Telescope Magnification Calculator
Find a telescope’s magnification from its focal length and eyepiece, plus focal ratio, exit pupil, and the useful magnification limit.
All lengths in millimetres. Magnification changes only with the eyepiece — a shorter eyepiece focal length gives a higher power.
1000 mm scope ÷ 10 mm eyepiece = 100×.
- Focal ratio
- f/10
- Exit pupil
- 1 mm
- Max useful mag
- ≈ 200×
Focal length ÷ aperture. Lower is “faster” (brighter, wider views).
Aperture ÷ magnification — the beam of light reaching your eye.
Rule of thumb ≈ 2 × aperture (mm); atmosphere and optics often lower it.
A telescope’s magnification is its focal length divided by the eyepiece focal length: M = scope focal length ÷ eyepiece focal length. A 1000 mm telescope with a 10 mm eyepiece gives 1000 ÷ 10 = 100×. Swap in a shorter eyepiece for more power, a longer one for a wider, brighter view.
How telescope magnification works
Unlike a camera lens, a telescope has no single “zoom” number — its magnification depends on which eyepiece you slot in. The telescope’s objective (its main lens or mirror) forms an image, and the eyepiece acts as a magnifier for that image. Divide the telescope’s focal length by the eyepiece’s focal length and you get the power. Because the eyepiece is on the bottom of the fraction, a shorter eyepiece focal length yields a higher magnification. A 25 mm eyepiece in the same 1000 mm scope gives 40×, while a 5 mm eyepiece pushes it to 200×. This is why observers carry a set of eyepieces rather than one — low power for finding and framing large objects, high power for splitting double stars and studying planets.
both focal lengths in the same unit (millimetres); a shorter eyepiece gives more magnification
Worked example
Take a common 100 mm (4-inch) refractor with a 1000 mm focal length and a 10 mm eyepiece. What magnification, focal ratio, and exit pupil does it give?
- 1 Note the two focal lengths. Telescope focal length = 1000 mm; eyepiece focal length = 10 mm.
- 2 Divide to get magnification. M = 1000 ÷ 10 = 100×.
- 3 Find the focal ratio. f/number = focal length ÷ aperture = 1000 ÷ 100 = f/10.
- 4 Find the exit pupil. exit pupil = aperture ÷ magnification = 100 ÷ 100 = 1.0 mm.
- 5 Check the useful limit. Max useful magnification ≈ 2 × aperture = 2 × 100 = 200×, so 100× is comfortably within it.
Eyepieces in a 1000 mm f/10 telescope (100 mm aperture)
Swapping eyepieces changes magnification, exit pupil, and how much sky you see.
| Eyepiece | Magnification | Exit pupil | Best for |
|---|---|---|---|
| 40 mm | 25× | 4.0 mm | Widest, brightest views — star fields, large nebulae |
| 25 mm | 40× | 2.5 mm | General low-power observing and finding targets |
| 10 mm | 100× | 1.0 mm | The Moon, planets, brighter deep-sky objects |
| 6 mm | 167× | 0.6 mm | High-power planetary and double-star work |
| 5 mm | 200× | 0.5 mm | At the ≈ 2 × aperture useful ceiling for this scope |
Why more magnification is not always better
It is tempting to reach for the shortest eyepiece, but magnification is limited by aperture and the atmosphere, not by arithmetic. A wider aperture gathers more light and resolves finer detail, so a small scope simply cannot support the same power as a large one. The common rule of thumb is a useful ceiling of about 2 × the aperture in millimetres (roughly 50× per inch). Push past it and you get “empty magnification”: the image grows but only becomes dimmer, softer, and shakier. On many nights unsteady air (poor “seeing”) caps you well below the theoretical limit. The exit pupil — the aperture divided by the magnification — is the width of the light beam leaving the eyepiece; when it shrinks below about 0.5 mm the view is dim and floaters become distracting, while an exit pupil larger than roughly 7 mm wastes light your pupil cannot admit.