Visual Detection Calculator

Aperture = inches millimeters
Sky background brightness =
Object name =
Object apparent magnitude =
Object size (arcminutes) = by

Limiting magnitude =

Interpreting the chart:

Sky background brightness is 21.5 for a dark site, 18.5 for a city site.

The chart plots the visibility of extended objects like nebulae and galaxies. The object is visible when the eye's perceived contrast is greater than zero. However, because of the impreciseness of object magnitudes and object sizes, it is better to divide the log contrast into zones. Log contrasts greater than 0.5 are easy, contrasts down to 0.25 are visible, contrasts between -.25 and 0.25 are difficult and log contrasts under -0.25 are not visible. For comparison, half the aperture and double the aperture are also plotted. The plot stops if the object is too big to fit into a 100 degree apparent field of view eyepiece.

The visibility is plotted logarithmically to match the eye's performance. The contrast is the object's brightness + the sky background brightness divided by the sky background brightness, mapped to the eye's response at different sky background brightnesses, object brightness and apparent object size. To be clear, the object's contrast never changes. But the eye's ability to detect the object depends on three factors: the sky background brightness (light pollution and exit pupil), object brightness and apparent size of the object.

The chart is plotted for a range of exit pupils. The exit pupil is calculated by dividing the eyepiece's focal length in mm by the telescope's focal ratio. For instance, a 30mm eyepiece with a f/5 telescope produces a (30/5) 6mm exit pupil. A 10mm eyepiece with the same telescope yields a 2mm exit pupil. A 6-7mm exit pupil is typically the widest field lowest practical magnification and a 1/2 to 1mm exit pupil the narrowest field highest practical magnification. The apparent sky background brightness at the eyepiece is solely mediated by the exit pupil. In other words, at a given location, the sky background brightness will be identical regardless of eyepiece and telescope when the exit pupils are the same.

Factors such as dark adaption, elevation (brightness is decreased by a magnitude when object is at 10 degrees elevation) greatly impact the results at the eyepiece. For more, see Airmass calculator, and my Visual Astronomy. The algorithm is from Clark's book, Visual Astronomy of the Deep Sky , with adjusted constants. See

Limiting magnitude is noted for 7mm exit pupil to 2mm exit pupils. Limiting magnitude improves as the exit pupil is made smaller (magnification is increased). There is no improvement beyond 1.5-2mm exit pupil because the background has become too dim to interfere. The magnitude is lowered if the sky background brightness is brighter than 21.5 (dark skies). For more, see, Nils Olof Carlin: on Schaefer's Telescopic limiting Magnitudes and my Visual Astronomy page.

Other calculators and dicussions: Nils Olaf Carlson, Roger Clark, Torres' calculator, Bill Ferris's analysis of Optimum Detection Magnification, Robert Houdart's limiting magnitude calculator.

Mel Bartels