diff --git a/spacy/tokens/span.pyx b/spacy/tokens/span.pyx
index 7087ba986..093e8c826 100644
--- a/spacy/tokens/span.pyx
+++ b/spacy/tokens/span.pyx
@@ -89,9 +89,10 @@ cdef class Span:
         start (int): The index of the first token of the span.
         end (int): The index of the first token after the span.
         label (uint64): A label to attach to the Span, e.g. for named entities.
-        kb_id (uint64): An identifier from a Knowledge Base to capture the meaning of a named entity.
         vector (ndarray[ndim=1, dtype='float32']): A meaning representation
             of the span.
+        vector_norm (float): The L2 norm of the span's vector representation.
+        kb_id (uint64): An identifier from a Knowledge Base to capture the meaning of a named entity.
 
         DOCS: https://spacy.io/api/span#init
         """
@@ -486,10 +487,10 @@ cdef class Span:
         """
         if "vector_norm" in self.doc.user_span_hooks:
             return self.doc.user_span_hooks["vector"](self)
-        vector = self.vector
-        xp = get_array_module(vector)
         if self._vector_norm is None:
+            vector = self.vector
             total = (vector*vector).sum()
+            xp = get_array_module(vector)
             self._vector_norm = xp.sqrt(total) if total != 0. else 0.
         return self._vector_norm
 
diff --git a/website/docs/api/span.md b/website/docs/api/span.md
index 48e310979..2938b4253 100644
--- a/website/docs/api/span.md
+++ b/website/docs/api/span.md
@@ -18,14 +18,15 @@ Create a `Span` object from the slice `doc[start : end]`.
 > assert [t.text for t in span] ==  ["it", "back", "!"]
 > ```
 
-| Name     | Description                                                                             |
-| -------- | --------------------------------------------------------------------------------------- |
-| `doc`    | The parent document. ~~Doc~~                                                            |
-| `start`  | The index of the first token of the span. ~~int~~                                       |
-| `end`    | The index of the first token after the span. ~~int~~                                    |
-| `label`  | A label to attach to the span, e.g. for named entities. ~~Union[str, int]~~             |
-| `kb_id`  | A knowledge base ID to attach to the span, e.g. for named entities. ~~Union[str, int]~~ |
-| `vector` | A meaning representation of the span. ~~numpy.ndarray[ndim=1, dtype=float32]~~          |
+| Name          | Description                                                                             |
+| ------------- | --------------------------------------------------------------------------------------- |
+| `doc`         | The parent document. ~~Doc~~                                                            |
+| `start`       | The index of the first token of the span. ~~int~~                                       |
+| `end`         | The index of the first token after the span. ~~int~~                                    |
+| `label`       | A label to attach to the span, e.g. for named entities. ~~Union[str, int]~~             |
+| `vector`      | A meaning representation of the span. ~~numpy.ndarray[ndim=1, dtype=float32]~~          |
+| `vector_norm` | The L2 norm of the document's vector representation. ~~float~~                          |
+| `kb_id`       | A knowledge base ID to attach to the span, e.g. for named entities. ~~Union[str, int]~~ |
 
 ## Span.\_\_getitem\_\_ {#getitem tag="method"}