Telescope Magnification
Calculate telescope magnification, resolving power, field of view, exit pupil, and stellar magnitude limit from aperture, f-ratio, and eyepiece specs.
About This Calculator
The Telescope Magnification Calculator helps amateur astronomers, stargazers, and optics enthusiasts compute the key optical properties of any telescope and eyepiece combination. Enter your telescope's aperture and f-ratio along with your eyepiece's focal length to instantly determine magnification, resolving power, field of view, exit pupil, surface brightness, and the faintest star you can see.
The fundamental formula is M = fo / fe, where fo = D × fr (focal length of the objective equals aperture times f-ratio) and fe is the eyepiece focal length. Additional derived properties include resolving power (Pr = 115.8" / D), scope field of view (FOVs = FOVe / M), exit pupil (Dep = D / M), surface brightness (SB = 2 × Dep²), and stellar magnitude limit (Lm = 2 + 5×log₁₀(D)).
The calculator also shows the recommended minimum magnification (aperture divided by 7) and maximum useful magnification (aperture times 2), helping you stay within the optical limits of your scope. The interactive chart displays how magnification changes across different eyepiece focal lengths, making it easy to plan your eyepiece collection.
Regional Notes
Global: Telescope specifications use metric units universally (mm for aperture and focal length). The formulas and optical physics are the same worldwide. Eyepiece apparent field of view is typically 50-60° for Plössl designs, 68-82° for wide-field designs, and up to 100° for ultra-wide eyepieces.
Limitations: Atmospheric conditions, light pollution, and optical quality affect real-world performance. The calculated values represent theoretical limits under ideal conditions. Surface brightness assumes a 7mm dark-adapted pupil size, which varies with age and ambient light.
Frequently Asked Questions
How is telescope magnification calculated?
Telescope magnification is calculated by dividing the focal length of the objective (aperture × f-ratio) by the focal length of the eyepiece. For example, a 130mm aperture telescope with f/5 has a 650mm focal length; using a 25mm eyepiece gives 26× magnification.
What is the maximum useful magnification of a telescope?
The maximum useful magnification is approximately twice the aperture in millimeters (2× per mm). For a 130mm telescope, this is about 260×. Beyond this point, the image becomes too dim and atmospheric turbulence degrades detail, regardless of eyepiece choice.
What does resolving power mean for a telescope?
Resolving power is the smallest angular separation at which a telescope can distinguish two adjacent objects as separate. It is calculated as 115.8 divided by the aperture in millimeters, measured in arcseconds. A 130mm telescope has about 0.89 arcsecond resolving power.
How does eyepiece focal length affect magnification?
Shorter eyepiece focal lengths produce higher magnification. For a telescope with 650mm focal length, a 10mm eyepiece gives 65× magnification while a 25mm eyepiece gives 26×. The eyepiece is the primary interchangeable component for changing magnification.
What is the exit pupil and why does it matter?
The exit pupil is the diameter of the light beam exiting the eyepiece, calculated as aperture divided by magnification. It should match your eye's pupil size (about 7mm in darkness) for optimal brightness. A 130mm telescope at 26× gives a 5mm exit pupil, which is comfortable for most observers.
What is surface brightness in a telescope?
Surface brightness describes the perceived brightness per unit area of the image, expressed as a percentage of maximum. It decreases as magnification increases since the same amount of light is spread over a larger area. A 5mm exit pupil yields about 50% surface brightness.
How do I choose the right eyepiece for my telescope?
Choose eyepieces that keep magnification between the minimum (aperture/7) and maximum (aperture×2) limits. Start with a medium-focal-length eyepiece (20-25mm) for wide-field views, then add a shorter one (10mm) for planetary observation. The eyepiece apparent field of view (typically 50-60°) also determines how much sky you see.
What is the star magnitude limit of a telescope?
The star magnitude limit is the faintest star visible through a telescope, calculated as 2 + 5×log₁₀(aperture in mm). A 130mm telescope can detect stars down to magnitude 12.6, while a 200mm scope reaches magnitude 13.5. Larger apertures collect more light, revealing fainter objects.