */
 export function wrapX(coordinate, projection) {
-  const projectionExtent = projection.getExtent();
-  if (
-    projection.canWrapX() &&
-    (coordinate[0] < projectionExtent[0] ||
-      coordinate[0] >= projectionExtent[2])
-  ) {
-    const worldWidth = getWidth(projectionExtent);
-    const worldsAway = Math.floor(
-      (coordinate[0] - projectionExtent[0]) / worldWidth
-    );
+  const worldWidth = getWidth(projection.getExtent());
+  const worldsAway = getWorldsAway(coordinate, projection, worldWidth);
+  if (worldsAway) {
     coordinate[0] -= worldsAway * worldWidth;
   }
   return coordinate;
 }
+/**
+ * @param {Coordinate} coordinate Coordinate.
+ * @param {import("./proj/Projection.js").default} projection Projection.
+ * @param {number=} opt_sourceExtentWidth Width of the source extent.
+ * @return {number} Offset in world widths.
+ */
+export function getWorldsAway(coordinate, projection, opt_sourceExtentWidth) {
+  const projectionExtent = projection.getExtent();
+  let worldsAway = 0;
+  if (
+    projection.canWrapX() &&
+    (coordinate[0] < projectionExtent[0] || coordinate[0] > projectionExtent[2])
+  ) {
+    const sourceExtentWidth =
+      opt_sourceExtentWidth || getWidth(projectionExtent);
+    worldsAway = Math.floor(
+      (coordinate[0] - projectionExtent[0]) / sourceExtentWidth
+    );
+  }
+  return worldsAway;
+}
diff --git a/src/ol/proj.js b/src/ol/proj.js
index ed4e1e00b4..347d4fa017 100644
--- a/src/ol/proj.js
+++ b/src/ol/proj.js
@@ -71,9 +71,17 @@ import {
   clear as clearTransformFuncs,
   get as getTransformFunc,
 } from './proj/transforms.js';
-import {applyTransform} from './extent.js';
+import {
+  applyTransform,
+  getBottomLeft,
+  getBottomRight,
+  getTopLeft,
+  getTopRight,
+  getWidth,
+} from './extent.js';
+import {clamp, modulo} from './math.js';
 import {getDistance} from './sphere.js';
-import {modulo} from './math.js';
+import {getWorldsAway} from './coordinate.js';
 
 /**
  * A projection as {@link module:ol/proj/Projection}, SRS identifier
@@ -625,6 +633,64 @@ export function fromUserExtent(extent, destProjection) {
   return transformExtent(extent, userProjection, destProjection);
 }
 
+/**
+ * Creates a safe coordinate transform function from a coordinate transform function.
+ * "Safe" means that it can handle wrapping of x-coordinates for global projections,
+ * and that coordinates exceeding the projection validity extent's range will be
+ * clamped to the validity range.
+ * @param {Projection} sourceProj Source projection.
+ * @param {Projection} destProj Destination projection.
+ * @param {function(import("./coordinate.js").Coordinate): import("./coordinate.js").Coordinate} forward Transform function (source to destiation).
+ * @param {function(import("./coordinate.js").Coordinate): import("./coordinate.js").Coordinate} inverse Transform function (destiation to source).
+ * @return {function(import("./coordinate.js").Coordinate): import("./coordinate.js").Coordinate} Safe transform function (source to destiation).
+ */
+export function createSafeCoordinateTransform(
+  sourceProj,
+  destProj,
+  forward,
+  inverse
+) {
+  return function (coord) {
+    let x, y, worldsAway;
+    if (sourceProj.canWrapX()) {
+      const sourceExtent = sourceProj.getExtent();
+      const sourceExtentWidth = getWidth(sourceExtent);
+      worldsAway = getWorldsAway(coord, sourceProj, sourceExtentWidth);
+      if (worldsAway) {
+        // Move x to the real world
+        x = coord[0] - worldsAway * sourceExtentWidth;
+      }
+    }
+    let transformed = forward(x === undefined ? coord : [x, coord[1]]);
+    const destExtent = destProj.getExtent();
+    if (!isFinite(transformed[0]) || !isFinite(transformed[1])) {
+      // Try to recover from out-of-bounds transform
+      if (destExtent) {
+        const corner1 = inverse(getBottomLeft(destExtent));
+        const corner2 = inverse(getBottomRight(destExtent));
+        const corner3 = inverse(getTopLeft(destExtent));
+        const corner4 = inverse(getTopRight(destExtent));
+        const minX = Math.min(corner1[0], corner2[0], corner3[0], corner4[0]);
+        const maxX = Math.max(corner1[0], corner2[0], corner3[0], corner4[0]);
+        const minY = Math.min(corner1[1], corner2[1], corner3[1], corner4[1]);
+        const maxY = Math.max(corner1[1], corner2[1], corner3[1], corner4[1]);
+        if (isFinite(minX) && isFinite(maxX)) {
+          x = clamp(x == undefined ? coord[1] : x, minX, maxX);
+        }
+        if (isFinite(minY) && isFinite(maxY)) {
+          y = clamp(coord[1], minY, maxY);
+        }
+        transformed = forward([x, y]);
+      }
+    }
+    if (worldsAway && destProj.canWrapX()) {
+      // Move transformed coordinate back to the offset world
+      transformed[0] += worldsAway * getWidth(destExtent);
+    }
+    return transformed;
+  };
+}
+
 /**
  * Add transforms to and from EPSG:4326 and EPSG:3857.  This function is called
  * by when this module is executed and should only need to be called again after
diff --git a/src/ol/proj/proj4.js b/src/ol/proj/proj4.js
index ca7c17cc35..f4fb255074 100644
--- a/src/ol/proj/proj4.js
+++ b/src/ol/proj/proj4.js
@@ -6,6 +6,7 @@ import {
   addCoordinateTransforms,
   addEquivalentProjections,
   addProjection,
+  createSafeCoordinateTransform,
   get,
 } from '../proj.js';
 import {assign} from '../obj.js';
@@ -60,8 +61,18 @@ export function register(proj4) {
           addCoordinateTransforms(
             proj1,
             proj2,
-            transform.forward,
-            transform.inverse
+            createSafeCoordinateTransform(
+              proj1,
+              proj2,
+              transform.forward,
+              transform.inverse
+            ),
+            createSafeCoordinateTransform(
+              proj2,
+              proj1,
+              transform.inverse,
+              transform.forward
+            )
           );
         }
       }
diff --git a/test/spec/ol/proj.test.js b/test/spec/ol/proj.test.js
index 4d9592267e..bc5990256b 100644
--- a/test/spec/ol/proj.test.js
+++ b/test/spec/ol/proj.test.js
@@ -560,6 +560,25 @@ describe('ol.proj', function () {
       });
       expect(getProjection('EPSG:4326')).to.equal(epsg4326);
     });
+
+    it('uses safe transform functions', function () {
+      register(proj4);
+      const wgs84 = getProjection('WGS84');
+      const epsg4326 = getProjection('EPSG:4326');
+      wgs84.setExtent(epsg4326.getExtent());
+      wgs84.setGlobal(true);
+      const google = getProjection('GOOGLE');
+      const epsg3857 = getProjection('EPSG:3857');
+      google.setExtent(epsg3857.getExtent());
+      google.setGlobal(true);
+      const coord = [-190, 90];
+      const transformed = transform(coord, wgs84, google);
+      expect(transformed).to.eql(transform(coord, epsg4326, epsg3857));
+      const got = transform(transformed, google, wgs84);
+      const expected = transform(transformed, epsg3857, epsg4326);
+      expect(got[0]).to.roughlyEqual(expected[0], 1e-9);
+      expect(got[1]).to.roughlyEqual(expected[1], 1e-9);
+    });
   });
 
   describe('ol.proj.getTransformFromProjections()', function () {