diff --git a/src/eval/ops.rs b/src/eval/ops.rs
index 56bfdf2eb..57390a65b 100644
--- a/src/eval/ops.rs
+++ b/src/eval/ops.rs
@@ -2,9 +2,9 @@
 
 use std::cmp::Ordering;
 
-use super::{Dynamic, RawAlign, RawStroke, Smart, StrExt, Value};
+use super::{Dynamic, RawAlign, RawLength, RawStroke, Smart, StrExt, Value};
 use crate::diag::StrResult;
-use crate::geom::{Numeric, Spec, SpecAxis};
+use crate::geom::{Numeric, Relative, Spec, SpecAxis};
 use crate::model;
 use Value::*;
 
@@ -204,6 +204,8 @@ pub fn div(lhs: Value, rhs: Value) -> StrResult<Value> {
 
         (Length(a), Int(b)) => Length(a / b as f64),
         (Length(a), Float(b)) => Length(a / b),
+        (Length(a), Length(b)) => Float(div_length(a, b)?),
+        (Length(a), Relative(b)) if b.rel.is_zero() => Float(div_length(a, b.abs)?),
 
         (Angle(a), Int(b)) => Angle(a / b as f64),
         (Angle(a), Float(b)) => Angle(a / b),
@@ -212,9 +214,13 @@ pub fn div(lhs: Value, rhs: Value) -> StrResult<Value> {
         (Ratio(a), Int(b)) => Ratio(a / b as f64),
         (Ratio(a), Float(b)) => Ratio(a / b),
         (Ratio(a), Ratio(b)) => Float(a / b),
+        (Ratio(a), Relative(b)) if b.abs.is_zero() => Float(a / b.rel),
 
         (Relative(a), Int(b)) => Relative(a / b as f64),
         (Relative(a), Float(b)) => Relative(a / b),
+        (Relative(a), Length(b)) if a.rel.is_zero() => Float(div_length(a.abs, b)?),
+        (Relative(a), Ratio(b)) if a.abs.is_zero() => Float(a.rel / b),
+        (Relative(a), Relative(b)) => Float(div_relative(a, b)?),
 
         (Fraction(a), Int(b)) => Fraction(a / b as f64),
         (Fraction(a), Float(b)) => Fraction(a / b),
@@ -224,6 +230,28 @@ pub fn div(lhs: Value, rhs: Value) -> StrResult<Value> {
     })
 }
 
+/// Try to divide two lengths.
+fn div_length(a: RawLength, b: RawLength) -> StrResult<f64> {
+    if a.length.is_zero() && b.length.is_zero() {
+        Ok(a.em / b.em)
+    } else if a.em.is_zero() && b.em.is_zero() {
+        Ok(a.length / b.length)
+    } else {
+        return Err("cannot divide these two lengths".into());
+    }
+}
+
+/// Try to divide two relative lengths.
+fn div_relative(a: Relative<RawLength>, b: Relative<RawLength>) -> StrResult<f64> {
+    if a.rel.is_zero() && b.rel.is_zero() {
+        div_length(a.abs, b.abs)
+    } else if a.abs.is_zero() && b.abs.is_zero() {
+        Ok(a.rel / b.rel)
+    } else {
+        return Err("cannot divide these two relative lengths".into());
+    }
+}
+
 /// Compute the logical "not" of a value.
 pub fn not(value: Value) -> StrResult<Value> {
     match value {
diff --git a/tests/typ/code/ops-invalid.typ b/tests/typ/code/ops-invalid.typ
index 4e7fdb040..3e9e54788 100644
--- a/tests/typ/code/ops-invalid.typ
+++ b/tests/typ/code/ops-invalid.typ
@@ -38,6 +38,26 @@
 // Error: 03-10 cannot add integer and string
 {(1 + "2", 40% - 1)}
 
+---
+// Error: 14-22 cannot add integer and string
+{ let x = 1; x += "2" }
+
+---
+// Error: 3-12 cannot divide ratio by length
+{ 10% / 5pt }
+
+---
+// Error: 3-12 cannot divide these two lengths
+{ 1em / 5pt }
+
+---
+// Error: 3-19 cannot divide relative length by ratio
+{ (10% + 1pt) / 5% }
+
+---
+// Error: 3-28 cannot divide these two relative lengths
+{ (10% + 1pt) / (20% + 1pt) }
+
 ---
 // Error: 12-19 cannot subtract integer from ratio
 {(1234567, 40% - 1)}
@@ -64,10 +84,6 @@
   {x * "abcdefgh"}
 }
 
----
-// Error: 14-22 cannot add integer and string
-{ let x = 1; x += "2" }
-
 ---
 // Error: 3-6 cannot mutate a temporary value
 { (x) = "" }
diff --git a/tests/typ/code/ops.typ b/tests/typ/code/ops.typ
index 1f2867bc8..33a1a4a4f 100644
--- a/tests/typ/code/ops.typ
+++ b/tests/typ/code/ops.typ
@@ -48,7 +48,15 @@
 #test({ let x; x = 1 + 4*5 >= 21 and { x = "a"; x + "b" == "ab" }; x }, true)
 
 // Mathematical identities.
-#let nums = (1, 3.14, 12pt, 45deg, 90%, 13% + 10pt)
+#let nums = (
+  1, 3.14,
+  12pt, 3em, 12pt + 3em,
+  45deg,
+  90%,
+  13% + 10pt, 5% + 1em + 3pt,
+  2.3fr,
+)
+
 #for v in nums {
   // Test plus and minus.
   test(v + v - v, v)
@@ -63,18 +71,16 @@
     test(v + v, 2.0 * v)
   }
 
-  // Lengths cannot be divided by themselves.
-  if "length" not in type(v) {
+  if "relative" not in type(v) and ("pt" not in repr(v) or "em" not in repr(v)) {
     test(v / v, 1.0)
-    test(v / v == 1, true)
   }
 }
 
 // Make sure length, ratio and relative length
 // - can all be added to / subtracted from each other,
 // - multiplied with integers and floats,
-// - divided by floats.
-#let dims = (10pt, 30%, 50% + 3cm)
+// - divided by integers and floats.
+#let dims = (10pt, 1em, 10pt + 1em, 30%, 50% + 3cm, 40% + 2em + 1cm)
 #for a in dims {
   for b in dims {
     test(type(a + b), type(a - b))
@@ -87,6 +93,15 @@
   }
 }
 
+// Test division of different numeric types with zero components.
+#for a in (0pt, 0em, 0%) {
+  for b in (10pt, 10em, 10%) {
+    test((2 * b) / b, 2)
+    test((a + b * 2) / b, 2)
+    test(b / (b * 2 + a), 0.5)
+  }
+}
+
 ---
 // Test boolean operators.