How to Calculate Telescope Magnification
Telescope magnification = telescope focal length ÷ eyepiece focal length. Learn exit pupil, field of view, Dawes’ limit and maximum useful power with examples.
The idea behind it
Magnification depends on both telescope and eyepiece. Exit pupil describes the diameter of the light beam leaving the eyepiece. A wider true field lets you see more of the sky at once.
The relationship to remember
1,000 / 25 = 40×. Exit pupil: 100 mm / 40 = 2.5 mm. Approximate true field: 60° / 40 = 1.5°. Dawes’ limit: 116 / 100 = 1.16 arcseconds. Maximum useful power ≈ 2 × 100 = 200×; light grasp ≈ 204× a 7 mm eye pupil.
Make your own discovery
Halve the eyepiece focal length. Magnification doubles and both exit pupil and true field shrink.
Open the Telescope Magnification & Eyepiece Calculator ↗Key formulas
| Quantity | Formula | Note or example |
|---|---|---|
| Magnification | M = telescope focal length ÷ eyepiece focal length | 1000 mm ÷ 25 mm = 40× |
| Exit pupil | exit pupil = aperture ÷ M | 100 mm ÷ 40 = 2.5 mm |
| True field of view | TFOV ≈ apparent field ÷ M | 60° ÷ 40 = 1.5° |
| Dawes’ limit | resolution ≈ 116 ÷ aperture (mm) arcseconds | 116 ÷ 100 mm = 1.16″ |
| Maximum useful magnification | ≈ 2 × aperture in mm (50× per inch) | 100 mm → about 200× |
| Focal ratio | f-number = focal length ÷ aperture | 1000 ÷ 100 = f/10 |
Worked examples
Each row uses one of this lab’s presets and the same model as the interactive tool.
| Example | Magnification | True field | Exit pupil | Dawes’ limit | Max useful power | Focal ratio |
|---|---|---|---|---|---|---|
| Wide view | 20× | 3.4° | 4 mm | 1.45″ | 160× | f/7.5 |
| Lunar detail | 120× | 0.5° | 1.25 mm | 0.77″ | 300× | f/8 |
| 8-inch Dobsonian | 48× | 1.08° | 4.17 mm | 0.58″ | 400× | f/6 |
What this model leaves out
True field ≈ apparent field / magnification. Dawes’ limit estimates resolution for double stars; atmosphere, optics, and target contrast affect actual results. Never view the Sun without a purpose-built front-mounted solar filter.
Check your understanding
Is higher magnification always better?
No. High power can make a view dimmer and amplify atmospheric blur. Aperture and observing conditions matter.
What does exit pupil mean?
It is the width of the light beam leaving the eyepiece, equal to aperture divided by magnification.
How do you calculate telescope magnification?
Divide the telescope’s focal length by the eyepiece’s focal length, in the same units. A 1,000 mm telescope with a 25 mm eyepiece magnifies 40×; a 10 mm eyepiece gives 100×.
What is the maximum useful magnification of a telescope?
A common rule of thumb is about twice the aperture in millimeters, or 50× per inch. A 100 mm telescope tops out near 200× in steady air; atmospheric turbulence often limits views to less.
What is Dawes’ limit?
An empirical estimate of the closest pair of equal stars a telescope can split: about 116 divided by the aperture in millimeters, in arcseconds. A 100 mm telescope resolves about 1.16″.
Continue with the formula reference or test yourself in space practice.