Limiting Magnitude Calculations

Use this form to calculate the faintest star you can see for a given place, time and observer.
Fill in the "Observer's Info" and click Calculate. To reset to the current time, click Current Time.

Observer's Info

Longitude (dd mm) West East
Latitude (dd mm) North South
Elevation (meters) above sea-level
Time (hh:mm:ss)
Daylight Savings
Year Month Day
Temperature (F) Humidity (%)
Where is the observer looking in the sky?
Altitude Azimuth

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This page utilizes Java Script:
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Hacked together by Ben Sugerman, Jan 2000.
Click for the Bibliography

Estimated Physical Conditions

Alt Az Elong-
% Illum-
V Mag
Limiting visual magnitude +/-
Extinction coefficient
[V mag per airmass]
[V magnitudes]
Total Sky
at pointing
Lunar Sky
at pointing
V Mag per arcsec2

Julian Date MLST

Altitude: Altitude is the number of degrees measured from the horizon toward the zenith (the point straight overhead). An object on the horizon has Altitude=0, and the zenith Altitude=90.

Azimuth: Azimuth is the number of degrees measured clockwise along the horizon from north. North=0, East=90, South=180 and West=270. To find the azimuth, draw an imaginary arc from the zenith through the point you are looking. You measure azimuth from due north to the point where this arc intersects the horizon.

Elongation: Elongation is simply the number of degrees on the sky between two points, in this case, from the sun (or moon) to the point where you are looking.

Snellen Ratio: This is the numerical value of dividing the numbers in your vision quality given by your optometrist. Normal vision is "20/20" so the snellen ratio = 1. Poor vision might be "20/100" = 0.2 while very good vision is "20/10" = 2. This ratio accounts for the fact that people with better seeing...see better!

Observer's Experience: This is a self-rating you must give yourself on a scale of 0-10. It doesn't test how well you see (that is the snellen ratio) but how sensitive your eyes are to faint light or how well you see in the dark. This is a very subjective question but here are my interpretive guidelines, in terms of observing experience, some sky objects, or daily experience.

Age: The observer's pupil will react differently from the standard adopted in this model depending on the observer's age. This correction term is added for completeness. Set age=25 to evaluate the limiting magnitude without an age correction.

Observed Moon/Sun Magnitude is the estimated visual magnitude of the moon given its phase and position on the sky. If the moon is below the horizon, then it is "down."

Limiting Visual Magnitude is the estimate of the faintest star you (the observer) can see for the conditions you input. This does not include city lights, cloud cover or weather conditions, or myriad other factors such as high dust levels (due to a recent volcanic eruption), the jet stream, etc. The quoted formal error assumes a 20% uncertainty in the sky brightness, unit error in observer experience and reasonable values for internal parameters. The "central value" assumes no error.

Total Sky Brightness includes the night sky (airglow, zodiacal light, etc.), brightness from the moon, the sun, sunset gradients and glare if the moon is less than 5 degree elongation. Brightnesses have roughly 20% uncertainty. These factors are calculated for average weather and air quality, and do not include human sources of light pollution (i.e. city lights). Lunar Sky Brightness is an estimate of the contribution of the moon only.

Model Testing Results

As I make more tests of this model, I will post them here.


The master copy of the source code for this page is on github