Telescope Magnification Calculator
Calculate telescope magnification (M = f_obj / f_eye), maximum useful magnification, true field of view, exit pupil, light gathering power, and angular resolution (Dawes limit & Rayleigh limit).
mm
mm
Magnification
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Focal Ratio (f/) —
Extended More scenarios, charts & detailed breakdown ▾
mm
mm
Magnification
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Magnification with Barlow —
Professional Full parameters & maximum detail ▾
mm
mm
mm
nm
Optical Performance
Magnification —
Focal Ratio (f/) —
Exit Pupil —
Light Gathering vs Eye —
Resolution Limits
Dawes' Limit (116/D) —
Rayleigh Limit (1.22λ/D) —
How to Use This Calculator
- Enter objective focal length and eyepiece focal length for instant magnification.
- Use Max Magnification tab to find the upper limit for your aperture.
- Use Field of View tab with eyepiece apparent FOV to get true sky FOV.
- Switch to Professional for exit pupil, light gathering power, Dawes limit, and Rayleigh limit.
Formula
M = f_obj / f_eye
Exit Pupil = D / M | Light Gathering = (D/7)²
Dawes Limit = 116/D_mm arcsec | Rayleigh = 1.22λ/D rad
Example
Example: 1000 mm objective, 25 mm eyepiece → M = 40×. Aperture 100 mm → exit pupil = 2.5 mm, Dawes limit = 1.16 arcsec.
Frequently Asked Questions
- Magnification M = focal length of objective (mm) ÷ focal length of eyepiece (mm). A 1000 mm telescope with a 25 mm eyepiece gives 40× magnification.
- A practical rule is 50× per inch of aperture (or 2× per mm). Above this, images become dim and blurry. So a 100 mm telescope has a maximum useful magnification of about 200×.
- Exit pupil = aperture ÷ magnification. At night the human eye dilates to ~7 mm. An exit pupil larger than 7 mm wastes light. An exit pupil of 3–7 mm is ideal for most visual observing.
- Dawes' Limit is the empirical angular resolution of a telescope: 116 / D_mm arcseconds. A 100 mm telescope resolves objects separated by 1.16 arcseconds. The theoretical Rayleigh limit uses 1.22λ/D.
- A Barlow lens multiplies the effective focal length of the telescope. A ×2 Barlow doubles magnification: with a 40× eyepiece you get 80×. It also reduces exit pupil proportionally.
Related Calculators
Sources & References (5) ▾
- Telescope Math — Sky & Telescope — Sky & Telescope
- NASA Telescope Basics — NASA Science
- University Physics Vol 3, Ch 2: Geometric Optics — OpenStax
- Celestron Educational Resources — Optics — Celestron
- HyperPhysics — Telescope — Georgia State University HyperPhysics