@@ -428,21 +428,25 @@ def brightness_temperature(beam_area, disp):
 
         >>> import numpy as np
         >>> from astropy import units as u
-        >>> beam_area = np.pi*(50*u.arcsec)**2
+        >>> beam_sigma = 50*u.arcsec
+        >>> beam_area = 2*np.pi*(beam_sigma)**2
         >>> freq = 5*u.GHz
         >>> equiv = u.brightness_temperature(beam_area, freq)
         >>> u.Jy.to(u.K, equivalencies=equiv)  # doctest: +FLOAT_CMP
-        7.052588858846446
+        3.526294429423223
         >>> (1*u.Jy).to(u.K, equivalencies=equiv)  # doctest: +FLOAT_CMP
-        <Quantity 7.052588858846446 K>
+        <Quantity 3.526294429423223 K>
 
     VLA synthetic beam::
 
-        >>> beam_area = np.pi*(15*u.arcsec)**2
+        >>> bmaj = 15*u.arcsec
+        >>> bmin = 15*u.arcsec
+        >>> fwhm_to_sigma = 1./(8*np.log(2))**0.5
+        >>> beam_area = 2.*np.pi*(bmaj*bmin/fwhm_to_sigma**2)
         >>> freq = 5*u.GHz
         >>> equiv = u.brightness_temperature(beam_area, freq)
         >>> u.Jy.to(u.K, equivalencies=equiv)  # doctest: +FLOAT_CMP
-        78.36209843162719
+        7.065788175060084
     """
     beam = beam_area.to(si.sr).value
     nu = disp.to(si.GHz, spectral())
 
@@ -173,14 +173,32 @@ only dependent on the aperture size.  See `Tools of Radio Astronomy
 <http://books.google.com/books?id=9KHw6R8rQEMC&pg=PA179&source=gbs_toc_r&cad=4#v=onepage&q&f=false>`__
 for details.
 
-The `~astropy.units.equivalencies.brightness_temperature` equivalency
-requires the beam area and frequency as arguments.  Example::
+The `~astropy.units.equivalencies.brightness_temperature` equivalency requires
+the beam area and frequency as arguments.  Recalling that the area of a 2D
+gaussian is :math:`2 \pi \sigma^2` (see `wikipedia
+<http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function>`_),
+here is an example::
 
     >>> import numpy as np
-    >>> omega_B = np.pi * (50 * u.arcsec)**2
+    >>> beam_sigma = 50*u.arcsec
+    >>> omega_B = 2 * np.pi * beam_sigma**2
     >>> freq = 5 * u.GHz
     >>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(omega_B, freq))
-    7.052588858...
+    3.526294...
+
+If you have beam full-width half-maxima (FWHM), which are often quoted and are
+the values stored in the FITS header keywords BMAJ and BMIN, a more appropriate
+example converts the FWHM to sigma::
+
+    >>> import numpy as np
+    >>> beam_fwhm = 50*u.arcsec
+    >>> fwhm_to_sigma = 1./(8*np.log(2))**0.5
+    >>> beam_sigma = beam_fwhm*fwhm_to_sigma
+    >>> omega_B = 2 * np.pi * beam_sigma**2
+    >>> freq = 5 * u.GHz
+    >>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(omega_B, freq))
+    19.55392833...
+
 
 Temperature Energy Equivalency
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^