diff --git a/crates/egui/src/atomics/atom.rs b/crates/egui/src/atomics/atom.rs
index 4f4b5b75032..ee5ff30d4cf 100644
--- a/crates/egui/src/atomics/atom.rs
+++ b/crates/egui/src/atomics/atom.rs
@@ -81,7 +81,7 @@ impl<'a> Atom<'a> {
             wrap_mode = Some(TextWrapMode::Truncate);
         }
 
-        let (preferred, kind) = self.kind.into_sized(ui, available_size, wrap_mode);
+        let (intrinsic, kind) = self.kind.into_sized(ui, available_size, wrap_mode);
 
         let size = self
             .size
@@ -89,7 +89,7 @@ impl<'a> Atom<'a> {
 
         SizedAtom {
             size,
-            preferred_size: preferred,
+            intrinsic_size: intrinsic.at_least(self.size.unwrap_or_default()),
             grow: self.grow,
             kind,
         }
diff --git a/crates/egui/src/atomics/atom_kind.rs b/crates/egui/src/atomics/atom_kind.rs
index 2672e646b41..b85b504a291 100644
--- a/crates/egui/src/atomics/atom_kind.rs
+++ b/crates/egui/src/atomics/atom_kind.rs
@@ -81,11 +81,10 @@ impl<'a> AtomKind<'a> {
     ) -> (Vec2, SizedAtomKind<'a>) {
         match self {
             AtomKind::Text(text) => {
-                let galley = text.into_galley(ui, wrap_mode, available_size.x, TextStyle::Button);
-                (
-                    galley.size(), // TODO(#5762): calculate the preferred size
-                    SizedAtomKind::Text(galley),
-                )
+                let wrap_mode = wrap_mode.unwrap_or(ui.wrap_mode());
+                let galley =
+                    text.into_galley(ui, Some(wrap_mode), available_size.x, TextStyle::Button);
+                (galley.intrinsic_size, SizedAtomKind::Text(galley))
             }
             AtomKind::Image(image) => {
                 let size = image.load_and_calc_size(ui, available_size);
diff --git a/crates/egui/src/atomics/atom_layout.rs b/crates/egui/src/atomics/atom_layout.rs
index a25a4b7c6bd..53819fbb037 100644
--- a/crates/egui/src/atomics/atom_layout.rs
+++ b/crates/egui/src/atomics/atom_layout.rs
@@ -183,10 +183,10 @@ impl<'a> AtomLayout<'a> {
 
         let mut desired_width = 0.0;
 
-        // Preferred width / height is the ideal size of the widget, e.g. the size where the
+        // intrinsic width / height is the ideal size of the widget, e.g. the size where the
         // text is not wrapped. Used to set Response::intrinsic_size.
-        let mut preferred_width = 0.0;
-        let mut preferred_height = 0.0;
+        let mut intrinsic_width = 0.0;
+        let mut intrinsic_height = 0.0;
 
         let mut height: f32 = 0.0;
 
@@ -203,7 +203,7 @@ impl<'a> AtomLayout<'a> {
         if atoms.len() > 1 {
             let gap_space = gap * (atoms.len() as f32 - 1.0);
             desired_width += gap_space;
-            preferred_width += gap_space;
+            intrinsic_width += gap_space;
         }
 
         for (idx, item) in atoms.into_iter().enumerate() {
@@ -224,10 +224,10 @@ impl<'a> AtomLayout<'a> {
             let size = sized.size;
 
             desired_width += size.x;
-            preferred_width += sized.preferred_size.x;
+            intrinsic_width += sized.intrinsic_size.x;
 
             height = height.at_least(size.y);
-            preferred_height = preferred_height.at_least(sized.preferred_size.y);
+            intrinsic_height = intrinsic_height.at_least(sized.intrinsic_size.y);
 
             sized_items.push(sized);
         }
@@ -243,10 +243,10 @@ impl<'a> AtomLayout<'a> {
             let size = sized.size;
 
             desired_width += size.x;
-            preferred_width += sized.preferred_size.x;
+            intrinsic_width += sized.intrinsic_size.x;
 
             height = height.at_least(size.y);
-            preferred_height = preferred_height.at_least(sized.preferred_size.y);
+            intrinsic_height = intrinsic_height.at_least(sized.intrinsic_size.y);
 
             sized_items.insert(index, sized);
         }
@@ -259,7 +259,7 @@ impl<'a> AtomLayout<'a> {
         let mut response = ui.interact(rect, id, sense);
 
         response.intrinsic_size =
-            Some((Vec2::new(preferred_width, preferred_height) + margin.sum()).at_least(min_size));
+            Some((Vec2::new(intrinsic_width, intrinsic_height) + margin.sum()).at_least(min_size));
 
         AllocatedAtomLayout {
             sized_atoms: sized_items,
diff --git a/crates/egui/src/atomics/sized_atom.rs b/crates/egui/src/atomics/sized_atom.rs
index 50fa443a98c..f1ae0f81b33 100644
--- a/crates/egui/src/atomics/sized_atom.rs
+++ b/crates/egui/src/atomics/sized_atom.rs
@@ -12,8 +12,8 @@ pub struct SizedAtom<'a> {
     /// size.x + gap.
     pub size: Vec2,
 
-    /// Preferred size of the atom. This is used to calculate `Response::intrinsic_size`.
-    pub preferred_size: Vec2,
+    /// Intrinsic size of the atom. This is used to calculate `Response::intrinsic_size`.
+    pub intrinsic_size: Vec2,
 
     pub kind: SizedAtomKind<'a>,
 }
diff --git a/crates/epaint/src/shapes/text_shape.rs b/crates/epaint/src/shapes/text_shape.rs
index b366c86cfb2..9505dc49b1e 100644
--- a/crates/epaint/src/shapes/text_shape.rs
+++ b/crates/epaint/src/shapes/text_shape.rs
@@ -130,10 +130,12 @@ impl TextShape {
             num_vertices: _,
             num_indices: _,
             pixels_per_point: _,
+            intrinsic_size,
         } = Arc::make_mut(galley);
 
         *rect = transform.scaling * *rect;
         *mesh_bounds = transform.scaling * *mesh_bounds;
+        *intrinsic_size = transform.scaling * *intrinsic_size;
 
         for text::PlacedRow { pos, row } in rows {
             *pos *= transform.scaling;
diff --git a/crates/epaint/src/text/fonts.rs b/crates/epaint/src/text/fonts.rs
index 5f90069157c..a08f3206e7d 100644
--- a/crates/epaint/src/text/fonts.rs
+++ b/crates/epaint/src/text/fonts.rs
@@ -1072,6 +1072,7 @@ mod tests {
     use core::f32;
 
     use super::*;
+    use crate::text::{TextWrapping, layout};
     use crate::{Stroke, text::TextFormat};
     use ecolor::Color32;
     use emath::Align;
@@ -1183,4 +1184,60 @@ mod tests {
             }
         }
     }
+
+    #[test]
+    fn test_intrinsic_size() {
+        let pixels_per_point = [1.0, 1.3, 2.0, 0.867];
+        let max_widths = [40.0, 80.0, 133.0, 200.0];
+        let rounded_output_to_gui = [false, true];
+
+        for pixels_per_point in pixels_per_point {
+            let mut fonts = FontsImpl::new(
+                pixels_per_point,
+                1024,
+                AlphaFromCoverage::default(),
+                FontDefinitions::default(),
+            );
+
+            for &max_width in &max_widths {
+                for round_output_to_gui in rounded_output_to_gui {
+                    for mut job in jobs() {
+                        job.wrap = TextWrapping::wrap_at_width(max_width);
+
+                        job.round_output_to_gui = round_output_to_gui;
+
+                        let galley_wrapped = layout(&mut fonts, job.clone().into());
+
+                        job.wrap = TextWrapping::no_max_width();
+
+                        let text = job.text.clone();
+                        let galley_unwrapped = layout(&mut fonts, job.into());
+
+                        let intrinsic_size = galley_wrapped.intrinsic_size;
+                        let unwrapped_size = galley_unwrapped.size();
+
+                        let difference = (intrinsic_size - unwrapped_size).length().abs();
+                        similar_asserts::assert_eq!(
+                            format!("{intrinsic_size:.4?}"),
+                            format!("{unwrapped_size:.4?}"),
+                            "Wrapped intrinsic size should almost match unwrapped size. Intrinsic: {intrinsic_size:.8?} vs unwrapped: {unwrapped_size:.8?}
+                                Difference: {difference:.8?}
+                                wrapped rows: {}, unwrapped rows: {}
+                                pixels_per_point: {pixels_per_point}, text: {text:?}, max_width: {max_width}, round_output_to_gui: {round_output_to_gui}",
+                            galley_wrapped.rows.len(),
+                            galley_unwrapped.rows.len()
+                            );
+                        similar_asserts::assert_eq!(
+                            format!("{intrinsic_size:.4?}"),
+                            format!("{unwrapped_size:.4?}"),
+                            "Unwrapped galley intrinsic size should exactly match its size. \
+                                {:.8?} vs {:8?}",
+                            galley_unwrapped.intrinsic_size,
+                            galley_unwrapped.size(),
+                        );
+                    }
+                }
+            }
+        }
+    }
 }
diff --git a/crates/epaint/src/text/text_layout.rs b/crates/epaint/src/text/text_layout.rs
index 7915bbf6187..6dc0aa03f0f 100644
--- a/crates/epaint/src/text/text_layout.rs
+++ b/crates/epaint/src/text/text_layout.rs
@@ -82,6 +82,7 @@ pub fn layout(fonts: &mut FontsImpl, job: Arc<LayoutJob>) -> Galley {
             num_indices: 0,
             pixels_per_point: fonts.pixels_per_point(),
             elided: true,
+            intrinsic_size: Vec2::ZERO,
         };
     }
 
@@ -94,6 +95,8 @@ pub fn layout(fonts: &mut FontsImpl, job: Arc<LayoutJob>) -> Galley {
 
     let point_scale = PointScale::new(fonts.pixels_per_point());
 
+    let intrinsic_size = calculate_intrinsic_size(point_scale, &job, &paragraphs);
+
     let mut elided = false;
     let mut rows = rows_from_paragraphs(paragraphs, &job, &mut elided);
     if elided {
@@ -124,7 +127,7 @@ pub fn layout(fonts: &mut FontsImpl, job: Arc<LayoutJob>) -> Galley {
     }
 
     // Calculate the Y positions and tessellate the text:
-    galley_from_rows(point_scale, job, rows, elided)
+    galley_from_rows(point_scale, job, rows, elided, intrinsic_size)
 }
 
 // Ignores the Y coordinate.
@@ -190,6 +193,46 @@ fn layout_section(
     }
 }
 
+/// Calculate the intrinsic size of the text.
+///
+/// The result is eventually passed to `Response::intrinsic_size`.
+/// This works by calculating the size of each `Paragraph` (instead of each `Row`).
+fn calculate_intrinsic_size(
+    point_scale: PointScale,
+    job: &LayoutJob,
+    paragraphs: &[Paragraph],
+) -> Vec2 {
+    let mut intrinsic_size = Vec2::ZERO;
+    for (idx, paragraph) in paragraphs.iter().enumerate() {
+        if paragraph.glyphs.is_empty() {
+            if idx == 0 {
+                intrinsic_size.y += point_scale.round_to_pixel(paragraph.empty_paragraph_height);
+            }
+            continue;
+        }
+        intrinsic_size.x = f32::max(
+            paragraph
+                .glyphs
+                .last()
+                .map(|l| l.max_x())
+                .unwrap_or_default(),
+            intrinsic_size.x,
+        );
+
+        let mut height = paragraph
+            .glyphs
+            .iter()
+            .map(|g| g.line_height)
+            .max_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal))
+            .unwrap_or(paragraph.empty_paragraph_height);
+        if idx == 0 {
+            height = f32::max(height, job.first_row_min_height);
+        }
+        intrinsic_size.y += point_scale.round_to_pixel(height);
+    }
+    intrinsic_size
+}
+
 // Ignores the Y coordinate.
 fn rows_from_paragraphs(
     paragraphs: Vec<Paragraph>,
@@ -610,6 +653,7 @@ fn galley_from_rows(
     job: Arc<LayoutJob>,
     mut rows: Vec<PlacedRow>,
     elided: bool,
+    intrinsic_size: Vec2,
 ) -> Galley {
     let mut first_row_min_height = job.first_row_min_height;
     let mut cursor_y = 0.0;
@@ -680,6 +724,7 @@ fn galley_from_rows(
         num_vertices,
         num_indices,
         pixels_per_point: point_scale.pixels_per_point,
+        intrinsic_size,
     };
 
     if galley.job.round_output_to_gui {
diff --git a/crates/epaint/src/text/text_layout_types.rs b/crates/epaint/src/text/text_layout_types.rs
index 016bfe10447..36d92479e54 100644
--- a/crates/epaint/src/text/text_layout_types.rs
+++ b/crates/epaint/src/text/text_layout_types.rs
@@ -560,6 +560,12 @@ pub struct Galley {
     /// so that we can warn if this has changed once we get to
     /// tessellation.
     pub pixels_per_point: f32,
+
+    /// This is the size that a non-wrapped, non-truncated, non-justified version of the text
+    /// would have.
+    ///
+    /// Useful for advanced layouting.
+    pub intrinsic_size: Vec2,
 }
 
 #[derive(Clone, Debug, PartialEq)]
@@ -821,6 +827,8 @@ impl Galley {
                 .at_most(rect.min.x + self.job.wrap.max_width)
                 .floor_ui();
         }
+
+        self.intrinsic_size = self.intrinsic_size.round_ui();
     }
 
     /// Append each galley under the previous one.
@@ -836,6 +844,7 @@ impl Galley {
             num_vertices: 0,
             num_indices: 0,
             pixels_per_point,
+            intrinsic_size: Vec2::ZERO,
         };
 
         for (i, galley) in galleys.iter().enumerate() {
@@ -872,6 +881,9 @@ impl Galley {
             // Note that if `galley.elided` is true this will be the last `Galley` in
             // the vector and the loop will end.
             merged_galley.elided |= galley.elided;
+            merged_galley.intrinsic_size.x =
+                f32::max(merged_galley.intrinsic_size.x, galley.intrinsic_size.x);
+            merged_galley.intrinsic_size.y += galley.intrinsic_size.y;
         }
 
         if merged_galley.job.round_output_to_gui {
diff --git a/tests/egui_tests/tests/test_atoms.rs b/tests/egui_tests/tests/test_atoms.rs
index abc9f2d0546..98e90c1c528 100644
--- a/tests/egui_tests/tests/test_atoms.rs
+++ b/tests/egui_tests/tests/test_atoms.rs
@@ -69,3 +69,35 @@ fn single_test(name: &str, mut f: impl FnMut(&mut Ui)) -> SnapshotResult {
 
     harness.try_snapshot(name)
 }
+
+#[test]
+fn test_intrinsic_size() {
+    let mut intrinsic_size = None;
+    for wrapping in [
+        TextWrapMode::Extend,
+        TextWrapMode::Wrap,
+        TextWrapMode::Truncate,
+    ] {
+        _ = HarnessBuilder::default()
+            .with_size(Vec2::new(100.0, 100.0))
+            .build_ui(|ui| {
+                ui.style_mut().wrap_mode = Some(wrapping);
+                let response = ui.add(Button::new(
+                    "Hello world this is a long text that should be wrapped.",
+                ));
+                if let Some(current_intrinsic_size) = intrinsic_size {
+                    assert_eq!(
+                        Some(current_intrinsic_size),
+                        response.intrinsic_size,
+                        "For wrapping: {wrapping:?}"
+                    );
+                }
+                assert!(
+                    response.intrinsic_size.is_some(),
+                    "intrinsic_size should be set for `Button`"
+                );
+                intrinsic_size = response.intrinsic_size;
+            });
+    }
+    assert_eq!(intrinsic_size.unwrap().round(), Vec2::new(305.0, 18.0));
+}