diff --git a/crates/render/src/lib.rs b/crates/render/src/lib.rs
index eb139555..b1d9fce0 100644
--- a/crates/render/src/lib.rs
+++ b/crates/render/src/lib.rs
@@ -1442,6 +1442,7 @@ pub(crate) fn stroke(
     if let Some(d) = &line.dash {
         let pat: Vec<f64> = d.pattern().iter().map(|v| v * lw.max(0.75)).collect();
         let pat = dash_with_caps(pat, cap, sw);
+        let pat = limit_dash_count(path, pat);
         if !pat.is_empty() && pat.iter().all(|v| *v > 0.0) {
             if cap == kurbo::Cap::Square {
                 sk = sk.with_caps(kurbo::Cap::Butt);
@@ -1582,6 +1583,30 @@ fn dash_with_caps(mut pat: Vec<f64>, cap: kurbo::Cap, width: f64) -> Vec<f64> {
     pat
 }
 
+/// The most dashes one stroke is cut into. Stroking expands every dash into its own outline, so a
+/// tiny dash on a huge shape (a 1 EMU-wide `custDash` on a 2147483647 EMU rectangle) would
+/// otherwise need gigabytes and abort the app when the slide is drawn. Past this count the
+/// pattern is scaled up evenly, which looks the same: the dashes are far below a pixel by then.
+const MAX_DASHES: f64 = 20_000.0;
+
+fn limit_dash_count(path: &BezPath, pat: Vec<f64>) -> Vec<f64> {
+    use kurbo::ParamCurveArclen;
+    let period: f64 = pat.iter().sum();
+    if !(period.is_finite() && period > 0.0) {
+        return pat;
+    }
+    let len: f64 = path.segments().map(|s| s.arclen(1e-2)).sum();
+    let dashes = len / period;
+    if !len.is_finite() {
+        return vec![];
+    }
+    if dashes <= MAX_DASHES {
+        return pat;
+    }
+    let k = dashes / MAX_DASHES;
+    pat.into_iter().map(|v| v * k).collect()
+}
+
 fn end_points(path: &BezPath) -> Option<((Point, Point), (Point, Point))> {
     let els: Vec<PathEl> = path.elements().to_vec();
     let mut pts: Vec<Point> = vec![];
diff --git a/crates/render/src/tests_wild.rs b/crates/render/src/tests_wild.rs
index 7e7f0eac..672e7dcd 100644
--- a/crates/render/src/tests_wild.rs
+++ b/crates/render/src/tests_wild.rs
@@ -744,3 +744,31 @@ fn a_3d_shapes_face_is_lit_even_without_a_bevel() {
     let img = render(vec![shape(r#"<a:scene3d><a:camera prst="orthographicFront"/><a:lightRig rig="threePt" dir="t"/></a:scene3d>"#)]);
     assert!(close(img.pixel(175, 150), base, 1));
 }
+
+#[test]
+fn a_tiny_dash_on_a_huge_shape_draws_without_running_out_of_memory() {
+    // Found by fuzzing the pptx round trip: a 1 EMU `custDash` on a 2147483647 EMU square asked
+    // the stroker for hundreds of thousands of dashes and aborted on a 7.5 GB allocation.
+    let sh = Shape {
+        id: ShapeId(12),
+        xfrm: Some(Xfrm::new(0.0, 0.0, 169_093.0, 169_093.0)),
+        geom: Geom::preset("rect"),
+        line: Some(Line {
+            fill: solid(RED),
+            width: Some(0.0001),
+            dash: Some(deckcraft_model::style::Dash::Custom { pattern: vec![(1.0, 1.0)] }),
+            ..Default::default()
+        }),
+        ..Default::default()
+    };
+    let img = render_slide(&deck_with(vec![sh]), 0, &RenderOpts { scale: 0.25, ..Default::default() });
+    assert!(img.width > 0);
+    // The pattern is scaled up only past the limit; ordinary lines keep theirs.
+    let mut p = BezPath::new();
+    p.move_to((0.0, 0.0));
+    p.line_to((100.0, 0.0));
+    assert_eq!(limit_dash_count(&p, vec![1.0, 1.0]), vec![1.0, 1.0]);
+    p.line_to((4.0e6, 0.0));
+    let pat = limit_dash_count(&p, vec![1.0, 1.0]);
+    assert!((4.0e6 / (pat[0] + pat[1]) - MAX_DASHES).abs() < 1.0, "{pat:?}");
+}