Schaefer Telescopic Limiting Magnitude Calculator

Larry Bogan's 1998 Javascript Implementation

Aperture = inches
Telescope Power = 
Visual Magnitude Limit = 
Your Age =  Cleanliness
Color Index of Star = 
Zenith Distance = degrees
Extinction Coefficient = 
Seeing Disk Diameter = arcseconds

Limiting Magnitude = 
Exit pupil diameters (in mm)
Telescope: Eye:

This program by Bradley Schaefer calculates the limiting stellar magnitude an observer can expect to see with various types and sizes of telescopes, and under various conditions. It is fully discussed in Sky & Telescope magazine, November, 1989, page 522.

The program was originally written in Basic and has been converted to Java Script by Larry Bogan. © May, 1998

Explanation of Parameters

Telescope Aperture
The diameter of the objective lens or mirror. (This is the most important determining parameter)

The magnifying power of the telescope. This changes with the focal length of the eyepiece you use.

Power = (focal length of the objective)/(focal length of the eyepiece)

Visual Limiting Magnitude
This is the magnitude of the dimmest star you can see near the zenith.

Use the link to vislimit.html page to calculate this for you OR:
See the section called Sky Transparency in "The Observer's Handbook" published by the Royal Astronomical Society of Canada for a guide to determining this using the stars around Polaris.

Type of telescope
Reflector has a mirror as its objective 

Refractor has a lens as its objective
The Schmidt-Cassegrain has a lens and a mirror

This is a qualitative evaluation - check the relative value for your telescope

Color Index of the star
This is the blue minus the visual magnitude. The bluer a star, the more negative is this value. You can find the CI of stars in atlas handbooks 
  • The Sun: yellow type G2: CI = 0.63 
  • Betelgeuse: very red: M2 type star: CI = 1.85
  • Sirius: whitish' star: A0 type:CI = 0.0
  • Regulus: bluish B7 type: CI=-0.11

Zenith Distance
The angle in degrees from the vertical direction

Extinction Coefficient
Typically 0.2-0.6 mag/airmass, but use the Vislimit.html Javascript page to calculate the extinction coefficient for your situation.

Seeing Disk in arc seconds.
The diameter of the image of a star. This varies on the turbulence of the atmosphere and can vary from 0.5 to several seconds of arc. You have to judge this at the telescope.

Experience in seeing dim stars helps, but this is a qualitative parameter.
Notes by K. Fisher 7/2006

Although Bogan's implementation appears to be a faithful rendering of Schaefer's Sky & Telescope code, it does not appear to yield correct values for red color index stars. Human eyes see fainter in the red color index portion of the spectrum. Bogan's implementation yields brighter TLM's for white color index stars than for red color index stars. As of this writing, I have not tracked down the nature of the bug. Schaefer's journal article explaining the development of his TLM algrorithm is of technical interest:

Schaefer, B.E. Feb. 1990. Telescopic Limiting Magnitude. PASP 102:212-229

Prepared K. Fisher rev. 7/30/2006