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Light gathering power is a telescope's theoretical ability to collect light compared to your fully dilated eye. It is directly proportional to the square of the aperture.

You can calculate this by first dividing the aperture of the telescope (in mm) by 7mm (dilated eye for a young person) and then squaring this result. For example, an 8" telescope has a light gathering power of 843. ((203.2/7)² =  843).

The faintest star you can see with a telescope (under excellent seeing conditions) is the telescope’s limiting magnitude. It’s another way to compare telescopes of different apertures to each other and to the eye. It’s directly related to aperture. Larger apertures allow you to see fainter stars. A rough formula for calculating visual limiting magnitude is: 7.7 + 5 LOG (aperture in cm). For example, the limiting magnitude of an 8" aperture telescope is 14.2:   7.7 + 5 LOG 20.32 = 7.7 + (5x1.3) = 14.2

Atmospheric conditions and the visual acuity of the observer will often reduce limiting magnitude. The unaided or naked-eye magnitude limit is usually considered as 6.0. With a given scope, photographic limiting magnitude is often two or more magnitudes fainter than visual limiting magnitude.

Aperture        Magnitude limit
3.1" (80mm)      12.2
4" (100mm)       12.7
5" (125mm)       13.2
6" (150mm)       13.6
8" (200mm)       14.2 
10" (250mm)     14.7 
12.5" (320mm)  15.2 
14" (355mm)     15.4 
16" (400mm)     15.7 
20" (500mm)     16.2