diff --git a/crates/geom/src/arc.rs b/crates/geom/src/arc.rs
index de66388de..c4fe640ae 100644
--- a/crates/geom/src/arc.rs
+++ b/crates/geom/src/arc.rs
@@ -22,7 +22,7 @@ impl ArcPath {
         let mut segs = Vec::new();
         let mut cum = 0.0;
         for s in path.to_bezpath().segments() {
-            let l = s.arclen(ACCURACY);
+            let l = crate::path::measured_arclen(&s, ACCURACY);
             if l.is_finite() && l > 1e-9 {
                 segs.push((s, cum, l));
                 cum += l;
@@ -51,7 +51,8 @@ impl ArcPath {
         let s = if self.closed && self.len > 0.0 { s.rem_euclid(self.len) } else { s.clamp(0.0, self.len) };
         let i = self.segs.partition_point(|(_, c, _)| *c <= s).saturating_sub(1);
         let Some(&(seg, c, l)) = self.segs.get(i) else { return (Point::ZERO, Vec2::new(1.0, 0.0)) };
-        let t = seg.inv_arclen((s - c).min(l), ACCURACY).clamp(0.0, 1.0);
+        // (The solver's precision is relative to the segment's length: a long one needs a looser one.)
+        let t = seg.inv_arclen((s - c).min(l), ACCURACY.max(l * 1e-9)).clamp(0.0, 1.0);
         let p = seg.eval(t);
         let (t0, t1) = ((t - 1e-4).max(0.0), (t + 1e-4).min(1.0));
         let d = seg.eval(t1) - seg.eval(t0);
diff --git a/crates/geom/src/corners.rs b/crates/geom/src/corners.rs
index 46449f43a..fe64d9e64 100644
--- a/crates/geom/src/corners.rs
+++ b/crates/geom/src/corners.rs
@@ -39,7 +39,7 @@ impl Side {
 
     /// The side's length.
     fn length(&self) -> f64 {
-        if self.straight() { self.curve.p0.distance(self.curve.p3) } else { self.curve.arclen(ARCLEN_ACCURACY) }
+        if self.straight() { self.curve.p0.distance(self.curve.p3) } else { crate::path::measured_arclen(&kurbo::PathSeg::Cubic(self.curve), ARCLEN_ACCURACY) }
     }
 
     /// The parameter `s` along the side from the corner, the point there and the direction the
diff --git a/crates/geom/src/path.rs b/crates/geom/src/path.rs
index 110997efc..f7828fb80 100644
--- a/crates/geom/src/path.rs
+++ b/crates/geom/src/path.rs
@@ -561,10 +561,27 @@ impl PathData {
     }
     /// Total length of all segments.
     pub fn length(&self) -> f64 {
-        self.to_bezpath().segments().map(|s| kurbo::ParamCurveArclen::arclen(&s, 1e-6)).sum()
+        self.to_bezpath().segments().map(|s| measured_arclen(&s, 1e-6)).sum()
     }
 }
 
+/// The largest x or y, in size, of a segment's control points for which its length is measured.
+/// Document coordinates are far inside it; past it (or not finite) the integrator's arithmetic
+/// overflows and it subdivides without end.
+const MEASURE_LIMIT: f64 = 1e9;
+
+/// The length of `seg` to `accuracy`; 0 for a segment whose control points are not finite or past
+/// [`MEASURE_LIMIT`].
+pub(crate) fn measured_arclen(seg: &PathSeg, accuracy: f64) -> f64 {
+    let ok = |p: Point| p.x.is_finite() && p.y.is_finite() && p.x.abs() <= MEASURE_LIMIT && p.y.abs() <= MEASURE_LIMIT;
+    let fits = match seg {
+        PathSeg::Line(l) => ok(l.p0) && ok(l.p1),
+        PathSeg::Quad(q) => ok(q.p0) && ok(q.p1) && ok(q.p2),
+        PathSeg::Cubic(c) => ok(c.p0) && ok(c.p1) && ok(c.p2) && ok(c.p3),
+    };
+    if fits { kurbo::ParamCurveArclen::arclen(seg, accuracy) } else { 0.0 }
+}
+
 /// The largest x or y, in size, of a segment's control points for which [`segment_bounds`]
 /// measures the segment by its extrema. kurbo adds up to eight coordinates together when it finds a
 /// segment's extrema and evaluates the segment there, and a sum of eight coordinates of this size or