diff --git a/changelog/upgrade-notes.md b/changelog/upgrade-notes.md
index d032dc71c2..600eec820f 100644
--- a/changelog/upgrade-notes.md
+++ b/changelog/upgrade-notes.md
@@ -37,12 +37,12 @@ The map and sources no longer accept a `logo` option.  Instead, if you wish to a
 
 #### Replacement of `ol/Sphere` constructor with `ol/sphere` functions
 
-The `ol/Sphere` constructor has been removed.  If you were using the `getGeodesicArea` method, use the `getArea` function instead.  If you were using the `haversineDistance` method, use the `getDistance` function instead.  The `circular` method in `ol/Polygon` no longer takes a sphere as the first argument.
+The `ol/Sphere` constructor has been removed.  If you were using the `getGeodesicArea` method, use the `getArea` function instead.  If you were using the `haversineDistance` method, use the `getDistance` function instead.  The `circular` method in `ol/geom/Polygon` no longer takes a sphere as the first argument.
 
 Examples before:
 ```js
 // using ol@4
-import Polygon from 'ol/Polygon';
+import Polygon from 'ol/geom/Polygon';
 import Sphere from 'ol/Sphere';
 
 var sphere = new Sphere(Sphere.DEFAULT_RADIUS);
@@ -54,7 +54,7 @@ var circle = Polygon.circular(sphere, center, radius);
 Examples after:
 ```js
 // using ol@5
-import {circular as circularPolygon} from 'ol/Polygon';
+import {circular as circularPolygon} from 'ol/geom/Polygon';
 import {getArea, getDistance} from 'ol/sphere'; // note the lowercase
 
 var area = getArea(polygon);
diff --git a/examples/tissot.js b/examples/tissot.js
index 03230af4e5..43fdd0c13e 100644
--- a/examples/tissot.js
+++ b/examples/tissot.js
@@ -1,7 +1,7 @@
 import _ol_Feature_ from '../src/ol/Feature.js';
 import _ol_Map_ from '../src/ol/Map.js';
 import _ol_View_ from '../src/ol/View.js';
-import Polygon from '../src/ol/geom/Polygon.js';
+import {circular as circularPolygon} from '../src/ol/geom/Polygon.js';
 import TileLayer from '../src/ol/layer/Tile.js';
 import _ol_layer_Vector_ from '../src/ol/layer/Vector.js';
 import _ol_source_TileWMS_ from '../src/ol/source/TileWMS.js';
@@ -60,7 +60,7 @@ var radius = 800000;
 var x, y;
 for (x = -180; x < 180; x += 30) {
   for (y = -90; y < 90; y += 30) {
-    var circle4326 = Polygon.circular([x, y], radius, 64);
+    var circle4326 = circularPolygon([x, y], radius, 64);
     var circle3857 = circle4326.clone().transform('EPSG:4326', 'EPSG:3857');
     vectorLayer4326.getSource().addFeature(new _ol_Feature_(circle4326));
     vectorLayer3857.getSource().addFeature(new _ol_Feature_(circle3857));
diff --git a/src/ol/Geolocation.js b/src/ol/Geolocation.js
index ae3f696817..546c4b22ed 100644
--- a/src/ol/Geolocation.js
+++ b/src/ol/Geolocation.js
@@ -6,7 +6,7 @@ import _ol_GeolocationProperty_ from './GeolocationProperty.js';
 import _ol_Object_ from './Object.js';
 import _ol_events_ from './events.js';
 import EventType from './events/EventType.js';
-import Polygon from './geom/Polygon.js';
+import {circular as circularPolygon} from './geom/Polygon.js';
 import _ol_has_ from './has.js';
 import {toRadians} from './math.js';
 import {get as getProjection, getTransformFromProjections, identityTransform} from './proj.js';
@@ -167,7 +167,7 @@ Geolocation.prototype.positionChange_ = function(position) {
   this.set(_ol_GeolocationProperty_.POSITION, projectedPosition);
   this.set(_ol_GeolocationProperty_.SPEED,
       coords.speed === null ? undefined : coords.speed);
-  var geometry = Polygon.circular(this.position_, coords.accuracy);
+  var geometry = circularPolygon(this.position_, coords.accuracy);
   geometry.applyTransform(this.transform_);
   this.set(_ol_GeolocationProperty_.ACCURACY_GEOMETRY, geometry);
   this.changed();
diff --git a/src/ol/View.js b/src/ol/View.js
index f2c27a17cc..4e37a0251e 100644
--- a/src/ol/View.js
+++ b/src/ol/View.js
@@ -15,7 +15,7 @@ import _ol_coordinate_ from './coordinate.js';
 import {inAndOut} from './easing.js';
 import {getForViewAndSize, getCenter, getHeight, getWidth, isEmpty} from './extent.js';
 import GeometryType from './geom/GeometryType.js';
-import Polygon from './geom/Polygon.js';
+import {fromExtent as polygonFromExtent} from './geom/Polygon.js';
 import SimpleGeometry from './geom/SimpleGeometry.js';
 import {clamp, modulo} from './math.js';
 import _ol_obj_ from './obj.js';
@@ -884,10 +884,10 @@ _ol_View_.prototype.fit = function(geometryOrExtent, opt_options) {
         24); // Invalid extent or geometry provided as `geometry`
     assert(!isEmpty(geometryOrExtent),
         25); // Cannot fit empty extent provided as `geometry`
-    geometry = Polygon.fromExtent(geometryOrExtent);
+    geometry = polygonFromExtent(geometryOrExtent);
   } else if (geometryOrExtent.getType() === GeometryType.CIRCLE) {
     geometryOrExtent = geometryOrExtent.getExtent();
-    geometry = Polygon.fromExtent(geometryOrExtent);
+    geometry = polygonFromExtent(geometryOrExtent);
     geometry.rotate(this.getRotation(), getCenter(geometryOrExtent));
   } else {
     geometry = geometryOrExtent;
diff --git a/src/ol/geom/Polygon.js b/src/ol/geom/Polygon.js
index 269e1dc0c7..22c8dbf902 100644
--- a/src/ol/geom/Polygon.js
+++ b/src/ol/geom/Polygon.js
@@ -367,6 +367,8 @@ Polygon.prototype.setFlatCoordinates = function(layout, flatCoordinates, ends) {
   this.changed();
 };
 
+export default Polygon;
+
 
 /**
  * Create an approximation of a circle on the surface of a sphere.
@@ -380,7 +382,7 @@ Polygon.prototype.setFlatCoordinates = function(layout, flatCoordinates, ends) {
  * @return {ol.geom.Polygon} The "circular" polygon.
  * @api
  */
-Polygon.circular = function(center, radius, opt_n, opt_sphereRadius) {
+export function circular(center, radius, opt_n, opt_sphereRadius) {
   var n = opt_n ? opt_n : 32;
   /** @type {Array.<number>} */
   var flatCoordinates = [];
@@ -393,7 +395,7 @@ Polygon.circular = function(center, radius, opt_n, opt_sphereRadius) {
   polygon.setFlatCoordinates(
       GeometryLayout.XY, flatCoordinates, [flatCoordinates.length]);
   return polygon;
-};
+}
 
 
 /**
@@ -402,7 +404,7 @@ Polygon.circular = function(center, radius, opt_n, opt_sphereRadius) {
  * @return {ol.geom.Polygon} The polygon.
  * @api
  */
-Polygon.fromExtent = function(extent) {
+export function fromExtent(extent) {
   var minX = extent[0];
   var minY = extent[1];
   var maxX = extent[2];
@@ -413,7 +415,7 @@ Polygon.fromExtent = function(extent) {
   polygon.setFlatCoordinates(
       GeometryLayout.XY, flatCoordinates, [flatCoordinates.length]);
   return polygon;
-};
+}
 
 
 /**
@@ -425,7 +427,7 @@ Polygon.fromExtent = function(extent) {
  * @return {ol.geom.Polygon} Polygon geometry.
  * @api
  */
-Polygon.fromCircle = function(circle, opt_sides, opt_angle) {
+export function fromCircle(circle, opt_sides, opt_angle) {
   var sides = opt_sides ? opt_sides : 32;
   var stride = circle.getStride();
   var layout = circle.getLayout();
@@ -437,10 +439,9 @@ Polygon.fromCircle = function(circle, opt_sides, opt_angle) {
   }
   var ends = [flatCoordinates.length];
   polygon.setFlatCoordinates(layout, flatCoordinates, ends);
-  Polygon.makeRegular(
-      polygon, circle.getCenter(), circle.getRadius(), opt_angle);
+  makeRegular(polygon, circle.getCenter(), circle.getRadius(), opt_angle);
   return polygon;
-};
+}
 
 
 /**
@@ -451,7 +452,7 @@ Polygon.fromCircle = function(circle, opt_sides, opt_angle) {
  * @param {number=} opt_angle Start angle for the first vertex of the polygon in
  *     radians. Default is 0.
  */
-Polygon.makeRegular = function(polygon, center, radius, opt_angle) {
+export function makeRegular(polygon, center, radius, opt_angle) {
   var flatCoordinates = polygon.getFlatCoordinates();
   var layout = polygon.getLayout();
   var stride = polygon.getStride();
@@ -466,5 +467,4 @@ Polygon.makeRegular = function(polygon, center, radius, opt_angle) {
     flatCoordinates[offset + 1] = center[1] + (radius * Math.sin(angle));
   }
   polygon.setFlatCoordinates(layout, flatCoordinates, ends);
-};
-export default Polygon;
+}
diff --git a/src/ol/interaction/Draw.js b/src/ol/interaction/Draw.js
index a7a2d1428c..4c1addd19a 100644
--- a/src/ol/interaction/Draw.js
+++ b/src/ol/interaction/Draw.js
@@ -18,7 +18,7 @@ import MultiLineString from '../geom/MultiLineString.js';
 import MultiPoint from '../geom/MultiPoint.js';
 import MultiPolygon from '../geom/MultiPolygon.js';
 import Point from '../geom/Point.js';
-import Polygon from '../geom/Polygon.js';
+import Polygon, {fromCircle, makeRegular} from '../geom/Polygon.js';
 import DrawEventType from '../interaction/DrawEventType.js';
 import _ol_interaction_Pointer_ from '../interaction/Pointer.js';
 import _ol_interaction_Property_ from '../interaction/Property.js';
@@ -795,10 +795,10 @@ Draw.createRegularPolygon = function(opt_sides, opt_angle) {
       var radius = Math.sqrt(
           _ol_coordinate_.squaredDistance(center, end));
       var geometry = opt_geometry ? /** @type {ol.geom.Polygon} */ (opt_geometry) :
-        Polygon.fromCircle(new Circle(center), opt_sides);
+        fromCircle(new Circle(center), opt_sides);
       var angle = opt_angle ? opt_angle :
         Math.atan((end[1] - center[1]) / (end[0] - center[0]));
-      Polygon.makeRegular(geometry, center, radius, angle);
+      makeRegular(geometry, center, radius, angle);
       return geometry;
     }
   );
diff --git a/src/ol/interaction/Extent.js b/src/ol/interaction/Extent.js
index 1479c1f9fd..bb19804f2c 100644
--- a/src/ol/interaction/Extent.js
+++ b/src/ol/interaction/Extent.js
@@ -10,7 +10,7 @@ import Event from '../events/Event.js';
 import {boundingExtent, getArea} from '../extent.js';
 import GeometryType from '../geom/GeometryType.js';
 import Point from '../geom/Point.js';
-import Polygon from '../geom/Polygon.js';
+import {fromExtent as polygonFromExtent} from '../geom/Polygon.js';
 import _ol_interaction_ExtentEventType_ from '../interaction/ExtentEventType.js';
 import _ol_interaction_Pointer_ from '../interaction/Pointer.js';
 import _ol_layer_Vector_ from '../layer/Vector.js';
@@ -376,7 +376,7 @@ _ol_interaction_Extent_.prototype.createOrUpdateExtentFeature_ = function(extent
     if (!extent) {
       extentFeature = new _ol_Feature_({});
     } else {
-      extentFeature = new _ol_Feature_(Polygon.fromExtent(extent));
+      extentFeature = new _ol_Feature_(polygonFromExtent(extent));
     }
     this.extentFeature_ = extentFeature;
     this.extentOverlay_.getSource().addFeature(extentFeature);
@@ -384,7 +384,7 @@ _ol_interaction_Extent_.prototype.createOrUpdateExtentFeature_ = function(extent
     if (!extent) {
       extentFeature.setGeometry(undefined);
     } else {
-      extentFeature.setGeometry(Polygon.fromExtent(extent));
+      extentFeature.setGeometry(polygonFromExtent(extent));
     }
   }
   return extentFeature;
diff --git a/src/ol/interaction/Snap.js b/src/ol/interaction/Snap.js
index 02b39e75ee..92a1627952 100644
--- a/src/ol/interaction/Snap.js
+++ b/src/ol/interaction/Snap.js
@@ -10,7 +10,7 @@ import EventType from '../events/EventType.js';
 import {boundingExtent, createEmpty} from '../extent.js';
 import {TRUE, FALSE} from '../functions.js';
 import GeometryType from '../geom/GeometryType.js';
-import Polygon from '../geom/Polygon.js';
+import {fromCircle} from '../geom/Polygon.js';
 import _ol_interaction_Pointer_ from '../interaction/Pointer.js';
 import _ol_obj_ from '../obj.js';
 import _ol_source_Vector_ from '../source/Vector.js';
@@ -435,7 +435,7 @@ _ol_interaction_Snap_.prototype.updateFeature_ = function(feature) {
  * @private
  */
 _ol_interaction_Snap_.prototype.writeCircleGeometry_ = function(feature, geometry) {
-  var polygon = Polygon.fromCircle(geometry);
+  var polygon = fromCircle(geometry);
   var coordinates = polygon.getCoordinates()[0];
   var i, ii, segment, segmentData;
   for (i = 0, ii = coordinates.length - 1; i < ii; ++i) {
diff --git a/test/spec/ol/geom/polygon.test.js b/test/spec/ol/geom/polygon.test.js
index 677841690e..1499b617ab 100644
--- a/test/spec/ol/geom/polygon.test.js
+++ b/test/spec/ol/geom/polygon.test.js
@@ -1,10 +1,10 @@
 import * as _ol_extent_ from '../../../../src/ol/extent.js';
 import Circle from '../../../../src/ol/geom/Circle.js';
 import LinearRing from '../../../../src/ol/geom/LinearRing.js';
-import Polygon from '../../../../src/ol/geom/Polygon.js';
+import Polygon, {fromCircle, fromExtent} from '../../../../src/ol/geom/Polygon.js';
 
 
-describe('ol.geom.Polygon', function() {
+describe('ol/geom/Polygon', function() {
 
   it('can be constructed with a null geometry', function() {
     expect(function() {
@@ -561,10 +561,10 @@ describe('ol.geom.Polygon', function() {
     });
   });
 
-  describe('ol.geom.Polygon.fromExtent', function() {
+  describe('fromExtent()', function() {
     it('creates the correct polygon', function() {
       var extent = [1, 2, 3, 5];
-      var polygon = Polygon.fromExtent(extent);
+      var polygon = fromExtent(extent);
       var flatCoordinates = polygon.getFlatCoordinates();
       expect(flatCoordinates).to.eql(
           [1, 2, 1, 5, 3, 5, 3, 2, 1, 2]);
@@ -574,11 +574,11 @@ describe('ol.geom.Polygon', function() {
     });
   });
 
-  describe('ol.geom.Polygon.fromCircle', function() {
+  describe('fromCircle()', function() {
 
     it('creates a regular polygon', function() {
       var circle = new Circle([0, 0, 0], 1, 'XYZ');
-      var polygon = Polygon.fromCircle(circle);
+      var polygon = fromCircle(circle);
       var coordinates = polygon.getLinearRing(0).getCoordinates();
       expect(coordinates[0].length).to.eql(3);
       expect(coordinates[0][2]).to.eql(0);
@@ -599,7 +599,7 @@ describe('ol.geom.Polygon', function() {
 
     it('creates a regular polygon with custom sides and angle', function() {
       var circle = new Circle([0, 0], 1);
-      var polygon = Polygon.fromCircle(circle, 4, Math.PI / 2);
+      var polygon = fromCircle(circle, 4, Math.PI / 2);
       var coordinates = polygon.getLinearRing(0).getCoordinates();
       expect(coordinates[4]).to.eql(coordinates[0]);
       expect(coordinates[0][0]).to.roughlyEqual(0, 1e-9);
diff --git a/test/spec/ol/interaction/dragzoom.test.js b/test/spec/ol/interaction/dragzoom.test.js
index bdb977af05..5007d28fd1 100644
--- a/test/spec/ol/interaction/dragzoom.test.js
+++ b/test/spec/ol/interaction/dragzoom.test.js
@@ -1,7 +1,7 @@
 import _ol_Map_ from '../../../../src/ol/Map.js';
 import _ol_View_ from '../../../../src/ol/View.js';
 import * as _ol_extent_ from '../../../../src/ol/extent.js';
-import Polygon from '../../../../src/ol/geom/Polygon.js';
+import {fromExtent as polygonFromExtent} from '../../../../src/ol/geom/Polygon.js';
 import DragZoom from '../../../../src/ol/interaction/DragZoom.js';
 import _ol_layer_Vector_ from '../../../../src/ol/layer/Vector.js';
 import _ol_render_Box_ from '../../../../src/ol/render/Box.js';
@@ -72,7 +72,7 @@ describe('ol.interaction.DragZoom', function() {
 
       var box = new _ol_render_Box_();
       var extent = [-110, 40, -90, 60];
-      box.geometry_ = Polygon.fromExtent(extent);
+      box.geometry_ = polygonFromExtent(extent);
       interaction.box_ = box;
 
       interaction.onBoxEnd();
@@ -94,7 +94,7 @@ describe('ol.interaction.DragZoom', function() {
 
       var box = new _ol_render_Box_();
       var extent = [-11.25, -11.25, 11.25, 11.25];
-      box.geometry_ = Polygon.fromExtent(extent);
+      box.geometry_ = polygonFromExtent(extent);
       interaction.box_ = box;
 
       map.getView().setResolution(0.25);