diff --git a/torchrl/envs/transforms/transforms.py b/torchrl/envs/transforms/transforms.py
index f2d38c66121..cacb1bf3607 100644
--- a/torchrl/envs/transforms/transforms.py
+++ b/torchrl/envs/transforms/transforms.py
@@ -6673,8 +6673,8 @@ def _update(self, key, value, N) -> torch.Tensor:
             )
 
         mean = _sum / _count
-        std = (_ssq / _count - mean.pow(2)).clamp_min(self.eps).sqrt()
-        return (value - mean) / std.clamp_min(self.eps)
+        std = (_ssq / _count - mean.pow(2)).clamp_min(self.eps**2).sqrt()
+        return (value - mean) / std
 
     def to_observation_norm(self) -> Compose | ObservationNorm:
         """Converts VecNorm into an ObservationNorm class that can be used at inference time.
@@ -6725,7 +6725,9 @@ def _get_loc_scale(self, loc_only=False, scale_only=False):
             _ssq = self._td.get(_append_last(key, "_ssq"))
             _count = self._td.get(_append_last(key, "_count"))
             loc[key] = _sum / _count
-            scale[key] = (_ssq / _count - loc[key].pow(2)).clamp_min(self.eps).sqrt()
+            scale[key] = (
+                (_ssq / _count - loc[key].pow(2)).clamp_min(self.eps**2).sqrt()
+            )
         if not scale_only:
             loc = TensorDict(loc)
         else: