diff --git a/kornia/geometry/boxes.py b/kornia/geometry/boxes.py
index c08ba867d51..a9bd12ae506 100644
--- a/kornia/geometry/boxes.py
+++ b/kornia/geometry/boxes.py
@@ -392,9 +392,19 @@ def filter_boxes_by_area(
 
     def compute_area(self) -> torch.Tensor:
         """Returns :math:`(B, N)`."""
-        w = self._data[..., 1, 0] - self._data[..., 0, 0]
-        h = self._data[..., 2, 1] - self._data[..., 0, 1]
-        return (w * h).unsqueeze(0) if self._data.ndim == 3 else (w * h)
+        coords = self._data.view((-1, 4, 2)) if self._data.ndim == 4 else self._data
+        # calculate centroid of the box
+        centroid = coords.mean(dim=1, keepdim=True)
+        # calculate the angle from centroid to each corner
+        angles = torch.atan2(coords[..., 1] - centroid[..., 1], coords[..., 0] - centroid[..., 0])
+        # sort the corners by angle to get an order for shoelace formula
+        _, clockwise_indices = torch.sort(angles, dim=1, descending=True)
+        # gather the corners in the new order
+        ordered_corners = torch.gather(coords, 1, clockwise_indices.unsqueeze(-1).expand(-1, -1, 2))
+        x, y = ordered_corners[..., 0], ordered_corners[..., 1]
+        # Gaussian/Shoelace formula https://en.wikipedia.org/wiki/Shoelace_formula
+        area = 0.5 * torch.abs(torch.sum((x * torch.roll(y, 1, 1)) - (y * torch.roll(x, 1, 1)), dim=1))
+        return area.view(self._data.shape[:2]) if self._data.ndim == 4 else area
 
     @classmethod
     def from_tensor(
diff --git a/tests/geometry/test_boxes.py b/tests/geometry/test_boxes.py
index 3f4f8c706dc..5d98711027b 100644
--- a/tests/geometry/test_boxes.py
+++ b/tests/geometry/test_boxes.py
@@ -278,6 +278,43 @@ def apply_boxes_method(tensor: torch.Tensor, method: str, **kwargs):
         self.gradcheck(lambda x: Boxes.from_tensor(x, mode="xyxy_plus").data, (t_boxes_xyxy,))
         self.gradcheck(lambda x: Boxes.from_tensor(x, mode="xywh").data, (t_boxes_xyxy1,))
 
+    def test_compute_area(self):
+        # Rectangle
+        box_1 = [[0.0, 0.0], [100.0, 0.0], [100.0, 50.0], [0.0, 50.0]]
+        # Trapezoid
+        box_2 = [[0.0, 0.0], [60.0, 0.0], [40.0, 50.0], [20.0, 50.0]]
+        # Parallelogram
+        box_3 = [[0.0, 0.0], [100.0, 0.0], [120.0, 50.0], [20.0, 50.0]]
+        # Random quadrilateral
+        box_4 = [
+            [50.0, 50.0],
+            [150.0, 250.0],
+            [0.0, 500.0],
+            [27.0, 80],
+        ]
+        # Random quadrilateral
+        box_5 = [
+            [0.0, 0.0],
+            [150.0, 0.0],
+            [150.0, 150.0],
+            [0.0, 0.5],
+        ]
+        # Rectangle with minus coordinates
+        box_6 = [[-500.0, -500.0], [-300.0, -500.0], [-300.0, -300.0], [-500.0, -300.0]]
+
+        expected_values = [5000.0, 2000.0, 5000.0, 31925.0, 11287.5, 40000.0]
+        box_coordinates = torch.tensor([box_1, box_2, box_3, box_4, box_5, box_6])
+        computed_areas = Boxes(box_coordinates).compute_area().tolist()
+        computed_areas_w_batch = Boxes(box_coordinates.reshape(2, 3, 4, 2)).compute_area().tolist()
+        flattened_computed_areas_w_batch = [area for batch in computed_areas_w_batch for area in batch]
+        assert all(
+            computed_area == expected_area for computed_area, expected_area in zip(computed_areas, expected_values)
+        )
+        assert all(
+            computed_area == expected_area
+            for computed_area, expected_area in zip(flattened_computed_areas_w_batch, expected_values)
+        )
+
 
 class TestTransformBoxes2D(BaseTester):
     def test_transform_boxes(self, device, dtype):