diff --git a/src/colour/colour_xyz.rs b/src/colour/colour_xyz.rs
new file mode 100644
index 0000000..2632bd0
--- /dev/null
+++ b/src/colour/colour_xyz.rs
@@ -0,0 +1,112 @@
+use crate::math::{Mat3, Vec3};
+
+use super::ColourRgbF;
+
+/// A CIE XYZ Colour Value
+#[derive(Default, Clone, Copy, Debug)]
+pub struct ColourXyz {
+    pub values: Vec3,
+}
+
+impl ColourXyz {
+    /// Construct a ColourXyz with the specified XYZ values
+    pub fn new(x: f64, y: f64, z: f64) -> ColourXyz {
+        ColourXyz {
+            values: Vec3::new(x, y, z),
+        }
+    }
+
+    /// Calculate the XYZ colour of a laser light with the given wavelength
+    ///
+    /// The wavelength is in nanometres.
+    pub fn for_wavelength(wavelength: f64) -> ColourXyz {
+        let values = Vec3::new(
+            colour_matching_function_x(wavelength),
+            colour_matching_function_y(wavelength),
+            colour_matching_function_z(wavelength),
+        );
+        ColourXyz { values }
+    }
+
+    pub fn x(&self) -> f64 {
+        self.values.x()
+    }
+
+    pub fn y(&self) -> f64 {
+        self.values.y()
+    }
+
+    pub fn z(&self) -> f64 {
+        self.values.z()
+    }
+
+    pub fn to_linear_rgb(&self) -> ColourRgbF {
+        let transform = Mat3::from_rows(
+            &Vec3::new(3.24096994, -1.53738318, -0.49861076),
+            &Vec3::new(-0.96924364, 1.87596750, 0.04155506),
+            &Vec3::new(0.05563008, -0.20397696, 1.05697151),
+        );
+        ColourRgbF::from_vec3(&(transform * self.values))
+    }
+
+    pub fn from_linear_rgb(rgb: &ColourRgbF) -> ColourXyz {
+        let transform = Mat3::from_rows(
+            &Vec3::new(0.41239080, 0.35758434, 0.18048079),
+            &Vec3::new(0.21263901, 0.71516868, 0.07219232),
+            &Vec3::new(0.01933082, 0.11919478, 0.95053215),
+        );
+        ColourXyz {
+            values: transform * rgb.values,
+        }
+    }
+}
+
+fn gaussian(wavelength: f64, alpha: f64, mu: f64, sigma1: f64, sigma2: f64) -> f64 {
+    let denominator = 2.0 * (if wavelength < mu { sigma1 } else { sigma2 }).powi(2);
+    alpha * (-(wavelength - mu).powi(2) / denominator).exp()
+}
+
+fn colour_matching_function_x(wavelength: f64) -> f64 {
+    gaussian(wavelength, 1.056, 599.8, 37.9, 31.0)
+        + gaussian(wavelength, 0.362, 442.0, 16.0, 26.7)
+        + gaussian(wavelength, -0.065, 501.1, 20.4, 26.2)
+}
+
+fn colour_matching_function_y(wavelength: f64) -> f64 {
+    gaussian(wavelength, 0.821, 568.8, 46.9, 40.5) + gaussian(wavelength, 0.286, 530.9, 16.3, 31.1)
+}
+
+fn colour_matching_function_z(wavelength: f64) -> f64 {
+    gaussian(wavelength, 1.217, 437.0, 11.8, 36.0) + gaussian(wavelength, 0.681, 459.0, 26.0, 13.8)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn x_returns_zero_for_default() {
+        let target: ColourXyz = Default::default();
+        assert!(target.x() == 0.0);
+    }
+
+    #[test]
+    fn x_returns_specified_value_after_constructioni_with_new() {
+        let target = ColourXyz::new(0.1, 0.2, 0.3);
+        assert!(target.x() == 0.1);
+    }
+
+    #[test]
+    fn z_returns_specified_value_after_constructioni_with_new() {
+        let target = ColourXyz::new(0.1, 0.2, 0.3);
+        assert!(target.z() == 0.3);
+    }
+
+    #[test]
+    fn roundtrip_to_linear_rgb_yields_original_values() {
+        let target = ColourXyz::new(0.1, 0.2, 0.3);
+        let rgb = target.to_linear_rgb();
+        let xyz = ColourXyz::from_linear_rgb(&rgb);
+        assert!((target.values - xyz.values).norm() < 0.00000001);
+    }
+}
diff --git a/src/colour/mod.rs b/src/colour/mod.rs
index 1fb5c1f..83c9332 100644
--- a/src/colour/mod.rs
+++ b/src/colour/mod.rs
@@ -3,3 +3,6 @@ pub use colour_rgb::{ColourRgbF, ColourRgbU8, NamedColour};
 
 pub mod photon;
 pub use photon::Photon;
+
+pub mod colour_xyz;
+pub use colour_xyz::ColourXyz;