diff --git a/src/sage/combinat/posets/linear_extensions.py b/src/sage/combinat/posets/linear_extensions.py
index d5082579372..3eeafabcf36 100644
--- a/src/sage/combinat/posets/linear_extensions.py
+++ b/src/sage/combinat/posets/linear_extensions.py
@@ -432,6 +432,35 @@ def poset(self):
         """
         return self._poset
 
+    def cardinality(self):
+        """
+        Return the number of linear extensions.
+
+        EXAMPLES::
+
+            sage: N = Poset({0: [2, 3], 1: [3]})
+            sage: N.linear_extensions().cardinality()
+            5
+
+        TESTS::
+
+            sage: Poset().linear_extensions().cardinality()
+            1
+            sage: Posets.ChainPoset(1).linear_extensions().cardinality()
+            1
+        """
+        from sage.rings.integer import Integer
+
+        H = self._poset.order_ideals_lattice(as_ideals=False)._hasse_diagram
+        L = H.level_sets()
+        c = [0] * H.order()
+        for l in L[0]:
+            c[l] = 1
+        for lev in L[1:]:
+            for l in lev:
+                c[l] = sum(c[i] for i in H.lower_covers_iterator(l))
+        return Integer(sum(c[i] for i in H.sinks()))
+    
     def __iter__(self):
         r"""
         Iterates through the linear extensions of the underlying poset.