diff --git a/lib/unit/class.rb b/lib/unit/class.rb
index 965a708..2266c23 100644
--- a/lib/unit/class.rb
+++ b/lib/unit/class.rb
@@ -131,8 +131,12 @@ def eql?(other)
 
   def <=>(other)
     if Numeric === other
-      other = coerce_numeric_compatible(other)
-      a, b = self.normalize, other.normalize
+      coerced = coerce_numeric(other)
+      unless compatible?(coerced)
+        raise ArgumentError,
+          "comparison of #{comparison_label(self)} with #{comparison_label(other)} failed"
+      end
+      a, b = self.normalize, coerced.normalize
       a.value <=> b.value
     elsif other.respond_to?(:coerce)
       apply_through_coercion(other, __method__)
@@ -294,6 +298,18 @@ def apply_through_coercion(obj, oper)
     raise TypeError, "#{obj.class} can't be coerced into #{self.class}"
   end
 
+  # Label an operand for a failed-comparison message. A dimensional unit keeps
+  # its informative #inspect (Unit("1 m")); a dimensionless unit is just a
+  # number — and a coerced bare numeric arrives wrapped as one — so it is
+  # reported by its underlying numeric class, matching how core Ruby names the
+  # operands of a failed comparison (and avoiding splatting an arbitrary
+  # #inspect into the message).
+  def comparison_label(operand)
+    return operand.inspect if Unit === operand && !operand.unit.empty?
+    operand = operand.value if Unit === operand
+    operand.class
+  end
+
   def coerce_numeric_compatible(object)
     object = coerce_numeric(object)
     raise IncompatibleUnitError, "#{inspect} and #{object.inspect} are incompatible" if !compatible?(object)
diff --git a/spec/unit_spec.rb b/spec/unit_spec.rb
index 5cad4bd..49d6a5d 100644
--- a/spec/unit_spec.rb
+++ b/spec/unit_spec.rb
@@ -86,6 +86,50 @@
     expect { Unit(1) < "string" }.to raise_error(ArgumentError)
   end
 
+  it "should raise a descriptive ArgumentError from <=> for incompatible dimensions" do
+    expect { Unit(1, 'm') <=> Unit(1, 's') }.to raise_error(
+      ArgumentError, 'comparison of Unit("1 m") with Unit("1 s") failed'
+    )
+    expect { Unit(1, 'g') <=> Unit(1, 'm') }.to raise_error(ArgumentError)
+  end
+
+  it "should show the operand's class, not a coerced unit, for non-Unit numerics" do
+    expect { Unit(1, 'm') > 1.2 }.to raise_error(
+      ArgumentError, 'comparison of Unit("1 m") with Float failed'
+    )
+    expect { Unit(1, 'm') > 5 }.to raise_error(
+      ArgumentError, 'comparison of Unit("1 m") with Integer failed'
+    )
+  end
+
+  it "should label operands symmetrically when the unit is on the right" do
+    expect { 1.2 > Unit(1, 'm') }.to raise_error(
+      ArgumentError, 'comparison of Float with Unit("1 m") failed'
+    )
+    expect { 5 < Unit(1, 'm') }.to raise_error(
+      ArgumentError, 'comparison of Integer with Unit("1 m") failed'
+    )
+  end
+
+  it "should still compare units with compatible dimensions" do
+    expect(Unit(100, 'cm') <=> Unit(1, 'm')).to eq(0)
+    expect(Unit(1, 'cm') <=> Unit(1, 'm')).to eq(-1)
+    expect(Unit(2, 'm') <=> Unit(1, 'm')).to eq(1)
+  end
+
+  it "should carry the descriptive error through every comparison path" do
+    expect { Unit(1, 'm') > Unit(1, 's') }.to raise_error(ArgumentError, /Unit\("1 m"\).*Unit\("1 s"\)/)
+    expect { [Unit(1, 'm'), Unit(2, 's')].sort }.to raise_error(ArgumentError, /incompatible|failed/)
+    expect { Unit(1, 'm').between?(Unit(1, 's'), Unit(2, 's')) }.to raise_error(ArgumentError)
+    expect { Unit(1, 'm').clamp(Unit(1, 's'), Unit(2, 's')) }.to raise_error(ArgumentError)
+  end
+
+  it "should sort and aggregate compatible units" do
+    sorted = [Unit(3, 'm'), Unit(1, 'm'), Unit(2, 'm')].sort
+    expect(sorted).to eq([Unit(1, 'm'), Unit(2, 'm'), Unit(3, 'm')])
+    expect([Unit(50, 'cm'), Unit(1, 'm')].max).to eq(Unit(1, 'm'))
+  end
+
   it "should support eql comparison" do
     expect(Unit(1)).to eql(Unit(1))
     expect(Unit(1.0)).not_to eql(Unit(1))
@@ -255,8 +299,8 @@
     expect(Unit(100, "m")).to be > Unit(0.0001, "km")
   end
 
-  it "should fail comparison on differing units" do
-    expect { Unit(1, "second") > Unit(1, "meter") }.to raise_error(Unit::IncompatibleUnitError)
+  it "should fail ordered comparison on differing units" do
+    expect { Unit(1, "second") > Unit(1, "meter") }.to raise_error(ArgumentError)
   end
 
   it "should keep units when the value is zero" do