diff --git a/modules/juce_graphics/geometry/juce_Rectangle.h b/modules/juce_graphics/geometry/juce_Rectangle.h
index 357904d736..780f46dfc5 100644
--- a/modules/juce_graphics/geometry/juce_Rectangle.h
+++ b/modules/juce_graphics/geometry/juce_Rectangle.h
@@ -26,6 +26,34 @@
 namespace juce
 {
 
+#ifndef DOXYGEN
+namespace detail
+{
+
+template <typename> struct Tag {};
+
+inline auto getNumericValue (StringRef s, Tag<int>)    { return s.text.getIntValue32(); }
+inline auto getNumericValue (StringRef s, Tag<double>) { return s.text.getDoubleValue(); }
+inline auto getNumericValue (StringRef s, Tag<float>)  { return static_cast<float> (s.text.getDoubleValue()); }
+
+template <typename ValueType>
+ValueType parseAfterSpace (StringRef s) noexcept
+{
+    return static_cast<ValueType> (getNumericValue (s.text.findEndOfWhitespace(),
+                                                    Tag<ValueType>{}));
+}
+
+inline int floorAsInt (int n) noexcept     { return n; }
+inline int floorAsInt (float n) noexcept   { return n > (float)  std::numeric_limits<int>::min() ? (int) std::floor (n) : std::numeric_limits<int>::min(); }
+inline int floorAsInt (double n) noexcept  { return n > (double) std::numeric_limits<int>::min() ? (int) std::floor (n) : std::numeric_limits<int>::min(); }
+
+inline int ceilAsInt (int n) noexcept      { return n; }
+inline int ceilAsInt (float n) noexcept    { return n < (float)  std::numeric_limits<int>::max() ? (int) std::ceil (n) : std::numeric_limits<int>::max(); }
+inline int ceilAsInt (double n) noexcept   { return n < (double) std::numeric_limits<int>::max() ? (int) std::ceil (n) : std::numeric_limits<int>::max(); }
+
+} // namespace detail
+#endif
+
 //==============================================================================
 /**
     Manages a rectangle and allows geometric operations to be performed on it.
@@ -811,10 +839,10 @@ public:
     */
     Rectangle<int> getSmallestIntegerContainer() const noexcept
     {
-        return Rectangle<int>::leftTopRightBottom (floorAsInt (pos.x),
-                                                   floorAsInt (pos.y),
-                                                   ceilAsInt  (pos.x + w),
-                                                   ceilAsInt  (pos.y + h));
+        return Rectangle<int>::leftTopRightBottom (detail::floorAsInt (pos.x),
+                                                   detail::floorAsInt (pos.y),
+                                                   detail::ceilAsInt  (pos.x + w),
+                                                   detail::ceilAsInt  (pos.y + h));
     }
 
     /** Casts this rectangle to a Rectangle<int>.
@@ -937,7 +965,7 @@ public:
 
     /** Parses a string containing a rectangle's details.
 
-        The string should contain 4 integer tokens, in the form "x y width height". They
+        The string should contain 4 numeric tokens, in the form "x y width height". They
         can be comma or whitespace separated.
 
         This method is intended to go with the toString() method, to form an easy way
@@ -950,10 +978,10 @@ public:
         StringArray toks;
         toks.addTokens (stringVersion.text.findEndOfWhitespace(), ",; \t\r\n", "");
 
-        return { parseIntAfterSpace (toks[0]),
-                 parseIntAfterSpace (toks[1]),
-                 parseIntAfterSpace (toks[2]),
-                 parseIntAfterSpace (toks[3]) };
+        return { detail::parseAfterSpace<ValueType> (toks[0]),
+                 detail::parseAfterSpace<ValueType> (toks[1]),
+                 detail::parseAfterSpace<ValueType> (toks[2]),
+                 detail::parseAfterSpace<ValueType> (toks[3]) };
     }
 
    #ifndef DOXYGEN
@@ -967,19 +995,9 @@ private:
     Point<ValueType> pos;
     ValueType w {}, h {};
 
-    static ValueType parseIntAfterSpace (StringRef s) noexcept
-        { return static_cast<ValueType> (s.text.findEndOfWhitespace().getIntValue32()); }
-
-    void copyWithRounding (Rectangle<int>& result) const noexcept    { result = getSmallestIntegerContainer(); }
-    void copyWithRounding (Rectangle<float>& result) const noexcept  { result = toFloat(); }
+    void copyWithRounding (Rectangle<int>&    result) const noexcept { result = getSmallestIntegerContainer(); }
+    void copyWithRounding (Rectangle<float>&  result) const noexcept { result = toFloat(); }
     void copyWithRounding (Rectangle<double>& result) const noexcept { result = toDouble(); }
-
-    static int floorAsInt (int n) noexcept     { return n; }
-    static int floorAsInt (float n) noexcept   { return n > (float)  std::numeric_limits<int>::min() ? (int) std::floor (n) : std::numeric_limits<int>::min(); }
-    static int floorAsInt (double n) noexcept  { return n > (double) std::numeric_limits<int>::min() ? (int) std::floor (n) : std::numeric_limits<int>::min(); }
-    static int ceilAsInt (int n) noexcept      { return n; }
-    static int ceilAsInt (float n) noexcept    { return n < (float)  std::numeric_limits<int>::max() ? (int) std::ceil (n) : std::numeric_limits<int>::max(); }
-    static int ceilAsInt (double n) noexcept   { return n < (double) std::numeric_limits<int>::max() ? (int) std::ceil (n) : std::numeric_limits<int>::max(); }
 };
 
 } // namespace juce
diff --git a/modules/juce_graphics/geometry/juce_Rectangle_test.cpp b/modules/juce_graphics/geometry/juce_Rectangle_test.cpp
new file mode 100644
index 0000000000..fe9a8fe4d3
--- /dev/null
+++ b/modules/juce_graphics/geometry/juce_Rectangle_test.cpp
@@ -0,0 +1,51 @@
+/*
+  ==============================================================================
+
+   This file is part of the JUCE library.
+   Copyright (c) 2020 - Raw Material Software Limited
+
+   JUCE is an open source library subject to commercial or open-source
+   licensing.
+
+   By using JUCE, you agree to the terms of both the JUCE 6 End-User License
+   Agreement and JUCE Privacy Policy (both effective as of the 16th June 2020).
+
+   End User License Agreement: www.juce.com/juce-6-licence
+   Privacy Policy: www.juce.com/juce-privacy-policy
+
+   Or: You may also use this code under the terms of the GPL v3 (see
+   www.gnu.org/licenses).
+
+   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
+   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
+   DISCLAIMED.
+
+  ==============================================================================
+*/
+
+namespace juce
+{
+
+struct RectangleUnitTest  : public UnitTest
+{
+    RectangleUnitTest() : UnitTest ("Rectangle", UnitTestCategories::graphics) {}
+
+    void runTest() override
+    {
+        beginTest ("Rectangle/string conversions can be round-tripped");
+        {
+            const Rectangle<float> a (0.1f, 0.2f, 0.3f, 0.4f);
+            expect (Rectangle<float>::fromString (a.toString()) == a);
+
+            const Rectangle<double> b (0.1, 0.2, 0.3, 0.4);
+            expect (Rectangle<double>::fromString (b.toString()) == b);
+
+            const Rectangle<int> c (1, 2, 3, 4);
+            expect (Rectangle<int>::fromString (c.toString()) == c);
+        }
+    }
+};
+
+static RectangleUnitTest rectangleUnitTest;
+
+} // namespace juce
diff --git a/modules/juce_graphics/juce_graphics.cpp b/modules/juce_graphics/juce_graphics.cpp
index 8c30c8c5fe..77d8270802 100644
--- a/modules/juce_graphics/juce_graphics.cpp
+++ b/modules/juce_graphics/juce_graphics.cpp
@@ -126,6 +126,10 @@
 #include "effects/juce_DropShadowEffect.cpp"
 #include "effects/juce_GlowEffect.cpp"
 
+#if JUCE_UNIT_TESTS
+ #include "geometry/juce_Rectangle_test.cpp"
+#endif
+
 #if JUCE_USE_FREETYPE
  #include "native/juce_freetype_Fonts.cpp"
 #endif