Magnification is a property of the pairing, not of the telescope
A telescope has no magnification of its own. Power appears only when you pair an objective of focal length F with an eyepiece of focal length fe, and it equals the ratio of the two. Swap eyepieces and the same telescope delivers 30× or 300×. That is why the number printed in large type on a department-store telescope box — "575× POWER!" — tells you nothing about the instrument and quite a lot about the seller.
The quantity that does belong to the telescope is aperture. Aperture sets how much light is collected, which scales as D2, and it sets the diffraction limit on resolution, which scales as 1/D. Magnification cannot add detail that the aperture never resolved; it can only spread the existing detail over a larger angle until it is comfortable to look at, and then keep spreading it until it looks soft.
Three quantities follow from the same pairing and matter as much as the power itself. The true field of view is how much sky you actually see, and it decides whether a target fits. The exit pupil is the diameter of the light cone leaving the eyepiece, and it decides how bright an extended object looks. The effective focal ratio changes when a Barlow or reducer is fitted, and it is what determines the exit pupil for a given eyepiece.
Where each formula comes from
Magnification, M = F/fe. The objective forms an image at its focal plane whose linear size is proportional to F. The eyepiece is a magnifier examining that image, and the shorter its focal length the closer it is held to the image, so the larger the angle it presents to your eye. The ratio of the two focal lengths is exactly the ratio of the angle you see to the angle the object really subtends.
A Barlow multiplies F, not M directly. Placing a negative lens ahead of focus increases the effective focal length by its stated factor. Because M is proportional to F, the result is the same multiple on magnification — but the effective focal ratio changes too, which is why a 2× Barlow on an f/6 scope makes it f/12 and halves the exit pupil for any given eyepiece. A focal reducer does the reverse.
Exit pupil = D/M. The aperture collects a beam of diameter D; the eyepiece delivers that beam compressed by the magnification. Equivalently, exit pupil = fe divided by the effective focal ratio, which is the more convenient form when you are choosing eyepieces: on an f/6 telescope, a 25 mm eyepiece always gives 25/6 = 4.17 mm regardless of aperture.
True field = AFOV/M. The eyepiece presents an apparent field — the angular size of the circle of light your eye sees, typically 50° for a Plössl and up to 100° for an ultra-wide. Divide it by the magnification and you get the patch of real sky inside that circle. This is an approximation that ignores field distortion, and a more exact route uses the eyepiece's field stop diameter: true field = 57.296 × field stop ÷ F. Where a manufacturer publishes the field stop, prefer that.
The two limits. Maximum useful magnification is conventionally taken as about 2× the aperture in millimetres, equivalently 50× per inch, because at that point the exit pupil has shrunk to 0.5 mm and the diffraction pattern is already spread across more than the eye's own resolving angle. Minimum useful magnification is D/7, the power at which the exit pupil reaches 7 mm — the widest a dark-adapted young pupil typically opens. Below it, light spills onto your iris and is lost. Both figures are conventions rooted in eye physiology, not standards, and 7 mm is generous for anyone past middle age, where 5 to 6 mm is more realistic.
Worked example: an 8-inch f/6 Newtonian
Take a common first telescope: 200 mm aperture, 1200 mm focal length, with a 25 mm Plössl of 52° apparent field.
- Effective focal length. No Barlow, so Feff = 1200 × 1 = 1200 mm.
- Magnification. M = 1200 ÷ 25 = 48×.
- Exit pupil. 200 ÷ 48 = 4.17 mm. Cross-check with the other route: 25 ÷ 6 = 4.17 mm. They agree, as they must.
- True field of view. 52 ÷ 48 = 1.083°, which is 65.0 arcminutes — a little over two full-Moon diameters, since the Moon runs about 31 arcminutes.
- Power ceiling. 2 × 200 = 400×. To reach it you would need a 3 mm eyepiece, since 1200 ÷ 400 = 3.
- Power floor. 200 ÷ 7 = 28.6×, which corresponds to 1200 ÷ 28.6 = 42 mm of eyepiece. A 40 mm eyepiece sits just inside the limit; a 50 mm one does not.
- Resolution. Dawes gives 116 ÷ 200 = 0.58 arcseconds, so the pair of stars in a 0.6″ double is at the edge of what this aperture can split on a still night.
Now add a 2× Barlow to the same 25 mm eyepiece: Feff becomes 2400 mm, M becomes 96×, the exit pupil halves to 2.08 mm, and the true field halves to 0.542°. Every one of those follows from the single change to Feff.
Magnification and exit pupil for a 200 mm f/6 telescope
| Eyepiece | Magnification | Exit pupil | True field | Typical use |
|---|---|---|---|---|
| 40 mm | 30× | 6.67 mm | 1.733° | Widest usable field, large open clusters |
| 32 mm | 37.5× | 5.33 mm | 1.387° | Finding and sweeping |
| 25 mm | 48× | 4.17 mm | 1.083° | General deep sky |
| 20 mm | 60× | 3.33 mm | 0.867° | Bright nebulae, whole Moon |
| 15 mm | 80× | 2.50 mm | 0.650° | Globular clusters, galaxies |
| 12 mm | 100× | 2.00 mm | 0.520° | Planets on average seeing |
| 9 mm | 133.3× | 1.50 mm | 0.390° | Planetary detail, double stars |
| 6 mm | 200× | 1.00 mm | 0.260° | Good seeing only |
| 4 mm | 300× | 0.67 mm | 0.173° | Excellent seeing, close doubles |
Exit pupil is D ÷ M, and equals the eyepiece focal length divided by 6 for every row because this telescope is f/6. Change the aperture and the magnifications stay the same while the exit pupils scale with D.
Choosing a power that the night will actually support
The atmosphere usually decides, not the optics. Typical suburban seeing limits useful power to something like 150–250× regardless of aperture; nights that support 400× on a 200 mm telescope are uncommon. The right method is to start low, increase power until the image stops improving, then step back one eyepiece.
Extended objects get dimmer at higher power; stars mostly do not. Surface brightness of a nebula or galaxy falls with the square of the exit pupil, because the same light is spread over a larger apparent area. A star is a point source, so its total brightness is essentially unchanged while the sky background behind it darkens — which is exactly why higher power helps on faint double stars and on planetary nebulae with small angular size, and hurts on large faint galaxies.
Match the exit pupil to the job. Around 5–7 mm gives the widest, brightest, lowest-power view and suits large nebulae under dark skies. Around 2–3 mm is the sweet spot for most deep-sky work from suburban sites because it darkens the sky background while keeping the object reasonably bright. Around 0.7–1 mm is the planetary and double-star range. Below 0.5 mm the view dims and floaters in your eye become distracting.
Field of view is often the real constraint. The Andromeda Galaxy spans about 3°; the Pleiades about 2°. Neither fits the 1.08° field of the worked example, and no eyepiece choice on a 1200 mm telescope will make them fit, because the maximum true field is capped by the largest field stop a 1.25-inch or 2-inch barrel can hold. If you want a genuinely wide field you need a shorter focal length instrument, not a longer eyepiece. The CCD field of view calculator answers the same question for a camera sensor rather than an eyepiece.
Advertised magnification is a marketing number
A 60 mm department-store refractor sold as "525×" has a genuine power ceiling of 2 × 60 = 120×. The 525× figure is achieved with a tiny eyepiece and an amplifying barrel, and it produces an image that is large, dim and unresolved — a phenomenon opticians call empty magnification. Judge any telescope by aperture and optical quality first; the magnification is whatever you choose to make it on the night.
Mistakes this calculator will not catch for you
- Mixing units between the two focal lengths. Telescope focal length is usually quoted in millimetres and aperture sometimes in inches. The unit selectors here convert both, but a hand calculation with 8 inches and 25 mm gives nonsense.
- Using aperture from the tube diameter. The clear aperture is the working diameter of the lens or mirror, which is smaller than the tube and, on some catadioptric designs, slightly smaller than the nominal figure.
- Trusting a nominal Barlow factor. The amplification of a Barlow depends on its distance from the focal plane. Adding a diagonal or an extension tube between Barlow and eyepiece increases the factor, sometimes by 20% or more, so a "2×" can behave as 2.4×.
- Ignoring the field-stop limit. A 1.25-inch barrel physically cannot pass a field stop larger than about 27 mm, which caps the true field no matter what focal length or apparent field the eyepiece claims.
- Assuming the AFOV/M field is exact. It ignores the distortion designed into wide-field eyepieces. The field-stop method, 57.296 × field stop ÷ F, is the accurate one where the field stop is published.
- Comparing the Dawes limit to what you can see. Dawes is an empirical limit for splitting equal-brightness double stars in excellent conditions with a good eye. Extended-object detail and unequal doubles behave differently.
How this relates to the other telescope numbers
Focal ratio, magnification and exit pupil are three views of one relationship. Fix the eyepiece and the exit pupil is set by focal ratio alone; fix the aperture and the exit pupil is set by magnification alone. The focal ratio calculator handles the first framing and the exit pupil calculator the second, and both agree with the figures here by construction.
Resolution is a separate axis and belongs to the aperture. The Dawes limit of 116/D arcseconds shown above is empirical, derived by William Dawes in the nineteenth century from his own double-star observations. The theoretical Rayleigh criterion for a circular aperture, 138/D arcseconds at visual wavelengths, is slightly more conservative; the resolving power calculator covers both and their wavelength dependence. A useful rule that connects the two topics: to see everything the aperture resolves you want an exit pupil of about 1 mm, which by M = D/exit pupil means a magnification numerically equal to the aperture in millimetres — 200× on a 200 mm telescope — because that is where the diffraction pattern is spread past the eye's own resolving limit.
For imaging rather than eyepiece use, magnification stops being the relevant quantity and image scale takes over, measured in arcseconds per pixel. That depends on focal length and pixel size, not on any eyepiece. Long-exposure imagers also care about how far a star drifts during an exposure, which the star trail length calculator covers, and about how large a target appears on the sky, which is the job of the angular size calculator.