diff --git a/intern/cycles/kernel/shaders/node_sky_texture.osl b/intern/cycles/kernel/shaders/node_sky_texture.osl
index 08bc8f85120..20d379939ab 100644
--- a/intern/cycles/kernel/shaders/node_sky_texture.osl
+++ b/intern/cycles/kernel/shaders/node_sky_texture.osl
@@ -122,6 +122,11 @@ vector geographical_to_direction(float lat, float lon)
   return vector(cos(lat) * cos(lon), cos(lat) * sin(lon), sin(lat));
 }
 
+float precise_angle(vector a, vector b)
+{
+  return 2.0 * atan2(length(a - b), length(a + b));
+}
+
 color sky_radiance_nishita(vector dir, float nishita_data[9], string filename)
 {
   /* definitions */
@@ -138,7 +143,7 @@ color sky_radiance_nishita(vector dir, float nishita_data[9], string filename)
   if (dir[2] >= 0.0) {
     /* definitions */
     vector sun_dir = geographical_to_direction(sun_elevation, sun_rotation + M_PI_2);
-    float sun_dir_angle = acos(dot(dir, sun_dir));
+    float sun_dir_angle = precise_angle(dir, sun_dir);
     float half_angular = angular_diameter / 2.0;
     float dir_elevation = M_PI_2 - direction[0];
 
diff --git a/intern/cycles/kernel/svm/svm_sky.h b/intern/cycles/kernel/svm/svm_sky.h
index e877bd9a5c8..214c0cd1a9a 100644
--- a/intern/cycles/kernel/svm/svm_sky.h
+++ b/intern/cycles/kernel/svm/svm_sky.h
@@ -145,7 +145,7 @@ ccl_device float3 sky_radiance_nishita(KernelGlobals *kg,
   if (dir.z >= 0.0f) {
     /* definitions */
     float3 sun_dir = geographical_to_direction(sun_elevation, sun_rotation + M_PI_2_F);
-    float sun_dir_angle = acos(dot(dir, sun_dir));
+    float sun_dir_angle = precise_angle(dir, sun_dir);
     float half_angular = angular_diameter / 2.0f;
     float dir_elevation = M_PI_2_F - direction.x;
 
diff --git a/intern/cycles/util/util_math.h b/intern/cycles/util/util_math.h
index 737c834e073..8caabf6eac3 100644
--- a/intern/cycles/util/util_math.h
+++ b/intern/cycles/util/util_math.h
@@ -787,6 +787,16 @@ ccl_device_inline float compare_floats(float a, float b, float abs_diff, int ulp
   return (abs(__float_as_int(a) - __float_as_int(b)) < ulp_diff);
 }
 
+/* Calculate the angle between the two vectors a and b.
+ * The usual approach acos(dot(a, b)) has severe precision issues for small angles,
+ * which are avoided by this method.
+ * Based on "Mangled Angles" from https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf
+ */
+ccl_device_inline float precise_angle(float3 a, float3 b)
+{
+  return 2.0f * atan2f(len(a - b), len(a + b));
+}
+
 CCL_NAMESPACE_END
 
 #endif /* __UTIL_MATH_H__ */