diff --git a/synapse/state/__init__.py b/synapse/state/__init__.py
index 48324b2437..8c84156678 100644
--- a/synapse/state/__init__.py
+++ b/synapse/state/__init__.py
@@ -442,11 +442,10 @@ class StateResolutionHandler(object):
         self._state_cache = None
         self.resolve_linearizer = Linearizer(name="state_resolve_lock")
 
-        cache_size = 100000 * hs.config.caches.get_factor_for("state_cache")
         self._state_cache = ExpiringCache(
             cache_name="state_cache",
             clock=self.clock,
-            max_len=cache_size,
+            max_len=100000,
             expiry_ms=EVICTION_TIMEOUT_SECONDS * 1000,
             iterable=True,
             reset_expiry_on_get=True,
diff --git a/synapse/util/caches/__init__.py b/synapse/util/caches/__init__.py
index d7cfb83624..07f725a4f7 100644
--- a/synapse/util/caches/__init__.py
+++ b/synapse/util/caches/__init__.py
@@ -103,7 +103,7 @@ def register_cache(
                     cache_hits.labels(cache_name).set(self.hits)
                     cache_evicted.labels(cache_name).set(self.evicted_size)
                     cache_total.labels(cache_name).set(self.hits + self.misses)
-                    if hasattr(cache, "max_size"):
+                    if getattr(cache, "max_size", None):
                         cache_max_size.labels(cache_name).set(cache.max_size)
                 if collect_callback:
                     collect_callback()
diff --git a/synapse/util/caches/expiringcache.py b/synapse/util/caches/expiringcache.py
index 6d41d9dc65..043289d2d7 100644
--- a/synapse/util/caches/expiringcache.py
+++ b/synapse/util/caches/expiringcache.py
@@ -18,6 +18,7 @@ from collections import OrderedDict
 
 from six import iteritems, itervalues
 
+from synapse.config import cache as cache_config
 from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.util.caches import register_cache
 
@@ -55,18 +56,19 @@ class ExpiringCache(object):
         """
         self._cache_name = cache_name
 
+        self.max_size = int(max_len * cache_config.DEFAULT_CACHE_SIZE_FACTOR)
+        self._original_max_size = max_len
+
         self._clock = clock
 
-        self._max_len = max_len
         self._expiry_ms = expiry_ms
-
         self._reset_expiry_on_get = reset_expiry_on_get
 
         self._cache = OrderedDict()
 
         self.iterable = iterable
 
-        self.metrics = register_cache("expiring", cache_name, self, resizable=False)
+        self.metrics = register_cache("expiring", cache_name, self)
 
         if not self._expiry_ms:
             # Don't bother starting the loop if things never expire
@@ -82,9 +84,11 @@ class ExpiringCache(object):
     def __setitem__(self, key, value):
         now = self._clock.time_msec()
         self._cache[key] = _CacheEntry(now, value)
+        self.evict()
 
+    def evict(self):
         # Evict if there are now too many items
-        while self._max_len and len(self) > self._max_len:
+        while self.max_size and len(self) > self.max_size:
             _key, value = self._cache.popitem(last=False)
             if self.iterable:
                 self.metrics.inc_evictions(len(value.value))
@@ -170,6 +174,23 @@ class ExpiringCache(object):
         else:
             return len(self._cache)
 
+    def set_cache_factor(self, factor: float) -> bool:
+        """
+        Set the cache factor for this individual cache.
+
+        This will trigger a resize if it changes, which may require evicting
+        items from the cache.
+
+        Returns:
+            bool: Whether the cache changed size or not.
+        """
+        new_size = int(self._original_max_size * factor)
+        if new_size != self.max_size:
+            self.max_size = new_size
+            self.evict()
+            return True
+        return False
+
 
 class _CacheEntry(object):
     __slots__ = ["time", "value"]
diff --git a/synapse/util/caches/lrucache.py b/synapse/util/caches/lrucache.py
index 3779617ff9..8ff23a72da 100644
--- a/synapse/util/caches/lrucache.py
+++ b/synapse/util/caches/lrucache.py
@@ -13,8 +13,6 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-
-import math
 import threading
 from functools import wraps
 
@@ -81,7 +79,7 @@ class LruCache(object):
 
         # Save the original max size, and apply the default size factor.
         self._original_max_size = max_size
-        self.max_size = math.floor(max_size * cache_config.DEFAULT_CACHE_SIZE_FACTOR)
+        self.max_size = int(max_size * cache_config.DEFAULT_CACHE_SIZE_FACTOR)
 
         list_root = _Node(None, None, None, None)
         list_root.next_node = list_root
@@ -285,7 +283,7 @@ class LruCache(object):
         Returns:
             bool: Whether the cache changed size or not.
         """
-        new_size = math.floor(self._original_max_size * factor)
+        new_size = int(self._original_max_size * factor)
         if new_size != self.max_size:
             self.max_size = new_size
             self._on_resize()
diff --git a/tests/util/test_expiring_cache.py b/tests/util/test_expiring_cache.py
index 50bc7702d2..49ffeebd0e 100644
--- a/tests/util/test_expiring_cache.py
+++ b/tests/util/test_expiring_cache.py
@@ -21,7 +21,7 @@ from tests.utils import MockClock
 from .. import unittest
 
 
-class ExpiringCacheTestCase(unittest.TestCase):
+class ExpiringCacheTestCase(unittest.HomeserverTestCase):
     def test_get_set(self):
         clock = MockClock()
         cache = ExpiringCache("test", clock, max_len=1)