diff --git a/geometry/src/algebra.hpp b/geometry/src/algebra.hpp
index 89a2406..5ffd37d 100644
--- a/geometry/src/algebra.hpp
+++ b/geometry/src/algebra.hpp
@@ -224,6 +224,7 @@ struct algebra
         return multivector<blade, blade<Js...>>{x, y};
       }
     }
+    friend constexpr auto& operator+=(blade& x, blade y) { return x = x + y; }
     /// @}
 
     /// subtraction
@@ -236,6 +237,7 @@ struct algebra
     {
       return x + -y;
     }
+    friend constexpr auto& operator-=(blade& x, blade y) { return x = x - y; }
     /// @}
 
     /// scalar multiplication
diff --git a/test/algebra_blade_test.cpp b/test/algebra_blade_test.cpp
index df26896..2fe48cd 100644
--- a/test/algebra_blade_test.cpp
+++ b/test/algebra_blade_test.cpp
@@ -59,6 +59,18 @@ auto main() -> int
   "blade subtraction"_ctest * param_ref<unit_blades> =  //
       [](auto ei) { return expect(eq(ei, 3 * ei - 2 * ei)); };
 
+  "blade addition assignment"_ctest * param_ref<unit_blades> =  //
+      [](auto ei) {
+        auto x = ei;
+        return expect(eq(3 * ei, x += 2 * ei));
+      };
+
+  "blade subtraction assignment"_ctest * param_ref<unit_blades> =  //
+      [](auto ei) {
+        auto x = ei;
+        return expect(eq(-ei, x -= 2 * ei));
+      };
+
   "blade uses canonical dimensions"_ctest = [] {
     return expect(
         eq(-e<1, 0>, e<0, 1>) and        //