diff --git a/specutils/analysis/location.py b/specutils/analysis/location.py
index ae6c8e487..edb646deb 100644
--- a/specutils/analysis/location.py
+++ b/specutils/analysis/location.py
@@ -120,13 +120,13 @@ def _centroid_single_region(spectrum, region=None):
         num_term_uncerts = flux*dispersion * np.sqrt((flux_uncert/flux)**2 +
                                                      (disp_uncert/dispersion)**2)
         # uncertainty for the numerator sum, added in quadrature
-        num_uncert = np.sqrt(np.sum(num_term_uncerts**2, axis=-1))
+        num_uncertsq = np.sum(num_term_uncerts**2, axis=-1)
         # uncertainty for the denom sum, added in quadrature
-        denom_uncert = np.sqrt(np.sum(flux_uncert**2, axis=-1))
+        denom_uncertsq = np.sum(flux_uncert**2, axis=-1)
 
         # centroid uncertainty, fractional added in quadrature of numerator and denom
-        centroid.uncertainty = numerator/denom * np.sqrt((num_uncert/numerator)**2 +
-                                                         (denom_uncert/denom)**2)
+        centroid.uncertainty = numerator/denom * np.sqrt(num_uncertsq * numerator**-2 +
+                                                         (denom_uncertsq * denom)**-2)
     else:
         centroid.uncertainty = None