diff --git a/crates/typst/src/layout/transform.rs b/crates/typst/src/layout/transform.rs
index ad3668d10..dcb178fdb 100644
--- a/crates/typst/src/layout/transform.rs
+++ b/crates/typst/src/layout/transform.rs
@@ -12,6 +12,7 @@ use crate::layout::{
     Abs, Alignment, Angle, Axes, BlockElem, FixedAlignment, Frame, HAlignment, Length,
     Point, Ratio, Region, Regions, Rel, Size, VAlignment,
 };
+use crate::utils::Numeric;
 
 /// Moves content without affecting layout.
 ///
@@ -153,12 +154,11 @@ fn layout_rotate(
     let align = elem.origin(styles).resolve(styles);
 
     // Compute the new region's approximate size.
-    let size = region
-        .size
-        .to_point()
-        .transform_inf(Transform::rotate(angle))
-        .map(Abs::abs)
-        .to_size();
+    let size = if region.size.is_finite() {
+        compute_bounding_box(region.size, Transform::rotate(-angle)).1
+    } else {
+        Size::splat(Abs::inf())
+    };
 
     measure_and_layout(
         engine,
@@ -248,7 +248,10 @@ fn layout_scale(
 ) -> SourceResult<Frame> {
     // Compute the new region's approximate size.
     let scale = elem.resolve_scale(engine, locator.relayout(), region.size, styles)?;
-    let size = region.size.zip_map(scale, |r, s| s.of(r)).map(Abs::abs);
+    let size = region
+        .size
+        .zip_map(scale, |r, s| if r.is_finite() { Ratio::new(1.0 / s).of(r) } else { r })
+        .map(Abs::abs);
 
     measure_and_layout(
         engine,
@@ -489,7 +492,7 @@ fn measure_and_layout(
             .pre_concat(Transform::translate(-x, -y));
 
         // Compute the bounding box and offset and wrap in a new frame.
-        let (offset, size) = compute_bounding_box(&frame, ts);
+        let (offset, size) = compute_bounding_box(frame.size(), ts);
         frame.transform(ts);
         frame.translate(offset);
         frame.set_size(size);
@@ -512,20 +515,20 @@ fn measure_and_layout(
     }
 }
 
-/// Computes the bounding box and offset of a transformed frame.
-fn compute_bounding_box(frame: &Frame, ts: Transform) -> (Point, Size) {
+/// Computes the bounding box and offset of a transformed area.
+fn compute_bounding_box(size: Size, ts: Transform) -> (Point, Size) {
     let top_left = Point::zero().transform_inf(ts);
-    let top_right = Point::new(frame.width(), Abs::zero()).transform_inf(ts);
-    let bottom_left = Point::new(Abs::zero(), frame.height()).transform_inf(ts);
-    let bottom_right = Point::new(frame.width(), frame.height()).transform_inf(ts);
+    let top_right = Point::with_x(size.x).transform_inf(ts);
+    let bottom_left = Point::with_y(size.y).transform_inf(ts);
+    let bottom_right = size.to_point().transform_inf(ts);
 
-    // We first compute the new bounding box of the rotated frame.
+    // We first compute the new bounding box of the rotated area.
     let min_x = top_left.x.min(top_right.x).min(bottom_left.x).min(bottom_right.x);
     let min_y = top_left.y.min(top_right.y).min(bottom_left.y).min(bottom_right.y);
     let max_x = top_left.x.max(top_right.x).max(bottom_left.x).max(bottom_right.x);
     let max_y = top_left.y.max(top_right.y).max(bottom_left.y).max(bottom_right.y);
 
-    // Then we compute the new size of the frame.
+    // Then we compute the new size of the area.
     let width = max_x - min_x;
     let height = max_y - min_y;
 
diff --git a/tests/ref/transform-scale-relative-sizing.png b/tests/ref/transform-scale-relative-sizing.png
index d10bd3ff4..a6c18a98e 100644
Binary files a/tests/ref/transform-scale-relative-sizing.png and b/tests/ref/transform-scale-relative-sizing.png differ
diff --git a/tests/ref/transform-scale.png b/tests/ref/transform-scale.png
index c95b90f1d..ea113aa1b 100644
Binary files a/tests/ref/transform-scale.png and b/tests/ref/transform-scale.png differ