diff --git a/adaptive/learner/average_learner.py b/adaptive/learner/average_learner.py
index ba7deb1f1..b571c19d3 100644
--- a/adaptive/learner/average_learner.py
+++ b/adaptive/learner/average_learner.py
@@ -118,9 +118,11 @@ def loss(self, real=True, *, n=None):
         if n < self.min_npoints:
             return np.inf
         standard_error = self.std / sqrt(n)
-        return max(
-            standard_error / self.atol, standard_error / abs(self.mean) / self.rtol
-        )
+        aloss = standard_error / self.atol
+        rloss = standard_error / self.rtol
+        if self.mean != 0:
+            rloss /= abs(self.mean)
+        return max(aloss, rloss)
 
     def _loss_improvement(self, n):
         loss = self.loss()
diff --git a/adaptive/tests/test_average_learner.py b/adaptive/tests/test_average_learner.py
index 42d4726d0..f35794a39 100644
--- a/adaptive/tests/test_average_learner.py
+++ b/adaptive/tests/test_average_learner.py
@@ -59,3 +59,11 @@ def constant_function(seed):
         )
         simple(learner, lambda l: l.loss() < 1)
         assert learner.npoints >= max(2, min_npoints)
+
+
+def test_zero_mean():
+    # see https://github.com/python-adaptive/adaptive/issues/275
+    learner = AverageLearner(None, rtol=0.01)
+    learner.tell(0, -1)
+    learner.tell(1, 1)
+    learner.loss()