diff --git a/src/potpourri3d/mesh.py b/src/potpourri3d/mesh.py
index e03e9e3..e8e6130 100644
--- a/src/potpourri3d/mesh.py
+++ b/src/potpourri3d/mesh.py
@@ -229,9 +229,18 @@ def cotan_laplacian(V, F, denom_eps=0.):
 def face_areas(V, F):
     validate_mesh(V, F, force_triangular=True)
 
+    integer_coordinates = np.issubdtype(V.dtype, np.integer)
+    if integer_coordinates:
+        # Keep coordinate differences exact, including unsigned and wide integers.
+        V = V.astype(np.int64 if V.dtype.itemsize < 8 else object)
+
     vec_ij = V[F[:,1],:] - V[F[:,0],:]
     vec_ik = V[F[:,2],:] - V[F[:,0],:]
 
+    if integer_coordinates:
+        vec_ij = vec_ij.astype(float)
+        vec_ik = vec_ik.astype(float)
+
     areas = 0.5 * np.linalg.norm(np.cross(vec_ij, vec_ik), axis=1)
     
     return areas
diff --git a/test/potpourri3d_test.py b/test/potpourri3d_test.py
index 33d9450..c949d1f 100644
--- a/test/potpourri3d_test.py
+++ b/test/potpourri3d_test.py
@@ -39,6 +39,32 @@ def is_nonnegative(A, eps=1e-6):
     return np.all(A.data > -eps)
 
 class TestCore(unittest.TestCase):
+
+    def test_integer_mesh_areas(self):
+        cases = [(np.int8, 16), (np.uint8, 16),
+                 (np.int16, 300), (np.uint16, 300),
+                 (np.int32, 100000), (np.uint32, 100000),
+                 (np.int64, 300), (np.uint64, 300),
+                 (np.float32, 300), (np.float64, 300)]
+        for dtype, side in cases:
+            for winding in [[0, 1, 2], [0, 2, 1]]:
+                with self.subTest(dtype=dtype, winding=winding):
+                    V = np.array([[0, 0, 0], [side, 0, 0], [0, side, 0]], dtype=dtype)
+                    F = np.array([winding])
+                    original = V.copy()
+                    area = 0.5 * side * side
+                    np.testing.assert_allclose(pp3d.face_areas(V, F), [area])
+                    np.testing.assert_allclose(pp3d.vertex_areas(V, F), [area / 3.] * 3)
+                    np.testing.assert_array_equal(V, original)
+
+    def test_integer_mesh_areas_large_offset(self):
+        for dtype in [np.int64, np.uint64]:
+            with self.subTest(dtype=dtype):
+                V = np.array([[0, 0, 0], [3, 0, 0], [0, 3, 0]], dtype=dtype)
+                V += 2**60
+                F = np.array([[0, 1, 2]])
+                np.testing.assert_allclose(pp3d.face_areas(V, F), [4.5])
+                np.testing.assert_allclose(pp3d.vertex_areas(V, F), [1.5] * 3)
     
     def test_write_read_mesh(self):