diff --git a/modules/juce_audio_plugin_client/VST3/juce_VST3_Wrapper.cpp b/modules/juce_audio_plugin_client/VST3/juce_VST3_Wrapper.cpp
index 3be9081511..35dbcb1480 100644
--- a/modules/juce_audio_plugin_client/VST3/juce_VST3_Wrapper.cpp
+++ b/modules/juce_audio_plugin_client/VST3/juce_VST3_Wrapper.cpp
@@ -1190,12 +1190,12 @@ private:
                     {
                         *rectToCheck = convertFromHostBounds (*rectToCheck);
 
-                        auto scale = editor->getTransform().getScaleFactor();
+                        auto transformScale = std::sqrt (std::abs (editor->getTransform().getDeterminant()));
 
-                        auto minW = (double) (constrainer->getMinimumWidth()  * scale);
-                        auto maxW = (double) (constrainer->getMaximumWidth()  * scale);
-                        auto minH = (double) (constrainer->getMinimumHeight() * scale);
-                        auto maxH = (double) (constrainer->getMaximumHeight() * scale);
+                        auto minW = (double) (constrainer->getMinimumWidth()  * transformScale);
+                        auto maxW = (double) (constrainer->getMaximumWidth()  * transformScale);
+                        auto minH = (double) (constrainer->getMinimumHeight() * transformScale);
+                        auto maxH = (double) (constrainer->getMaximumHeight() * transformScale);
 
                         auto width  = (double) (rectToCheck->right - rectToCheck->left);
                         auto height = (double) (rectToCheck->bottom - rectToCheck->top);
diff --git a/modules/juce_graphics/geometry/juce_AffineTransform.cpp b/modules/juce_graphics/geometry/juce_AffineTransform.cpp
index 588253f091..ceb15deb6a 100644
--- a/modules/juce_graphics/geometry/juce_AffineTransform.cpp
+++ b/modules/juce_graphics/geometry/juce_AffineTransform.cpp
@@ -236,9 +236,46 @@ bool AffineTransform::isOnlyTranslation() const noexcept
         && mat11 == 1.0f;
 }
 
+float AffineTransform::getDeterminant() const noexcept
+{
+    return (mat00 * mat11) - (mat01 * mat10);
+}
+
 float AffineTransform::getScaleFactor() const noexcept
 {
     return (std::abs (mat00) + std::abs (mat11)) / 2.0f;
 }
 
+
+//==============================================================================
+//==============================================================================
+#if JUCE_UNIT_TESTS
+
+class AffineTransformTests  : public UnitTest
+{
+public:
+    AffineTransformTests()
+        : UnitTest ("AffineTransform", UnitTestCategories::maths)
+    {}
+
+    void runTest() override
+    {
+        beginTest ("Determinant");
+        {
+            constexpr float scale1 = 1.5f, scale2 = 1.3f;
+
+            auto transform = AffineTransform::scale (scale1)
+                                             .followedBy (AffineTransform::rotation (degreesToRadians (72.0f)))
+                                             .followedBy (AffineTransform::translation (100.0f, 20.0f))
+                                             .followedBy (AffineTransform::scale (scale2));
+
+            expect (approximatelyEqual (std::sqrt (std::abs (transform.getDeterminant())), scale1 * scale2));
+        }
+    }
+};
+
+static AffineTransformTests timeTests;
+
+#endif
+
 } // namespace juce
diff --git a/modules/juce_graphics/geometry/juce_AffineTransform.h b/modules/juce_graphics/geometry/juce_AffineTransform.h
index 06452d4990..66b87d378a 100644
--- a/modules/juce_graphics/geometry/juce_AffineTransform.h
+++ b/modules/juce_graphics/geometry/juce_AffineTransform.h
@@ -264,11 +264,23 @@ public:
     */
     float getTranslationY() const noexcept                  { return mat12; }
 
-    /** Returns the approximate scale factor by which lengths will be transformed.
+    /** Returns the determinant of the transform. */
+    float getDeterminant() const noexcept;
+
+    /** This method has been deprecated.
+
+        You can calculate the scale factor using:
+        @code
+        std::sqrt (std::abs (AffineTransform::getDeterminant()))
+        @endcode
+
+        This method produces incorrect values for transforms containing rotations.
+
+        Returns the approximate scale factor by which lengths will be transformed.
         Obviously a length may be scaled by entirely different amounts depending on its
         direction, so this is only appropriate as a rough guide.
     */
-    float getScaleFactor() const noexcept;
+    JUCE_DEPRECATED (float getScaleFactor() const noexcept);
 
     /* A ready-to-use identity transform - now deprecated.
        @deprecated If you need an identity transform, just use AffineTransform() or {}.
diff --git a/modules/juce_graphics/native/juce_RenderingHelpers.h b/modules/juce_graphics/native/juce_RenderingHelpers.h
index 0935b2d1e0..d194f638ab 100644
--- a/modules/juce_graphics/native/juce_RenderingHelpers.h
+++ b/modules/juce_graphics/native/juce_RenderingHelpers.h
@@ -96,7 +96,7 @@ public:
 
     float getPhysicalPixelScaleFactor() const noexcept
     {
-        return isOnlyTranslated ? 1.0f : std::abs (complexTransform.getScaleFactor());
+        return isOnlyTranslated ? 1.0f : std::sqrt (std::abs (complexTransform.getDeterminant()));
     }
 
     void moveOriginInDeviceSpace (Point<int> delta) noexcept
diff --git a/modules/juce_graphics/native/juce_win32_Direct2DGraphicsContext.cpp b/modules/juce_graphics/native/juce_win32_Direct2DGraphicsContext.cpp
index 3913247b69..be79b6d41f 100644
--- a/modules/juce_graphics/native/juce_win32_Direct2DGraphicsContext.cpp
+++ b/modules/juce_graphics/native/juce_win32_Direct2DGraphicsContext.cpp
@@ -580,7 +580,7 @@ void Direct2DLowLevelGraphicsContext::addTransform (const AffineTransform& trans
 
 float Direct2DLowLevelGraphicsContext::getPhysicalPixelScaleFactor()
 {
-    return currentState->transform.getScaleFactor();
+    return std::sqrt (std::abs (currentState->transform.getDeterminant()));
 }
 
 bool Direct2DLowLevelGraphicsContext::clipToRectangle (const Rectangle<int>& r)
diff --git a/modules/juce_gui_basics/components/juce_Component.cpp b/modules/juce_gui_basics/components/juce_Component.cpp
index d7734de4d2..67d6445dec 100644
--- a/modules/juce_gui_basics/components/juce_Component.cpp
+++ b/modules/juce_gui_basics/components/juce_Component.cpp
@@ -1300,7 +1300,8 @@ float Component::getApproximateScaleFactorForComponent (Component* targetCompone
             transform = transform.scaled (target->getDesktopScaleFactor());
     }
 
-    return (transform.getScaleFactor() / Desktop::getInstance().getGlobalScaleFactor());
+    auto transformScale = std::sqrt (std::abs (transform.getDeterminant()));
+    return transformScale / Desktop::getInstance().getGlobalScaleFactor();
 }
 
 //==============================================================================
diff --git a/modules/juce_gui_basics/drawables/juce_SVGParser.cpp b/modules/juce_gui_basics/drawables/juce_SVGParser.cpp
index 2d003e3565..cdaec0206e 100644
--- a/modules/juce_gui_basics/drawables/juce_SVGParser.cpp
+++ b/modules/juce_gui_basics/drawables/juce_SVGParser.cpp
@@ -1024,7 +1024,8 @@ private:
 
     float getStrokeWidth (const String& strokeWidth) const noexcept
     {
-        return transform.getScaleFactor() * getCoordLength (strokeWidth, viewBoxW);
+        auto transformScale = std::sqrt (std::abs (transform.getDeterminant()));
+        return transformScale * getCoordLength (strokeWidth, viewBoxW);
     }
 
     PathStrokeType getStrokeFor (const XmlPath& xml) const