![The Six Numbers on Every Telescope Box, Decoded](https://cdn.slatesource.com/8/d/7/8d76b1b9-08fb-4df9-a55f-39851e7f46c7.webp) # The Six Numbers on Every Telescope Box, Decoded - [Made in Slatesource](https://slatesource.com/@steph/the-six-numbers-on-every-telescope-box-decoded) - By [Steph](https://slatesource.com/@steph) - Created on Oct 18, 2026 ## Aperture wins. Everything else is arithmetic. Every telescope box prints six key numbers: aperture, focal length, focal ratio, magnification, exit pupil, and limiting magnitude. Retailers highlight the magnification figure because it looks impressive. Astronomers ignore it. The number that determines what you can actually see is aperture, the diameter of the main lens or mirror in millimeters. Once you know aperture, four of the other five numbers follow from simple arithmetic. The sixth (limiting magnitude) follows from a two-step formula. This reference puts all six in one place. ![](https://cdn.slatesource.com/8/d/7/8d76b1b9-08fb-4df9-a55f-39851e7f46c7.webp) Teleskop Timau, Indonesia (CC0). A 3.8m optical telescope at the Timau National Observatory. Spec Formula | What it controls Aperture (D) Given in mm on the box | Light gathered, resolution, limiting magnitude Focal length (F) Given in mm on the box | Magnification potential and image scale Focal ratio (f/) F / D | Image brightness; smaller = faster (wider field) Magnification (M) F / eyepiece focal length | How large the object appears Exit pupil (EP) eyepiece focal length / f-ratio | Brightness at your eye; max 7mm Limiting magnitude 2 + 5 x log(D) | Faintest star the scope can show ## Aperture: the number that actually matters Aperture (D) is the diameter of the objective lens or primary mirror in millimeters. Doubling the aperture collects four times as much light, because light-gathering area scales with the square of the radius. More light means brighter images, finer detail, and fainter objects within reach. A 200mm telescope gathers 816 times more light than the 7mm dark-adapted human eye. A 70mm grabs only 100 times more. The gap is enormous. Good backyard telescopes range from 70mm (beginners, light pollution) to 300mm or more (dedicated dark-sky observing). Aperture is also the only spec that controls resolution: the Dawes limit for resolving two stars 0.1 arcseconds apart requires about 1,160mm of aperture. For a 100mm scope the limit is 116 / 100 = 1.16 arcseconds. [Cosmic Pursuits: The Five Numbers That Explain a Telescope](https://cosmicpursuits.com/943/telescopes-explained/?utm_source=slatesource) ## Focal length and focal ratio: what they govern together Focal length (F) is the distance in millimeters from the objective to the focal point, printed on every telescope body. It is a fixed property of the optics; you cannot change it. Focal ratio is F divided by D, written as f/5, f/8, or f/10. A lower number (f/4 or f/5) is called "fast": it produces a wider, brighter field of view, and requires shorter photographic exposures. A higher number (f/10 or f/12) is called "slow": it narrows the field and concentrates the light onto a smaller area, which suits planetary viewing but makes wide-field photography impractical. An f/4 scope needs one quarter the exposure time of an f/8 scope to record the same brightness. Focal ratio does not affect your visual limiting magnitude; that depends only on aperture. ## Magnification and exit pupil: the two you calculate yourself Magnification (M) equals the telescope focal length divided by the eyepiece focal length: M = F / f\_eyepiece. A 1000mm scope with a 10mm eyepiece gives 100x; swap to a 25mm eyepiece and you get 40x. The practical upper limit is roughly 50x per inch of aperture (about 2x per mm), beyond which turbulence and diffraction make the image dim and blurry. For a 100mm scope that ceiling is about 200x. Exit pupil (EP) is eyepiece focal length divided by focal ratio: EP = f\_eyepiece / f-ratio. It describes the beam width your eye receives. Keep it between 0.5mm and 7mm: below 0.5mm the image dims sharply; above 7mm your iris rejects the excess light. That 7mm ceiling drops with age: roughly 5mm at age 50, 4mm at age 60. A 6mm exit pupil suits wide star-field sweeps; 1mm suits the Moon and planets. Scope (D x F) f-ratio | 25mm EP gives | 10mm EP gives | EP at 25mm 70mm x 700mm f/10 | 28x | 70x | 2.5mm 90mm x 900mm f/10 | 36x | 90x | 2.5mm 130mm x 650mm f/5 | 26x | 65x | 5.0mm 200mm x 1000mm f/5 | 40x | 100x | 5.0mm [RocketMime Astronomy: Limiting Magnitude Formula for Telescopes](https://www.rocketmime.com/astronomy/Telescope/MagnitudeGain.html?utm_source=slatesource) ## Limiting magnitude: how faint can you go? Limiting magnitude is the faintest star the telescope can show, stated on the Pogson scale where lower numbers are brighter and each step of 1 is a factor of 2.5 in brightness. The naked eye reaches about magnitude 6.0 under dark skies. The formula is: Lmag = 2 + 5 x log(D), where D is aperture in millimeters. For a 90mm telescope: 2 + 5 x log(90) = 2 + 5 x 1.954 = 11.8. For a 200mm telescope: 2 + 5 x log(200) = 2 + 5 x 2.301 = 13.5. This is independent of magnification: cranking up the power does not reveal fainter stars, it only makes bright ones larger. Light pollution subtracts from this ceiling; a Bortle 7 suburban sky costs roughly 1.5 to 2 magnitudes. Limiting magnitude applies to stars (point sources); extended objects like nebulae are harder to see against a bright background and need wider exit pupils and darker skies, not more magnification. Aperture Limiting magnitude | Example objects at limit 50mm 10.5 | Brightest asteroids, dense globular cores 70mm 11.2 | Most globular clusters fully resolved 90mm 11.8 | Asteroid Melpomene (mag 8.6), many PNe 130mm 12.6 | Faint galaxies in Virgo Cluster 200mm 13.5 | Quasar 3C 273 (mag 12.9), thousands of galaxies 300mm 14.4 | Pluto at opposition (mag 14.3) The magnification trap: ignore the big number on the box. A "525x magnification" claim on a 70mm telescope is physically possible (700mm / 1.33mm eyepiece) but useless. At that power the image is dim, shaky, and a blurry mess of diffraction. The useful ceiling for a 70mm scope is about 140x. Aperture is the only number worth buying for. [Sky and Telescope: A Pupil Primer, How Big Should a Telescope Exit Pupil Be](https://skyandtelescope.org/astronomy-equipment/a-pupil-primer/?utm_source=slatesource)