diff --git a/spatial/r2/vector.go b/spatial/r2/vector.go
index 16b458ba..b48cebfd 100644
--- a/spatial/r2/vector.go
+++ b/spatial/r2/vector.go
@@ -4,6 +4,8 @@
 
 package r2
 
+import "math"
+
 // Vec is a 2D vector.
 type Vec struct {
 	X, Y float64
@@ -40,6 +42,18 @@ func (p Vec) Cross(q Vec) float64 {
 	return p.X*q.Y - p.Y*q.X
 }
 
+// Norm returns the Euclidean norm of p
+//  |p| = sqrt(p_x^2 + p_y^2).
+func Norm(p Vec) float64 {
+	return math.Hypot(p.X, p.Y)
+}
+
+// Norm returns the Euclidean squared norm of p
+//  |p|^2 = p_x^2 + p_y^2.
+func Norm2(p Vec) float64 {
+	return p.X*p.X + p.Y*p.Y
+}
+
 // Box is a 2D bounding box.
 type Box struct {
 	Min, Max Vec
diff --git a/spatial/r2/vector_test.go b/spatial/r2/vector_test.go
index 521b9f3a..46955efa 100644
--- a/spatial/r2/vector_test.go
+++ b/spatial/r2/vector_test.go
@@ -4,7 +4,10 @@
 
 package r2
 
-import "testing"
+import (
+	"math"
+	"testing"
+)
 
 func TestAdd(t *testing.T) {
 	for _, test := range []struct {
@@ -135,3 +138,46 @@ func TestCross(t *testing.T) {
 		})
 	}
 }
+
+func TestNorm(t *testing.T) {
+	for _, test := range []struct {
+		v    Vec
+		want float64
+	}{
+		{Vec{0, 0}, 0},
+		{Vec{0, 1}, 1},
+		{Vec{1, 1}, math.Sqrt2},
+		{Vec{1, 2}, math.Sqrt(5)},
+		{Vec{3, -4}, 5},
+		{Vec{1, 1e-16}, 1},
+		{Vec{4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 6.101625315155041e-196},
+	} {
+		t.Run("", func(t *testing.T) {
+			if got, want := Norm(test.v), test.want; got != want {
+				t.Fatalf("|%v| = %v, want %v", test.v, got, want)
+			}
+		})
+	}
+}
+
+func TestNorm2(t *testing.T) {
+	for _, test := range []struct {
+		v    Vec
+		want float64
+	}{
+		{Vec{0, 0}, 0},
+		{Vec{0, 1}, 1},
+		{Vec{1, 1}, 2},
+		{Vec{1, 2}, 5},
+		{Vec{3, -4}, 25},
+		{Vec{1, 1e-16}, 1},
+		// This will underflow and return zero.
+		{Vec{4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 0},
+	} {
+		t.Run("", func(t *testing.T) {
+			if got, want := Norm2(test.v), test.want; got != want {
+				t.Fatalf("|%v|^2 = %v, want %v", test.v, got, want)
+			}
+		})
+	}
+}
diff --git a/spatial/r3/vector.go b/spatial/r3/vector.go
index f10c2c08..95d75f2a 100644
--- a/spatial/r3/vector.go
+++ b/spatial/r3/vector.go
@@ -4,6 +4,8 @@
 
 package r3
 
+import "math"
+
 // Vec is a 3D vector.
 type Vec struct {
 	X, Y, Z float64
@@ -47,6 +49,18 @@ func (p Vec) Cross(q Vec) Vec {
 	}
 }
 
+// Norm returns the Euclidean norm of p
+//  |p| = sqrt(p_x^2 + p_y^2 + p_z^2).
+func Norm(p Vec) float64 {
+	return math.Hypot(p.X, math.Hypot(p.Y, p.Z))
+}
+
+// Norm returns the Euclidean squared norm of p
+//  |p|^2 = p_x^2 + p_y^2 + p_z^2.
+func Norm2(p Vec) float64 {
+	return p.X*p.X + p.Y*p.Y + p.Z*p.Z
+}
+
 // Box is a 3D bounding box.
 type Box struct {
 	Min, Max Vec
diff --git a/spatial/r3/vector_test.go b/spatial/r3/vector_test.go
index 0966a0d5..5580f73e 100644
--- a/spatial/r3/vector_test.go
+++ b/spatial/r3/vector_test.go
@@ -135,3 +135,44 @@ func TestCross(t *testing.T) {
 		})
 	}
 }
+
+func TestNorm(t *testing.T) {
+	for _, test := range []struct {
+		v    Vec
+		want float64
+	}{
+		{Vec{0, 0, 0}, 0},
+		{Vec{0, 1, 0}, 1},
+		{Vec{3, -4, 12}, 13},
+		{Vec{1, 1e-16, 1e-32}, 1},
+		{Vec{-0, 4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 6.101625315155041e-196},
+	} {
+		t.Run("", func(t *testing.T) {
+			if got, want := Norm(test.v), test.want; got != want {
+				t.Fatalf("|%v| = %v, want %v", test.v, got, want)
+			}
+		})
+	}
+}
+
+func TestNorm2(t *testing.T) {
+	for _, test := range []struct {
+		v    Vec
+		want float64
+	}{
+		{Vec{0, 0, 0}, 0},
+		{Vec{0, 1, 0}, 1},
+		{Vec{1, 1, 1}, 3},
+		{Vec{1, 2, 3}, 14},
+		{Vec{3, -4, 12}, 169},
+		{Vec{1, 1e-16, 1e-32}, 1},
+		// This will underflow and return zero.
+		{Vec{-0, 4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 0},
+	} {
+		t.Run("", func(t *testing.T) {
+			if got, want := Norm2(test.v), test.want; got != want {
+				t.Fatalf("|%v|^2 = %v, want %v", test.v, got, want)
+			}
+		})
+	}
+}