diff --git a/crates/gpui/src/taffy.rs b/crates/gpui/src/taffy.rs
index 4844748d6c767d..eb3c391dc5e2b4 100644
--- a/crates/gpui/src/taffy.rs
+++ b/crates/gpui/src/taffy.rs
@@ -111,6 +111,36 @@ impl TaffyLayoutEngine {
             .into()
     }
 
+    /// Treats any `auto` dimension of the given node's style as filling `size`.
+    ///
+    /// This is applied to window roots before layout so they behave like the
+    /// root element on the web, which stretches to fill the initial containing
+    /// block (the viewport) unless given an explicit size. Explicitly styled
+    /// dimensions are preserved.
+    pub fn stretch_auto_size_to_fill(
+        &mut self,
+        id: LayoutId,
+        size: Size<Pixels>,
+        scale_factor: f32,
+    ) {
+        let style = self.taffy.style(id.0).expect(EXPECT_MESSAGE);
+        let stretch_width = style.size.width.is_auto();
+        let stretch_height = style.size.height.is_auto();
+        if !stretch_width && !stretch_height {
+            return;
+        }
+        let mut style = style.clone();
+        if stretch_width {
+            style.size.width =
+                taffy::style::Dimension::length(round_to_device_pixel(size.width.0, scale_factor));
+        }
+        if stretch_height {
+            style.size.height =
+                taffy::style::Dimension::length(round_to_device_pixel(size.height.0, scale_factor));
+        }
+        self.taffy.set_style(id.0, style).expect(EXPECT_MESSAGE);
+    }
+
     // Used to understand performance
     #[allow(dead_code)]
     fn count_all_children(&self, parent: LayoutId) -> anyhow::Result<u32> {
diff --git a/crates/gpui/src/window.rs b/crates/gpui/src/window.rs
index 7059cf863a60ff..f65a696a8e93a3 100644
--- a/crates/gpui/src/window.rs
+++ b/crates/gpui/src/window.rs
@@ -2823,8 +2823,16 @@ impl Window {
             }
         };
 
-        // Layout all root elements.
+        // Layout all root elements. Like the root element on the web, which
+        // stretches to fill the viewport unless explicitly sized, window roots
+        // fill the window when their size is `auto`.
+        let scale_factor = self.scale_factor();
         let mut root_element = self.root.as_ref().unwrap().clone().into_any_element();
+        let root_layout_id = root_element.request_layout(self, cx);
+        self.layout_engine
+            .as_mut()
+            .unwrap()
+            .stretch_auto_size_to_fill(root_layout_id, root_size, scale_factor);
         root_element.prepaint_as_root(Point::default(), root_size.into(), self, cx);
 
         #[cfg(any(feature = "inspector", debug_assertions))]
@@ -2837,6 +2845,11 @@ impl Window {
         let mut tooltip_element = None;
         if let Some(prompt) = self.prompt.take() {
             let mut element = prompt.view.any_view().into_any_element();
+            let prompt_layout_id = element.request_layout(self, cx);
+            self.layout_engine
+                .as_mut()
+                .unwrap()
+                .stretch_auto_size_to_fill(prompt_layout_id, root_size, scale_factor);
             element.prepaint_as_root(Point::default(), root_size.into(), self, cx);
             prompt_element = Some(element);
             self.prompt = Some(prompt);
@@ -6312,3 +6325,77 @@ pub fn outline(
         border_style,
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use crate::{
+        AppContext as _, Bounds, Context, IntoElement, ParentElement as _, Pixels, Render,
+        Styled as _, TestAppContext, Window, canvas, div, px, size,
+    };
+    use std::{cell::Cell, rc::Rc};
+
+    struct RootView {
+        explicit_size: bool,
+        child_bounds: Rc<Cell<Bounds<Pixels>>>,
+    }
+
+    impl Render for RootView {
+        fn render(&mut self, _: &mut Window, _: &mut Context<Self>) -> impl IntoElement {
+            let child_bounds = self.child_bounds.clone();
+            let root = div().flex().flex_col().child(
+                canvas(
+                    move |bounds, _, _| child_bounds.set(bounds),
+                    |_, _, _, _| {},
+                )
+                .size_full(),
+            );
+            if self.explicit_size {
+                root.w(px(300.)).h(px(200.))
+            } else {
+                root
+            }
+        }
+    }
+
+    #[test]
+    fn auto_sized_window_root_fills_the_window() {
+        let mut cx = TestAppContext::single();
+        let child_bounds = Rc::new(Cell::new(Bounds::default()));
+        let window = cx.add_window({
+            let child_bounds = child_bounds.clone();
+            move |_, _| RootView {
+                explicit_size: false,
+                child_bounds,
+            }
+        });
+
+        let viewport_size = cx
+            .update_window(window.into(), |_, window, cx| {
+                window.draw(cx).clear();
+                window.viewport_size()
+            })
+            .unwrap();
+
+        assert_eq!(child_bounds.get().size, viewport_size);
+    }
+
+    #[test]
+    fn explicitly_sized_window_root_keeps_its_size() {
+        let mut cx = TestAppContext::single();
+        let child_bounds = Rc::new(Cell::new(Bounds::default()));
+        let window = cx.add_window({
+            let child_bounds = child_bounds.clone();
+            move |_, _| RootView {
+                explicit_size: true,
+                child_bounds,
+            }
+        });
+
+        cx.update_window(window.into(), |_, window, cx| {
+            window.draw(cx).clear();
+        })
+        .unwrap();
+
+        assert_eq!(child_bounds.get().size, size(px(300.), px(200.)));
+    }
+}