diff --git a/packages/flutter/lib/src/widgets/safe_area.dart b/packages/flutter/lib/src/widgets/safe_area.dart
index 03adc9010b..78ac59237c 100644
--- a/packages/flutter/lib/src/widgets/safe_area.dart
+++ b/packages/flutter/lib/src/widgets/safe_area.dart
@@ -2,6 +2,8 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+import 'dart:math' as math;
+
 import 'package:flutter/foundation.dart';
 
 import 'basic.dart';
@@ -9,8 +11,8 @@ import 'debug.dart';
 import 'framework.dart';
 import 'media_query.dart';
 
-/// A widget that insets its child by sufficient padding to avoid
-/// intrusions by the operating system.
+/// A widget that insets its child by sufficient padding to avoid intrusions by
+/// the operating system.
 ///
 /// For example, this will indent the child by enough to avoid the status bar at
 /// the top of the screen.
@@ -18,6 +20,9 @@ import 'media_query.dart';
 /// It will also indent the child by the amount necessary to avoid The Notch on
 /// the iPhone X, or other similar creative physical features of the display.
 ///
+/// When a [minimum] padding is specified, the greater of the minimum padding
+/// or the safe area padding will be applied.
+///
 /// See also:
 ///
 ///  * [SliverSafeArea], for insetting slivers to avoid operating system
@@ -29,13 +34,15 @@ import 'media_query.dart';
 class SafeArea extends StatelessWidget {
   /// Creates a widget that avoids operating system interfaces.
   ///
-  /// The [left], [top], [right], and [bottom] arguments must not be null.
+  /// The [left], [top], [right], [bottom], and [minimum] arguments must not be
+  /// null.
   const SafeArea({
     Key key,
     this.left: true,
     this.top: true,
     this.right: true,
     this.bottom: true,
+    this.minimum: EdgeInsets.zero,
     @required this.child,
   }) : assert(left != null),
        assert(top != null),
@@ -56,6 +63,11 @@ class SafeArea extends StatelessWidget {
   /// Whether to avoid system intrusions on the bottom side of the screen.
   final bool bottom;
 
+  /// This minimum padding to apply.
+  ///
+  /// The greater of the minimum insets and the media padding will be applied.
+  final EdgeInsets minimum;
+
   /// The widget below this widget in the tree.
   ///
   /// The padding on the [MediaQuery] for the [child] will be suitably adjusted
@@ -70,10 +82,10 @@ class SafeArea extends StatelessWidget {
     final EdgeInsets padding = MediaQuery.of(context).padding;
     return new Padding(
       padding: new EdgeInsets.only(
-        left: left ? padding.left : 0.0,
-        top: top ? padding.top : 0.0,
-        right: right ? padding.right : 0.0,
-        bottom: bottom ? padding.bottom : 0.0,
+        left: math.max(left ? padding.left : 0.0, minimum.left),
+        top: math.max(top ? padding.top : 0.0, minimum.top),
+        right: math.max(right ? padding.right : 0.0, minimum.right),
+        bottom: math.max(bottom ? padding.bottom : 0.0, minimum.bottom),
       ),
       child: new MediaQuery.removePadding(
         context: context,
@@ -106,6 +118,9 @@ class SafeArea extends StatelessWidget {
 /// on the iPhone X, or other similar creative physical features of the
 /// display.
 ///
+/// When a [minimum] padding is specified, the greater of the minimum padding
+/// or the safe area padding will be applied.
+///
 /// See also:
 ///
 ///  * [SafeArea], for insetting widgets to avoid operating system intrusions.
@@ -116,13 +131,14 @@ class SafeArea extends StatelessWidget {
 class SliverSafeArea extends StatelessWidget {
   /// Creates a sliver that avoids operating system interfaces.
   ///
-  /// The [left], [top], [right], and [bottom] arguments must not be null.
+  /// The [left], [top], [right], [bottom], and [minimum] arguments must not be null.
   const SliverSafeArea({
     Key key,
     this.left: true,
     this.top: true,
     this.right: true,
     this.bottom: true,
+    this.minimum: EdgeInsets.zero,
     @required this.sliver,
   }) : assert(left != null),
        assert(top != null),
@@ -143,6 +159,11 @@ class SliverSafeArea extends StatelessWidget {
   /// Whether to avoid system intrusions on the bottom side of the screen.
   final bool bottom;
 
+  /// This minimum padding to apply.
+  ///
+  /// The greater of the minimum padding and the media padding is be applied.
+  final EdgeInsets minimum;
+
   /// The sliver below this sliver in the tree.
   ///
   /// The padding on the [MediaQuery] for the [sliver] will be suitably adjusted
@@ -155,10 +176,10 @@ class SliverSafeArea extends StatelessWidget {
     final EdgeInsets padding = MediaQuery.of(context).padding;
     return new SliverPadding(
       padding: new EdgeInsets.only(
-        left: left ? padding.left : 0.0,
-        top: top ? padding.top : 0.0,
-        right: right ? padding.right : 0.0,
-        bottom: bottom ? padding.bottom : 0.0,
+        left: math.max(left ? padding.left : 0.0, minimum.left),
+        top: math.max(top ? padding.top : 0.0, minimum.top),
+        right: math.max(right ? padding.right : 0.0, minimum.right),
+        bottom: math.max(bottom ? padding.bottom : 0.0, minimum.bottom),
       ),
       sliver: new MediaQuery.removePadding(
         context: context,
diff --git a/packages/flutter/test/widgets/safe_area_test.dart b/packages/flutter/test/widgets/safe_area_test.dart
index e7a99237d1..176c3af7e1 100644
--- a/packages/flutter/test/widgets/safe_area_test.dart
+++ b/packages/flutter/test/widgets/safe_area_test.dart
@@ -22,6 +22,21 @@ void main() {
       expect(tester.getBottomRight(find.byType(Placeholder)), const Offset(780.0, 580.0));
     });
 
+    testWidgets('SafeArea - with minimums', (WidgetTester tester) async {
+      await tester.pumpWidget(
+        const MediaQuery(
+          data: const MediaQueryData(padding: const EdgeInsets.all(20.0)),
+          child: const SafeArea(
+            top: false,
+            minimum: const EdgeInsets.fromLTRB(0.0, 10.0, 20.0, 30.0),
+            child: const Placeholder(),
+          ),
+        ),
+      );
+      expect(tester.getTopLeft(find.byType(Placeholder)), const Offset(20.0, 10.0));
+      expect(tester.getBottomRight(find.byType(Placeholder)), const Offset(780.0, 570.0));
+    });
+
     testWidgets('SafeArea - nested', (WidgetTester tester) async {
       await tester.pumpWidget(
         const MediaQuery(
@@ -119,6 +134,24 @@ void main() {
       ]);
     });
 
+    testWidgets('SliverSafeArea - basic', (WidgetTester tester) async {
+      await tester.pumpWidget(
+        buildWidget(
+          const EdgeInsets.all(20.0),
+          const SliverSafeArea(
+            top: false,
+            minimum: const EdgeInsets.fromLTRB(0.0, 10.0, 20.0, 30.0),
+            sliver: const SliverToBoxAdapter(child: const SizedBox(width: 800.0, height: 100.0, child: const Text('padded'))),
+          ),
+        ),
+      );
+      verify(tester, <Rect>[
+        new Rect.fromLTWH(0.0, 0.0, 800.0, 100.0),
+        new Rect.fromLTWH(20.0, 110.0, 760.0, 100.0),
+        new Rect.fromLTWH(0.0, 240.0, 800.0, 100.0),
+      ]);
+    });
+
     testWidgets('SliverSafeArea - nested', (WidgetTester tester) async {
       await tester.pumpWidget(
         buildWidget(