diff --git a/apps/openmw/mwmechanics/character.cpp b/apps/openmw/mwmechanics/character.cpp
index d4ba561ed..ea6b39481 100644
--- a/apps/openmw/mwmechanics/character.cpp
+++ b/apps/openmw/mwmechanics/character.cpp
@@ -855,7 +855,8 @@ void CharacterController::updateIdleStormState()
     {
         osg::Vec3f stormDirection = MWBase::Environment::get().getWorld()->getStormDirection();
         osg::Vec3f characterDirection = mPtr.getRefData().getBaseNode()->getAttitude() * osg::Vec3f(0,1,0);
-        inStormDirection = std::acos(stormDirection * characterDirection) > osg::DegreesToRadians(120.f);
+        inStormDirection = std::acos(stormDirection * characterDirection / (stormDirection.length() * characterDirection.length()))
+                > osg::DegreesToRadians(120.f);
     }
     if (inStormDirection && mUpperBodyState == UpperCharState_Nothing && mAnimation->hasAnimation("idlestorm"))
     {
diff --git a/apps/openmw/mwmechanics/mechanicsmanagerimp.cpp b/apps/openmw/mwmechanics/mechanicsmanagerimp.cpp
index b89b8c94a..7bc6a34ae 100644
--- a/apps/openmw/mwmechanics/mechanicsmanagerimp.cpp
+++ b/apps/openmw/mwmechanics/mechanicsmanagerimp.cpp
@@ -1388,7 +1388,9 @@ namespace MWMechanics
         osg::Vec3f vec = pos1 - pos2;
         if (observer.getRefData().getBaseNode())
         {
-            float angleRadians = std::acos((observer.getRefData().getBaseNode()->getAttitude() * osg::Vec3f(0,1,0)) * vec);
+            osg::Vec3f observerDir = (observer.getRefData().getBaseNode()->getAttitude() * osg::Vec3f(0,1,0));
+
+            float angleRadians = std::acos(observerDir * vec / (observerDir.length() * vec.length()));
             if (angleRadians < osg::DegreesToRadians(90.f))
                 y = obsTerm * observerStats.getFatigueTerm() * fSneakNoViewMult;
             else
diff --git a/apps/openmw/mwworld/worldimp.cpp b/apps/openmw/mwworld/worldimp.cpp
index 9179f94f6..a2e66a96f 100644
--- a/apps/openmw/mwworld/worldimp.cpp
+++ b/apps/openmw/mwworld/worldimp.cpp
@@ -1827,7 +1827,7 @@ namespace MWWorld
         if (result.mHit)
         {
             // check if the wanted position is on a flat surface, and not e.g. against a vertical wall
-            if (std::acos(result.mHitNormalWorld * osg::Vec3f(0,0,1)) >= osg::DegreesToRadians(30.f))
+            if (std::acos((result.mHitNormalWorld/result.mHitNormalWorld.length()) * osg::Vec3f(0,0,1)) >= osg::DegreesToRadians(30.f))
                 return false;
 
             return true;