diff --git a/CHANGELOG.md b/CHANGELOG.md
index daac394..ab8f8da 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 - Support for `u8` and `i8` scalars, mapping to `glam::U8Vec{N}` and `glam::I8Vec{N}`.
 - Implement right-hand side scalar `Add`, `Sub`, and `Mul` (#69).
+- Implement scalar `Point` operations (#71).
 - Implement `Mul<Vector{2,3}>` and `Mul<Point{2,3}>` for `Matrix{3,4}`.
 
 ### Breaking changes
diff --git a/src/impl_ops.rs b/src/impl_ops.rs
index e92e5e4..d63bcde 100644
--- a/src/impl_ops.rs
+++ b/src/impl_ops.rs
@@ -57,12 +57,14 @@ pub(crate) use vector_ops;
 macro_rules! point_ops {
     ($point_type_name:ident, $vector_type_name:ident) => {
         crate::impl_ops::impl_ops! {
+            Add<$point_type_name>::add for $point_type_name -> $point_type_name;
             Add<$vector_type_name>::add for $point_type_name -> $point_type_name;
             Sub<$point_type_name>::sub for $point_type_name -> $vector_type_name;
             Sub<$vector_type_name>::sub for $point_type_name -> $point_type_name;
             Rem<$point_type_name>::rem for $point_type_name -> $vector_type_name;
         }
         crate::impl_ops::impl_assign_ops! {
+            AddAssign<$point_type_name>::add_assign for $point_type_name;
             AddAssign<$vector_type_name>::add_assign for $point_type_name;
             SubAssign<$vector_type_name>::sub_assign for $point_type_name;
             RemAssign<$vector_type_name>::rem_assign for $point_type_name;
@@ -74,7 +76,35 @@ macro_rules! point_ops {
                 crate::wrap(core::ops::Neg::neg(crate::peel(self)))
             }
         }
+
+        // Need specific impls for each scalar types because the scalar is an associated type,
+        // so the compiler would think that the trait impls could overlap.
+        crate::impl_ops::point_ops!(@scalar $point_type_name, [f32, f64, i32, u32, i64, u64, i16, u16]);
     };
+
+    (@scalar $base_type_name:ident, [$($scalar:ident),*]) => {
+        $(
+            crate::impl_ops::impl_scalar_ops! {
+                Add<$scalar>::add for $base_type_name -> $base_type_name;
+                Sub<$scalar>::sub for $base_type_name -> $base_type_name;
+                Mul<$scalar>::mul for $base_type_name -> $base_type_name;
+                Div<$scalar>::div for $base_type_name -> $base_type_name;
+                Rem<$scalar>::rem for $base_type_name -> $base_type_name;
+            }
+            crate::impl_ops::impl_scalar_ops_rhs! {
+                Add<$scalar>::add for $base_type_name -> $base_type_name;
+                Sub<$scalar>::sub for $base_type_name -> $base_type_name;
+                Mul<$scalar>::mul for $base_type_name -> $base_type_name;
+            }
+            crate::impl_ops::impl_scalar_assign_ops! {
+                AddAssign<$scalar>::add_assign for $base_type_name;
+                SubAssign<$scalar>::sub_assign for $base_type_name;
+                MulAssign<$scalar>::mul_assign for $base_type_name;
+                DivAssign<$scalar>::div_assign for $base_type_name;
+                RemAssign<$scalar>::rem_assign for $base_type_name;
+            }
+        )*
+    }
 }
 pub(crate) use point_ops;
 
diff --git a/src/point.rs b/src/point.rs
index ca95352..d561f5d 100644
--- a/src/point.rs
+++ b/src/point.rs
@@ -323,6 +323,45 @@ mod tests {
 
     type Point = super::Point3<f32>;
 
+    #[test]
+    #[expect(clippy::op_ref)]
+    fn ops_by_scalar_ref() {
+        let a = Point::new(1.0, 2.0, 3.0);
+        let b = 2.0;
+        let added = a + b;
+        let subtracted = a - b;
+        let multiplied = a * b;
+
+        assert_eq!(a + &b, added);
+        assert_eq!(&a + b, added);
+        assert_eq!(&a + &b, added);
+        assert_eq!(b + &a, added);
+        assert_eq!(&b + a, added);
+        assert_eq!(&b + &a, added);
+        assert_eq!(a - &b, subtracted);
+        assert_eq!(&a - b, subtracted);
+        assert_eq!(&a - &b, subtracted);
+        assert_eq!(b - &a, subtracted);
+        assert_eq!(&b - a, subtracted);
+        assert_eq!(&b - &a, subtracted);
+        assert_eq!(a * &b, multiplied);
+        assert_eq!(&a * b, multiplied);
+        assert_eq!(&a * &b, multiplied);
+        assert_eq!(b * &a, multiplied);
+        assert_eq!(&b * a, multiplied);
+        assert_eq!(&b * &a, multiplied);
+
+        let mut a2 = a;
+        a2 += &b;
+        assert_eq!(a2, added);
+        let mut a2 = a;
+        a2 -= &b;
+        assert_eq!(a2, subtracted);
+        let mut a2 = a;
+        a2 *= &b;
+        assert_eq!(a2, multiplied);
+    }
+
     #[test]
     fn subtraction_yields_vector() {
         let p = Point::ONE;
@@ -331,16 +370,6 @@ mod tests {
         assert_eq!(v, Vector3::<f32>::ZERO);
     }
 
-    #[test]
-    fn not_scalable() {
-        let p = Point::default();
-
-        // This should not compile:
-        // let q = p * 2.0;
-
-        let _ = p;
-    }
-
     #[test]
     fn vec3a() {
         let a: glam::Vec3A = Point::new(0.0, 1.0, 2.0).to_vec3a();