diff --git a/crates/engine/src/cmd/mesh.rs b/crates/engine/src/cmd/mesh.rs
index 82db91e..e1029df 100644
--- a/crates/engine/src/cmd/mesh.rs
+++ b/crates/engine/src/cmd/mesh.rs
@@ -250,6 +250,7 @@ pub(super) fn quality_json(q: &TetQuality) -> Value {
         "max_dihedral": q.max_dihedral,
         "min_radius_ratio": q.min_radius_ratio,
         "mean_radius_ratio": q.mean_radius_ratio,
+        "min_scaled_jacobian": q.min_scaled_jacobian,
         "slivers": q.slivers,
         "inadmissible": q.inadmissible,
     })
diff --git a/crates/mesh/src/quality/tests.rs b/crates/mesh/src/quality/tests.rs
index 113444a..b002884 100644
--- a/crates/mesh/src/quality/tests.rs
+++ b/crates/mesh/src/quality/tests.rs
@@ -44,6 +44,43 @@ fn regular_tetrahedron_scores_one() {
     }
 }
 
+/// The dihedral angles and the scaled Jacobian measure different things on the same corners
+/// (#547): a flat tetrahedron is low on both; a needle has every dihedral angle between 60° and
+/// 90° but a nearly flat apex corner, so only the scaled Jacobian sees it. A tet10 with straight
+/// edges scores what its corners score, and the tet mesher's report reads the same numbers.
+#[test]
+fn dihedral_angles_and_scaled_jacobian_on_the_same_tetrahedra() {
+    let both = |p: &[[f64; 3]]| {
+        let q = element_quality(ElementKind::Tet4, p).unwrap();
+        (metric(&q, Metric::MinDihedral), metric(&q, Metric::MaxDihedral), metric(&q, Metric::ScaledJacobian))
+    };
+    let (lo, hi, sj) = both(&regular_tet());
+    assert!((lo - 70.528_779).abs() < 1e-5 && (hi - lo).abs() < 1e-9 && close(sj, 1.0), "{lo} {hi} {sj}");
+
+    let flat = [[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [1., 1., 0.01]];
+    let (lo, hi, sj) = both(&flat);
+    assert!(lo < 2.0 && hi > 178.0 && sj > 0.0 && sj < 0.02, "{lo} {hi} {sj}");
+
+    // Equilateral base of side 1, apex 12 above its centre.
+    let h = 3.0_f64.sqrt() / 2.0;
+    let needle = [[0., 0., 0.], [1., 0., 0.], [0.5, h, 0.], [0.5, h / 3.0, 12.0]];
+    let (lo, hi, sj) = both(&needle);
+    assert!(lo > 59.0 && hi < 91.0, "{lo} {hi}");
+    // Apex corner: 6V = (√3/2)·12, edges √(1/3 + 144) each.
+    let edge = (1.0 / 3.0 + 144.0_f64).sqrt();
+    assert!(close(sj, 2.0_f64.sqrt() * h * 12.0 / edge.powi(3)), "{sj}");
+    assert!(sj < 0.01);
+
+    for p in [regular_tet(), flat, needle] {
+        let tet10 = element_quality(ElementKind::Tet10, &midpoints(&p, &jacobian::TET_EDGES)).unwrap();
+        let (lo, hi, sj) = both(&p);
+        assert!(close(metric(&tet10, Metric::MinDihedral), lo) && close(metric(&tet10, Metric::MaxDihedral), hi));
+        assert!(close(metric(&tet10, Metric::ScaledJacobian), sj));
+        let r = crate::tet::tet_quality_stats(&p, &[[0, 1, 2, 3]]).unwrap();
+        assert!(close(r.min_dihedral, lo) && close(r.max_dihedral, hi) && close(r.min_scaled_jacobian, sj), "{r:?}");
+    }
+}
+
 #[test]
 fn right_corner_tetrahedron() {
     let q = element_quality(ElementKind::Tet4, &RIGHT_TET).unwrap();
diff --git a/crates/mesh/src/tet/mod.rs b/crates/mesh/src/tet/mod.rs
index a877b6a..27e69d3 100644
--- a/crates/mesh/src/tet/mod.rs
+++ b/crates/mesh/src/tet/mod.rs
@@ -140,6 +140,10 @@ pub struct TetQuality {
     pub max_dihedral: f64,
     pub min_radius_ratio: f64,
     pub mean_radius_ratio: f64,
+    /// The smallest scaled Jacobian at the worst corner (as `mesh.quality` reports it). The
+    /// dihedral range does not bound it: a needle has every dihedral angle near 60° or 90° and a
+    /// nearly flat corner (#547).
+    pub min_scaled_jacobian: f64,
     /// Tetrahedra with a dihedral angle below 10° or above 170°.
     pub slivers: usize,
     /// Tetrahedra not admissible by FieldCraft's validity criterion.
@@ -149,7 +153,7 @@ pub struct TetQuality {
 /// The quality of tetrahedra given by corner coordinates, with the metrics `mesh.quality`
 /// reports ([`crate::quality::element_quality`]).
 pub fn tet_quality_stats(points: &[[f64; 3]], tets: &[[u32; 4]]) -> Result<TetQuality> {
-    let mut s = TetQuality { min_dihedral: 180.0, min_radius_ratio: 1.0, ..TetQuality::default() };
+    let mut s = TetQuality { min_dihedral: 180.0, min_radius_ratio: 1.0, min_scaled_jacobian: 1.0, ..TetQuality::default() };
     let mut sum = 0.0;
     for t in tets {
         let p = |v: u32| points.get(v as usize).copied().ok_or_else(|| Error::Failed("quality: vertex id".into()));
@@ -159,6 +163,7 @@ pub fn tet_quality_stats(points: &[[f64; 3]], tets: &[[u32; 4]]) -> Result<TetQu
         s.min_dihedral = s.min_dihedral.min(lo);
         s.max_dihedral = s.max_dihedral.max(hi);
         s.min_radius_ratio = s.min_radius_ratio.min(rr);
+        s.min_scaled_jacobian = s.min_scaled_jacobian.min(m(Metric::ScaledJacobian));
         sum += rr;
         s.slivers += usize::from(!(lo >= 10.0 && hi <= 170.0));
         s.inadmissible += usize::from(q.validity() != Some(Validity::Valid));
@@ -167,6 +172,7 @@ pub fn tet_quality_stats(points: &[[f64; 3]], tets: &[[u32; 4]]) -> Result<TetQu
     if tets.is_empty() {
         s.min_dihedral = 0.0;
         s.min_radius_ratio = 0.0;
+        s.min_scaled_jacobian = 0.0;
     } else {
         s.mean_radius_ratio = sum / tets.len() as f64;
     }
diff --git a/crates/testkit/tests/tet_metric_547.rs b/crates/testkit/tests/tet_metric_547.rs
new file mode 100644
index 0000000..cdf489f
--- /dev/null
+++ b/crates/testkit/tests/tet_metric_547.rs
@@ -0,0 +1,33 @@
+//! Sphere-on-plate at size 4 (#547): the tet mesher's report and `mesh.quality` measure the same
+//! final elements, tet4 and tet10 alike, and no needle is left below the skill's scaled Jacobian
+//! limit although every dihedral angle is fine.
+#![allow(clippy::unwrap_used, clippy::expect_used, clippy::panic)]
+
+use fieldcraft_engine::Session;
+use fieldcraft_testkit::corpus;
+use serde_json::json;
+
+#[test]
+fn sphere_on_plate_report_and_quality_agree() {
+    let parts = corpus::parts().unwrap();
+    let p = parts.iter().find(|p| p.name == "sphere-on-plate").unwrap();
+    let dir = std::env::temp_dir().join(format!("fieldcraft-tet-metric-{}", std::process::id()));
+    std::fs::create_dir_all(&dir).unwrap();
+    let path = dir.join("part.solidcraft");
+    std::fs::write(&path, corpus::design_bytes(p).unwrap()).unwrap();
+    for order in ["linear", "quadratic"] {
+        let mut s = Session::default();
+        s.execute("geometry.open", &json!({"path": path})).unwrap();
+        let r = s.execute("mesh.tet.generate", &json!({"body": "Plate", "size": 4.0, "order": order})).unwrap();
+        let mesh = &r["bodies"][0]["quality"]["mesh"];
+        let q = s.execute("mesh.quality", &json!({})).unwrap();
+        let m = &q["metrics"];
+        let f = |v: &serde_json::Value| v.as_f64().unwrap();
+        assert_eq!(f(&mesh["min_dihedral"]), f(&m["min_dihedral"]["min"]), "{order}");
+        assert_eq!(f(&mesh["max_dihedral"]), f(&m["max_dihedral"]["max"]), "{order}");
+        assert_eq!(f(&mesh["min_scaled_jacobian"]), f(&m["scaled_jacobian"]["min"]), "{order}");
+        assert!(f(&mesh["min_dihedral"]) > 30.0 && f(&mesh["max_dihedral"]) < 145.0, "{order}: {mesh}");
+        assert!(f(&mesh["min_scaled_jacobian"]) >= 0.3, "{order}: {mesh}");
+    }
+    let _ = std::fs::remove_dir_all(&dir);
+}