diff --git a/extras/JuceDemo/Source/demos/OpenGLDemo.cpp b/extras/JuceDemo/Source/demos/OpenGLDemo.cpp
index 42ebb37a0f..b98eefc845 100644
--- a/extras/JuceDemo/Source/demos/OpenGLDemo.cpp
+++ b/extras/JuceDemo/Source/demos/OpenGLDemo.cpp
@@ -109,7 +109,9 @@ public:
         OpenGLHelpers::clear (Colours::darkgrey.withAlpha (1.0f));
 
         updateTextureImage();  // this will update our dynamically-changing texture image.
-        drawBackground2DStuff(); // draws some 2D content to demonstrate the OpenGLGraphicsContext class
+
+        const float scale = (float) openGLContext.getRenderingScale();
+        drawBackground2DStuff (scale); // draws some 2D content to demonstrate the OpenGLGraphicsContext class
 
         // Having used the juce 2D renderer, it will have messed-up a whole load of GL state, so
         // we'll put back any important settings before doing our normal GL 3D drawing..
@@ -120,8 +122,9 @@ public:
         glEnable (GL_TEXTURE_2D);
 
        #if JUCE_USE_OPENGL_FIXED_FUNCTION
-        OpenGLHelpers::prepareFor2D (getContextWidth(), getContextHeight());
-        OpenGLHelpers::setPerspective (45.0, getContextWidth() / (double) getContextHeight(), 0.1, 100.0);
+        OpenGLHelpers::prepareFor2D (roundToInt (scale * getWidth()),
+                                     roundToInt (scale * getHeight()));
+        OpenGLHelpers::setPerspective (45.0, getWidth() / (double) getHeight(), 0.1, 100.0);
 
         glTranslatef (0.0f, 0.0f, -5.0f);
         draggableOrientation.applyToOpenGLMatrix();
@@ -163,23 +166,23 @@ public:
         }
     }
 
-    void drawBackground2DStuff()
+    void drawBackground2DStuff (float scale)
     {
         // Create an OpenGLGraphicsContext that will draw into this GL window..
         ScopedPointer<LowLevelGraphicsContext> glRenderer (createOpenGLGraphicsContext (openGLContext,
-                                                                                        getContextWidth(),
-                                                                                        getContextHeight()));
+                                                                                        roundToInt (scale * getWidth()),
+                                                                                        roundToInt (scale * getHeight())));
 
         if (glRenderer != nullptr)
         {
             Graphics g (glRenderer);
-            g.addTransform (AffineTransform::scale ((float) getScale()));
+            g.addTransform (AffineTransform::scale (scale));
 
             // This stuff just creates a spinning star shape and fills it..
             Path p;
-            const float scale = getHeight() * 0.4f;
             p.addStar (Point<float> (getWidth() * 0.7f, getHeight() * 0.4f), 7,
-                       scale * (float) sizeSlider.getValue(), scale,
+                       getHeight() * 0.4f * (float) sizeSlider.getValue(),
+                       getHeight() * 0.4f,
                        rotation / 50.0f);
 
             g.setGradientFill (ColourGradient (Colours::green.withRotatedHue (fabsf (::sinf (rotation / 300.0f))),
@@ -190,10 +193,6 @@ public:
         }
     }
 
-    double getScale() const         { return Desktop::getInstance().getDisplays().getDisplayContaining (getScreenBounds().getCentre()).scale; }
-    int getContextWidth() const     { return roundToInt (getScale() * getWidth()); }
-    int getContextHeight() const    { return roundToInt (getScale() * getHeight()); }
-
     void timerCallback()
     {
         rotation += (float) speedSlider.getValue();
diff --git a/modules/juce_opengl/opengl/juce_OpenGLContext.cpp b/modules/juce_opengl/opengl/juce_OpenGLContext.cpp
index 35f5e37953..e239641940 100644
--- a/modules/juce_opengl/opengl/juce_OpenGLContext.cpp
+++ b/modules/juce_opengl/opengl/juce_OpenGLContext.cpp
@@ -164,6 +164,7 @@ public:
         if (context.renderer != nullptr)
         {
             glViewport (0, 0, viewportArea.getWidth(), viewportArea.getHeight());
+            context.currentRenderScale = scale;
             context.renderer->renderOpenGL();
             clearGLError();
         }
@@ -527,8 +528,8 @@ private:
 
 //==============================================================================
 OpenGLContext::OpenGLContext()
-    : nativeContext (nullptr), renderer (nullptr), contextToShareWith (nullptr),
-      renderComponents (true), useMultisampling (false)
+    : nativeContext (nullptr), renderer (nullptr), currentRenderScale (1.0),
+      contextToShareWith (nullptr), renderComponents (true), useMultisampling (false)
 {
 }
 
diff --git a/modules/juce_opengl/opengl/juce_OpenGLContext.h b/modules/juce_opengl/opengl/juce_OpenGLContext.h
index e56b7f6263..5ca6ba3939 100644
--- a/modules/juce_opengl/opengl/juce_OpenGLContext.h
+++ b/modules/juce_opengl/opengl/juce_OpenGLContext.h
@@ -200,6 +200,16 @@ public:
     */
     int getSwapInterval() const;
 
+    //==============================================================================
+    /** Returns the scale factor used by the display that is being rendered.
+
+        The scale is that of the display - see Desktop::Displays::Display::scale
+
+        Note that this should only be called during an OpenGLRenderer::renderOpenGL()
+        callback - at other times the value it returns is undefined.
+    */
+    double getRenderingScale() const noexcept   { return currentRenderScale; }
+
     //==============================================================================
     /** Returns an OS-dependent handle to some kind of underlting OS-provided GL context.
 
@@ -209,7 +219,6 @@ public:
     */
     void* getRawContext() const noexcept;
 
-
     //==============================================================================
     /** Draws the currently selected texture into this context at its original size.
 
@@ -240,6 +249,7 @@ private:
     class Attachment;
     NativeContext* nativeContext;
     OpenGLRenderer* renderer;
+    double currentRenderScale;
     ScopedPointer<Attachment> attachment;
     OpenGLPixelFormat pixelFormat;
     void* contextToShareWith;