Understanding how power, or magnification, is calculated when using a telescope will require the understanding of a relationship between two independent optical systems - the telescope itself and the eyepiece you are using. To understand this we must first understand the term Focal Length.
Focal Length is the distance measured in millimeters (mm) in an optical system from the lens or primary mirror to the point where the telescope is in focus. This point is called the Focal Point. The longer the focal length of the telescope, generally the more power it has, the larger the image and the smaller the field of view. For example, a telescope with a focal length of 2000mm has twice the power and half the field of view of a 1000mm telescope.
Calculating Magnification (power)
To determine power in a telescope, divide the focal length of the telescope by the focal length of the eyepiece. By exchanging an eyepiece of one focal length for another, you can increase or decrease the power of the telescope. For example, a 25mm eyepiece used on a telescope with a 1000mm focal length would yield a power of 40x (1000 / 25 = 40) and a 10mm eyepiece used on the same telescope would yield a power of 100x (1000 / 10 = 100). Since eyepieces are interchangeable, a telescope can be used at a variety of powers for different applications.
There are practical lower and upper limits of power for telescopes. These are determined by the laws of optics and the nature of the human eye. As a rule of thumb, the maximum usable power is equal to 60 times the aperture of the telescope (in inches) under ideal conditions. Powers higher than this usually give you a dim, lower contrast image. For example, the maximum power on a 60mm telescope (2.4" aperture) is 142x. As power increases, the sharpness and detail seen will be diminished. The higher powers are mainly used for lunar, planetary, and binary star observations.
Be very cautious of manufacturers who advertise a 375 or 750 power telescope which is only 60mm in aperture, as this is false and misleading. Many department store brand telescopes know that customers are not informed how telescopes operate. These manufacturers of telescopes market their products to the misconception that magnification is the most important feature on a telescope.
Most of your observing will be done with lower powers 6 to 25 times the aperture of the telescope (in inches). With these lower powers, the images will be much brighter and crisper, providing more enjoyment and satisfaction with the wider fields of view.
There is also a lower limit of power which is between 3 to 4 times the aperture of the telescope at night. During the day the lower limit is about 8 to 10 times the aperture. Powers lower than this are not useful with most telescope and a dark spot may appear in the center of the eyepiece in a Catadioptric or Newtonian Reflector telescope due to the secondary or diagonal mirrors shadow.
When choosing an eyepiece it is good to remember this rule of thumb. The telescope is only as good as the eyepiece. You could have the most amazing telescope quality, but if you use a poorly manufactured eyepiece, you are not getting the advantage of the telescope. There should be a balance between the quality of your telescope and the quality of your eyepiece. If you have a top-of-the-line telescope, it is wise to spend the extra money on a suburb quality eyepiece.
Here is a list of manufacturers that make exceptionally high quality eyepieces. Although these eyepieces are amazing in quality - some of the prices for an eyepiece alone could purchase a complete telescope!
Here is a list of manufacturers that make some very good eyepieces at a good price.