diff --git a/gym/spaces/box.py b/gym/spaces/box.py
index a2981861c..a4af9c2f8 100644
--- a/gym/spaces/box.py
+++ b/gym/spaces/box.py
@@ -25,16 +25,29 @@ class Box(Space):
         assert dtype is not None, 'dtype must be explicitly provided. '
         self.dtype = np.dtype(dtype)
 
-        if shape is None:
-            assert low.shape == high.shape, 'box dimension mismatch. '
-            self.shape = low.shape
-            self.low = low
-            self.high = high
+        # determine shape if it isn't provided directly
+        if shape is not None:
+            shape = tuple(shape)
+            assert np.isscalar(low) or low.shape == shape, "low.shape doesn't match provided shape"
+            assert np.isscalar(high) or high.shape == shape, "high.shape doesn't match provided shape"
+        elif not np.isscalar(low):
+            shape = low.shape
+            assert np.isscalar(high) or high.shape == shape, "high.shape doesn't match low.shape"
+        elif not np.isscalar(high):
+            shape = high.shape
+            assert np.isscalar(low) or low.shape == shape, "low.shape doesn't match high.shape"
         else:
-            assert np.isscalar(low) and np.isscalar(high), 'box requires scalar bounds. '
-            self.shape = tuple(shape)
-            self.low = np.full(self.shape, low, dtype=dtype)
-            self.high = np.full(self.shape, high, dtype=dtype)
+            raise ValueError("shape must be provided or inferred from the shapes of low or high")
+
+        if np.isscalar(low):
+            low = np.full(shape, low)
+
+        if np.isscalar(high):
+            high = np.full(shape, high)
+
+        self.shape = shape
+        self.low = low
+        self.high = high
 
         def _get_precision(dtype):
             if np.issubdtype(dtype, np.floating):