Astronomy
Telescope & eyepiece calculator
Works out magnification, true field of view, exit pupil and maximum useful magnification for any telescope and eyepiece combination — and says plainly when a combination is a waste of time.
The question this answers: “The box says 675× magnification. What will this telescope actually show me, and which eyepiece should I use for what?”
Result
- Magnification
- 48×
- Exit pupil
- 3.13 mm
- Bright, low-power views want 4–7mm; planetary detail wants around 1mm.
- True field of view
- 1.08°
- About 2.2 full-Moon widths.
- Maximum useful magnification
- 300×
- The conventional 2×-aperture rule.
- Focal ratio
- f/8
Show the working
- Magnification
1200 mm ÷ 25 mm48× - Exit pupil
150 mm ÷ 48×3.13 mm - True field of view
52° ÷ 48×1.08° - Maximum useful magnification
150 mm × 2300× - Focal ratio
1200 mm ÷ 150 mmf/8
Magnification: 48×. Exit pupil: 3.13 mm. True field of view: 1.08°. Maximum useful magnification: 300×. Focal ratio: f/8
Magnification is telescope focal length divided by eyepiece focal length. Exit pupil is aperture divided by magnification. True field of view is the eyepiece’s apparent field divided by magnification. Maximum useful magnification is taken as twice the aperture in millimetres, the conventional rule derived from the resolution limit of the optics.
- The 2×-aperture rule for maximum useful magnification is a long-standing convention, not a physical constant. It approximates the point at which the exit pupil becomes so small that the image is dim and the eye’s own optics start to limit the view.
- Atmospheric seeing in Britain frequently caps genuinely useful magnification well below the optical limit — often around 150–200× regardless of aperture.
- True field of view calculated this way is an approximation. The exact figure depends on the eyepiece’s field stop diameter, which manufacturers do not always publish.
- A dark-adapted pupil is assumed to dilate to roughly 5–7mm. This declines with age, so an older observer may not use the full exit pupil of a low-power eyepiece.
- Says nothing about optical quality. A poor 200mm telescope will not outperform an excellent 150mm one, and no arithmetic here captures that.
- Ignores the mount entirely, which in practice limits usable magnification more often than the optics do.
- Barlow lenses and focal reducers change the effective focal length; enter the modified value rather than the native one.
Sources for this section
- British Astronomical Association (opens in a new tab) — British Astronomical Association · Specialist publisher · corroborated indirectly
- Astronomy guides (opens in a new tab) — Royal Museums Greenwich · Institutional · corroborated indirectly
Runs entirely in your browser — nothing you type is sent anywhere. Last reviewed 2026-08-13. More on Astronomy.