diff --git a/crates/engine/src/cmd/props.rs b/crates/engine/src/cmd/props.rs
index 75dc0b04..c89204c2 100644
--- a/crates/engine/src/cmd/props.rs
+++ b/crates/engine/src/cmd/props.rs
@@ -539,10 +539,17 @@ impl Interactive for LtscaleM {
     }
 }
 
+/// The largest THICKNESS, either way.
+const MAX_THICKNESS: f64 = 1e12;
+
+fn thickness_in_range(t: f64) -> bool {
+    t.is_finite() && t.abs() <= MAX_THICKNESS
+}
+
 fn run_thickness(s: &mut Session, p: &Value) -> Result<Value> {
     let t = f64_req("thickness", p, "thickness")?;
-    if !t.is_finite() || t.abs() > 1e12 {
-        return Err(bad("thickness", "thickness is out of range"));
+    if !thickness_in_range(t) {
+        return Err(bad("thickness", "thickness is out of range (-1e12 to 1e12)"));
     }
     s.doc_mut()?.header.set_f64("THICKNESS", t);
     Ok(json!({ "thickness": t }))
@@ -565,9 +572,16 @@ impl Interactive for ThicknessM {
             Input::Text(t) => t,
             _ => return Ok(Step::Continue),
         };
-        match super::machines::number(&text).map(|t| run_thickness(s, &json!({ "thickness": t }))) {
-            Some(Ok(_)) => Ok(Step::Done),
-            _ => {
+        match super::machines::number(&text) {
+            Some(t) if thickness_in_range(t) => {
+                run_thickness(s, &json!({ "thickness": t }))?;
+                Ok(Step::Done)
+            }
+            Some(_) => {
+                s.echo("Requires a value between -1e12 and 1e12.");
+                Ok(Step::Continue)
+            }
+            None => {
                 s.echo("Requires a number.");
                 Ok(Step::Continue)
             }
diff --git a/crates/engine/src/tests.rs b/crates/engine/src/tests.rs
index 73125610..8c590dd9 100644
--- a/crates/engine/src/tests.rs
+++ b/crates/engine/src/tests.rs
@@ -1317,6 +1317,12 @@ fn format_thickness_asks_for_the_thickness() {
     // After text that is not a number, the prompt asks again.
     s.cmdline("thick").unwrap();
     assert!(s.current_prompt().is_some(), "asked again");
+    assert_eq!(s.log.last().map(String::as_str), Some("Requires a number."));
+    // A value out of range says so, and the prompt asks again.
+    s.cmdline("2e12").unwrap();
+    assert!(s.current_prompt().is_some(), "asked again");
+    assert_eq!(s.log.last().map(String::as_str), Some("Requires a value between -1e12 and 1e12."));
+    assert_eq!(s.doc().unwrap().header.f64("THICKNESS", 0.0), 0.0);
     // A negative thickness is accepted.
     s.cmdline("-1.5").unwrap();
     assert!(s.current_prompt().is_none());