diff --git a/CHANGES.md b/CHANGES.md
index 4ea469cd70f0..08544ab89201 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -13,6 +13,7 @@
 - Fixed render crash when creating a `polylineVolume` with very close points. [#9669](https://github.com/CesiumGS/cesium/pull/9669)
 - Fixed a bug in `PolylineGeometry` that incorrectly shifted colors when duplicate positions were removed. [#9676](https://github.com/CesiumGS/cesium/pull/9676)
 - Fixed a crash that would hang the browser if a `Label` was created with a soft hyphen in its text. [#9682](https://github.com/CesiumGS/cesium/pull/9682)
+- Fixed the incorrect calculation of `distanceSquaredTo` in `BoundingSphere`. [#9686](https://github.com/CesiumGS/cesium/pull/9686)
 
 ### 1.83 - 2021-07-01
 
diff --git a/Source/Core/BoundingSphere.js b/Source/Core/BoundingSphere.js
index 98610e009512..3d95c017ec15 100644
--- a/Source/Core/BoundingSphere.js
+++ b/Source/Core/BoundingSphere.js
@@ -1113,7 +1113,7 @@ var distanceSquaredToScratch = new Cartesian3();
  *
  * @param {BoundingSphere} sphere The sphere.
  * @param {Cartesian3} cartesian The point
- * @returns {Number} The estimated distance squared from the bounding sphere to the point.
+ * @returns {Number} The distance squared from the bounding sphere to the point. Returns 0 if the point is inside the sphere.
  *
  * @example
  * // Sort bounding spheres from back to front
@@ -1132,7 +1132,13 @@ BoundingSphere.distanceSquaredTo = function (sphere, cartesian) {
     cartesian,
     distanceSquaredToScratch
   );
-  return Cartesian3.magnitudeSquared(diff) - sphere.radius * sphere.radius;
+
+  var distance = Cartesian3.magnitude(diff) - sphere.radius;
+  if (distance <= 0.0) {
+    return 0.0;
+  }
+
+  return distance * distance;
 };
 
 /**
diff --git a/Source/Core/OrientedBoundingBox.js b/Source/Core/OrientedBoundingBox.js
index f9e1927afe26..85825c1d1c15 100644
--- a/Source/Core/OrientedBoundingBox.js
+++ b/Source/Core/OrientedBoundingBox.js
@@ -693,7 +693,7 @@ var scratchPPrime = new Cartesian3();
  *
  * @param {OrientedBoundingBox} box The box.
  * @param {Cartesian3} cartesian The point
- * @returns {Number} The estimated distance squared from the bounding sphere to the point.
+ * @returns {Number} The distance squared from the oriented bounding box to the point. Returns 0 if the point is inside the box.
  *
  * @example
  * // Sort bounding boxes from back to front
diff --git a/Specs/Core/BoundingSphereSpec.js b/Specs/Core/BoundingSphereSpec.js
index 3c0909dc09df..8a8ce0428061 100644
--- a/Specs/Core/BoundingSphereSpec.js
+++ b/Specs/Core/BoundingSphereSpec.js
@@ -703,11 +703,20 @@ describe("Core/BoundingSphere", function () {
     ).toEqual(expected);
   });
 
-  it("estimated distance squared to point", function () {
+  it("distance squared to point outside of sphere", function () {
     var bs = new BoundingSphere(Cartesian3.ZERO, 1.0);
     var position = new Cartesian3(-2.0, 1.0, 0.0);
-    var expected = Cartesian3.magnitudeSquared(position) - 1.0;
-    expect(BoundingSphere.distanceSquaredTo(bs, position)).toEqual(expected);
+    var expected = 1.52786405;
+    expect(BoundingSphere.distanceSquaredTo(bs, position)).toEqualEpsilon(
+      expected,
+      CesiumMath.EPSILON6
+    );
+  });
+
+  it("distance squared to point inside sphere", function () {
+    var bs = new BoundingSphere(Cartesian3.ZERO, 1.0);
+    var position = new Cartesian3(-0.5, 0.5, 0.0);
+    expect(BoundingSphere.distanceSquaredTo(bs, position)).toEqual(0.0);
   });
 
   it("projectTo2D", function () {