Telescope Magnification Calculator

Telescope magnification is simply the ratio of objective focal length to eyepiece focal length. A longer objective or shorter eyepiece gives more magnification.

🔭 Optics📐 M = fₒₕⱼ/fᵉᵙᵉ🌟 Astronomy
Objective Focal Length (mm)
Eyepiece Focal Length (mm)
Objective Aperture (mm) optional
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
MagnificationMM = fobj/feye×
Focal Length ObjfobjObjective lens/mirror focal lengthmm
Focal Length EyefeyeEyepiece focal lengthmm
Exit PupildexitDobj/Mmm

Step-by-Step Examples

Example 1
Beginner Telescope

f_obj=700 mm, eyepiece f_eye=25 mm.

  • M = 700/25 = 28x
✓ 28x magnification
Example 2
High Power View

f_obj=1200 mm, eyepiece f_eye=6 mm.

  • M = 1200/6 = 200x
✓ 200x — good for planetary detail
Example 3
Exit Pupil Check

f_obj=1000 mm, D=100 mm, M=50x.

  • Exit pupil = D/M = 100/50 = 2 mm
  • Night sky: need exit pupil 5-7 mm for full dark adaptation
✓ 2 mm exit pupil — too small for wide-field viewing

Real-World Applications

🌟
Planetary Viewing
High magnification reveals surface detail on planets. Jupiter moons at 50x, cloud bands at 150x.
🌌
Deep Sky Objects
Low magnification (wide field of view) better for nebulae and galaxies — more sky in view.
🔭
Terrestrial Telescopes
Spotting scopes use variable eyepieces for flexible magnification.
📷
Astrophotography
Camera focal length replaces eyepiece for imaging; image scale = 206*pixel_size/f_obj arcsec/pixel.

Common Mistakes to Avoid

⚠️
Maximum useful magnification

Roughly 50x per inch of aperture (2x per mm). Above this, atmospheric seeing and diffraction degrade image.

⚠️
More magnification is not always better

High magnification reduces brightness (exit pupil shrinks) and field of view. Use minimum magnification for the task.

⚠️
Exit pupil should match eye pupil

Night adapted eye pupil: 6-7 mm. Exit pupil = D/M should match for maximum light gathering.

Frequently Asked Questions

What is the maximum useful magnification? ▾
About 50-60x per inch of aperture (2x per mm). A 100 mm telescope: max ~200x before diffraction and atmosphere limit resolution.
Why does more magnification make images darker? ▾
Brightness scales as (exit pupil)^2 = (D/M)^2. Doubling magnification reduces image brightness by 4x.
What is field of view? ▾
Apparent FOV of eyepiece divided by magnification gives true FOV. 50 degree eyepiece at 50x = 1 degree true FOV.
How does atmosphere limit magnification? ▾
Atmospheric turbulence (seeing) typically limits useful magnification to 150-250x regardless of telescope aperture.
What is focal ratio (f/number)? ▾
f/ratio = f_obj/D. Lower f/ratio = faster (brighter) system, shorter tube. Higher f/ratio better for planets (less coma).

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Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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