diff --git a/nutils/evaluable.py b/nutils/evaluable.py
index fa15704cc..89f774b48 100644
--- a/nutils/evaluable.py
+++ b/nutils/evaluable.py
@@ -2261,6 +2261,25 @@ def return_type(dividend, divisor):
             raise ValueError(f'The boolean floor division is not supported.')
         return dividend
 
+    def _intbounds_impl(self):
+        lower, upper = self.args[0]._intbounds
+        divisor_lower, divisor_upper = self.args[1]._intbounds
+        if divisor_upper < 0:
+            divisor_lower, divisor_upper = -divisor_upper, -divisor_lower
+            lower, upper = -upper, -lower
+        elif divisor_lower <= 0:
+            # The divisor range includes zero.
+            return float('-inf'), float('inf')
+        # `divisor_lower` is always finite and positive. `divisor_upper` may be
+        # `float('inf')` in which case the floordiv of a finite `lower` or
+        # `upper` with `divisor_upper` gives a float `0.0` or `-1.0`. To
+        # prevent the float, we bound `divisor_upper` by the dividend.
+        if isinstance(lower, int):
+            lower //= divisor_lower if lower <= 0 else min(lower + 1, divisor_upper)
+        if isinstance(upper, int):
+            upper //= divisor_lower if upper >= 0 else min(1 - upper, divisor_upper)
+        return lower, upper
+
 
 class Absolute(Pointwise):
     evalf = staticmethod(numpy.absolute)
diff --git a/tests/test_evaluable.py b/tests/test_evaluable.py
index d10e4b389..3a5022c7c 100644
--- a/tests/test_evaluable.py
+++ b/tests/test_evaluable.py
@@ -734,6 +734,13 @@ def test_mod_wrap_positive(self):
     def test_mod_negative_divisor(self):
         self.assertEqual(evaluable.Mod(evaluable.Argument('d', (evaluable.constant(2),), int), self.R(-3, [2]))._intbounds, (float('-inf'), float('inf')))
 
+    def test_floordiv(self):
+        self.assertBounds(evaluable.FloorDivide(evaluable.insertaxis(self.R(2, [9]), 1, evaluable.constant(2)), evaluable.insertaxis(self.R(3, [2]), 0, evaluable.constant(9))))
+        self.assertBounds(evaluable.FloorDivide(evaluable.insertaxis(self.R(-12, [9]), 1, evaluable.constant(2)), evaluable.insertaxis(self.R(3, [2]), 0, evaluable.constant(9))))
+        self.assertBounds(evaluable.FloorDivide(evaluable.insertaxis(self.R(-15, [9]), 1, evaluable.constant(2)), evaluable.insertaxis(self.R(-3, [2]), 0, evaluable.constant(9))))
+        self.assertBounds(evaluable.FloorDivide(evaluable.insertaxis(self.R(-4, [9]), 1, evaluable.constant(2)), evaluable.insertaxis(self.R(8, [2]), 0, evaluable.constant(9))))
+        self.assertEqual(evaluable.FloorDivide(self.S('dividend', 2, 4), self.S('divisor', float('-inf'), float('inf')))._intbounds, (float('-inf'), float('inf')))
+
     def test_sign(self):
         for i in range(-2, 3):
             for j in range(i, 3):