diff --git a/src/rastr/raster.py b/src/rastr/raster.py
index 093441b..6f8a9ad 100644
--- a/src/rastr/raster.py
+++ b/src/rastr/raster.py
@@ -1107,6 +1107,65 @@ def sum(self) -> float:
         with suppress_slice_warning():
             return float(np.nansum(self.arr))
 
+    def _cx_stat(
+        self,
+        nanarg_func: Callable[[NDArray], np.intp],
+        name: str,
+    ) -> tuple[float, float]:
+        """Get the coordinate of the cell centre identified by a nanarg* function.
+
+        Args:
+            nanarg_func: A NumPy nanarg function (e.g. np.nanargmax, np.nanargmin)
+                that returns a flat index into the array.
+            name: Human-readable name of the statistic, used in error messages.
+
+        Returns:
+            A tuple (x, y) representing the coordinate of the identified cell centre.
+
+        Raises:
+            ValueError: If all values in the raster are NaN.
+        """
+        if np.all(np.isnan(self.arr)):
+            msg = f"Cannot find {name} of an all-NaN raster."
+            raise ValueError(msg)
+        idx = np.unravel_index(nanarg_func(self.arr), self.arr.shape)
+        row, col = int(idx[0]), int(idx[1])
+        x_coords = self.raster_meta.get_cell_x_coords(self.arr.shape[1])
+        y_coords = self.raster_meta.get_cell_y_coords(self.arr.shape[0])
+        return float(x_coords[col]), float(y_coords[row])
+
+    def cxmax(self) -> tuple[float, float]:
+        """Get the coordinate of the cell centre with the maximum value.
+
+        Returns the (x, y) coordinate of the centre of the pixel containing the
+        maximum value in the raster, ignoring NaN values. If multiple pixels share
+        the maximum value, the first occurrence in row-major order is returned.
+
+        Returns:
+            A tuple (x, y) representing the coordinate of the cell centre with
+            the maximum value.
+
+        Raises:
+            ValueError: If all values in the raster are NaN.
+        """
+        return self._cx_stat(np.nanargmax, "cxmax")
+
+    def cxmin(self) -> tuple[float, float]:
+        """Get the coordinate of the cell centre with the minimum value.
+
+        Returns the (x, y) coordinate of the centre of the pixel containing the
+        minimum value in the raster, ignoring NaN values. If multiple pixels share
+        the minimum value, the first occurrence in row-major order is returned.
+
+        Returns:
+            A tuple (x, y) representing the coordinate of the cell centre with
+            the minimum value.
+
+        Raises:
+            ValueError: If all values in the raster are NaN.
+        """
+        return self._cx_stat(np.nanargmin, "cxmin")
+
     def unique(self) -> NDArray:
         """Get the unique cell values in the raster, including NaN.
 
diff --git a/tests/rastr/test_raster.py b/tests/rastr/test_raster.py
index ff54863..4610439 100644
--- a/tests/rastr/test_raster.py
+++ b/tests/rastr/test_raster.py
@@ -5026,6 +5026,82 @@ def test_quantile_all_nan_raster_no_warning(self) -> None:
         all_nan_slice_raster.quantile(0.8)
 
 
+class TestCxmax:
+    """Test the cxmax method of the Raster class."""
+
+    def test_basic(self, stats_test_raster: Raster) -> None:
+        """Test cxmax returns coordinate of maximum value."""
+        # The 3x3 array is [[1,2,3],[4,5,6],[7,8,9]] with cell size 2.
+        # Max value 9 is at row=2, col=2.
+        # x = (2 + 0.5) * 2 = 5, y = (2 + 0.5) * 2 = 5
+        x, y = stats_test_raster.cxmax()
+        assert x == pytest.approx(5.0)
+        assert y == pytest.approx(5.0)
+
+    def test_with_nans(self, stats_test_raster_with_nans: Raster) -> None:
+        """Test cxmax ignores NaN values."""
+        # Array is [[1,2,nan],[4,nan,6],[7,8,9]], max=9 at row=2, col=2
+        x, y = stats_test_raster_with_nans.cxmax()
+        assert x == pytest.approx(5.0)
+        assert y == pytest.approx(5.0)
+
+    def test_all_nan_raises(self) -> None:
+        """Test cxmax raises ValueError for all-NaN raster."""
+        meta = RasterMeta(
+            crs=CRS.from_epsg(2193),
+            transform=Affine(1.0, 0.0, 0.0, 0.0, 1.0, 0.0),
+        )
+        all_nan = Raster(arr=np.full((3, 3), np.nan), raster_meta=meta)
+        with pytest.raises(ValueError, match="Cannot find cxmax"):
+            all_nan.cxmax()
+
+    def test_negative_scale(self, example_neg_scaled_raster: Raster) -> None:
+        """Test cxmax with negative y-scale transform."""
+        # Array is [[1,2],[3,4]], max=4 at row=1, col=1
+        # transform Affine(2.0, 0.0, 0.0, 0.0, -2.0, 0.0)
+        # x = (1 + 0.5) * 2 = 3, y = (1 + 0.5) * -2 = -3
+        x, y = example_neg_scaled_raster.cxmax()
+        assert x == pytest.approx(3.0)
+        assert y == pytest.approx(-3.0)
+
+
+class TestCxmin:
+    """Test the cxmin method of the Raster class."""
+
+    def test_basic(self, stats_test_raster: Raster) -> None:
+        """Test cxmin returns coordinate of minimum value."""
+        # Min value 1 is at row=0, col=0.
+        # x = (0 + 0.5) * 2 = 1, y = (0 + 0.5) * 2 = 1
+        x, y = stats_test_raster.cxmin()
+        assert x == pytest.approx(1.0)
+        assert y == pytest.approx(1.0)
+
+    def test_with_nans(self, stats_test_raster_with_nans: Raster) -> None:
+        """Test cxmin ignores NaN values."""
+        # Array is [[1,2,nan],[4,nan,6],[7,8,9]], min=1 at row=0, col=0
+        x, y = stats_test_raster_with_nans.cxmin()
+        assert x == pytest.approx(1.0)
+        assert y == pytest.approx(1.0)
+
+    def test_all_nan_raises(self) -> None:
+        """Test cxmin raises ValueError for all-NaN raster."""
+        meta = RasterMeta(
+            crs=CRS.from_epsg(2193),
+            transform=Affine(1.0, 0.0, 0.0, 0.0, 1.0, 0.0),
+        )
+        all_nan = Raster(arr=np.full((3, 3), np.nan), raster_meta=meta)
+        with pytest.raises(ValueError, match="Cannot find cxmin"):
+            all_nan.cxmin()
+
+    def test_negative_scale(self, example_neg_scaled_raster: Raster) -> None:
+        """Test cxmin with negative y-scale transform."""
+        # Array is [[1,2],[3,4]], min=1 at row=0, col=0
+        # x = (0 + 0.5) * 2 = 1, y = (0 + 0.5) * -2 = -1
+        x, y = example_neg_scaled_raster.cxmin()
+        assert x == pytest.approx(1.0)
+        assert y == pytest.approx(-1.0)
+
+
 class TestNormalize:
     def test_example(self, example_raster: Raster):
         # Act