Moon Brightness Model Page


The form above allows to calculate the background sky brightness at any given (azimuth, altitude) location in the sky when the Moon is above the horizon. In order to use this form, the following quantities must be entered in their respective fields:

  • Local date in the form YYYYMMDD. For example, 1st January 2023 is 20230101, 17th October 1978 is 19781017. Make sure to type in the correct value, because no format checks are performed.
  • Time (UT) in (24-hour format). For example, 2:30 am is “2.30”, 6.44 pm becomes “18.44”. Leading zeros are often not shown, this will not affect the result. Here again, make sure you type in the correct value.
  • Azimuth and altitude on the local horizon (in degrees + decimals) of the target for which the calculation is to be performed. These must be calculated with a planetarium program.
  • Azimuth and altitude on the local horizon (in degrees + decimals) of the Moon at the same time. Again, these must be calculated with a planetarium program.
  • Extinction coefficient (magnitudes/airmass).
  • Zenithal luminance (background sky brightness) in mag/arcsec^2. This is a quantity familiar to amateur astronomers, being the readout of a SQM reader.

Pressing the “Calculate” button will yield the estimated difference in background sky brightness at the target location in the sky with coordinates (azimuth, altitude), and the absolute value of the background sky brightness at the target location. Background sky brightness is given in mag/arcsec^2.

If you happen to know the field sizes (in degrees + decimals) of your detector’s field of view, and its orientation angle to the horizon (0 = parallel to the horizon, i.e. horizontal; 90 degrees = perpendicular to the local horizon, i.e. vertical) you can get the absolute values of the background sky brightness at the four corners of the field of view. If these values are not known, just leave them unchanged at 0.


Results of this model were found to be reasonably accurate by its developers, but a number of factors can affect the quality of the estimate, namely:

  • Make sure to type in the local date and UT time correctly. These quantities are needed to calculate the Moon’s phase, in order to determine the extent to which moonlight “floods” the sky.
  • Make sure the azimuth and altitude coordinates for your target and the Moon are accurate and have been calculated for the same date and time entered in the respective fields above. You can easily figure them out with a planetarium program.
  • The zenithal background sky brightness is the readout given by a SQM reader on a clean, moonless night. You could make some measurements on multiple moonless nights in order to get a better understanding of how this value varies at your site under different transparency conditions. Using a narrow-field SQM reader (“SQM-L”) is highly recommended.
  • Knowing the local extinction coefficient can be tricky as it is affected by a number of factors, namely elevation and transparency. Common values range from 0.2 magnitudes/airmass (on a clean, trasparent night) to 0.3 or 0.4 mag/airmass (under murkier sky conditions).
  • This model does not take light pollution into account, except for the zenithal background sky brightness, which is itself affected by local light pollution. Actual values may differ from those calculated by the model, and the closer the target is to the horizon, the bigger this difference can get.