This page is for simple equations that allow for useful calculations.

Magnification of a Telescope
mag = f / d , where f is the focal length of the telescope, and d is the focal length of the eyepiece.

Focal ratio or F#
The focal ratio of a telescope is defined as N = f / D, where f is the focal length and D is the diameter of the telescope. It is often reported as f/N. The focal ratio determines the field of view of a telescope: a higher f-number, the smaller the field of view.

Parallax
Parallax is used to measure the distance to solar system bodies and nearby stars by looking for relative motions against background stars as the earth moves through its orbit. There are technically several different equations for parallax, but the most used is the simplest. Since parallax deals with very small angles, (< 1 arcsec) the small angle approximation, sin(θ) ~ θ is accurate enough for all calculations. The parralax angle is the change in angular position of a star after 6 months with respect to background stars.

The equation is simply d = 1AU / angle(radians)

A commonly used modification of this is d = 1 / angle(arcseconds),
in which case d will be reported in parsecs. A parsec is the distance with a parallax of 1 arcsecond . ! Parsec = 31 trillion kilometres or about 3.26 light-years.

Although the equation for parallax is very simple, finding parallax is usually difficult for amateurs because it requires finding a small angular change over 6 months, which requires highly consistent measurements. If one wishes to track an object for less than 6 months, there are simple modifications to the above formula, which take into account the distance the earth has moved.