Focal Ratio Calculator
Focal ratio is focal length divided by aperture. A 1200 mm telescope with a 203 mm mirror is f/5.9. Lower numbers mean shorter exposures on nebulae and galaxies and a wider field, but focal ratio does not change how bright a star appears, because a star is a point source and only aperture governs it.
Focal ratio is focal length divided by aperture. It is the single number that tells you the character of a telescope: how wide a field it can reach, how demanding it is of eyepieces, how quickly it collects light on an extended object, and whether it leans toward planets or toward nebulae. It is also the number most often misapplied, because the photographic rule about f numbers is only half true under the stars.
Focal ratio calculator
Enter any two of the three and the third follows. A Barlow multiplies the focal length and a reducer divides it, so both change the effective focal ratio without touching the aperture.
How do you calculate focal ratio?
Focal ratio = focal length ÷ aperture
Both in the same units, normally millimetres, and the answer has no units because it is a pure ratio. An 8 inch Dobsonian with a 203 mm mirror and a 1200 mm focal length is 1200 divided by 203, which is f/5.9. An 8 inch Schmidt-Cassegrain with the same aperture but 2032 mm of focal length is f/10. Same mirror diameter, entirely different instrument.
Two vocabulary notes that come up constantly. A low f number is called fast, because it exposes a photograph quickly. A high f number is called slow. And a Barlow multiplies the effective focal length, which raises the f number, while a focal reducer divides it, which lowers the f number. Neither changes the aperture, so neither changes how much light the telescope actually collects.
| Focal ratio | Typical design | Field | Eyepiece demands | Leans toward |
|---|---|---|---|---|
| f/3.5 to f/4 | Fast imaging Newtonian, astrograph | Very wide | Premium only, coma corrector needed | Wide field imaging |
| f/4.7 to f/5 | Large Dobsonian, small refractor | Wide | Good eyepieces, coma visible at the edge | Deep sky visual |
| f/5.9 to f/6 | 8 inch Dobsonian, ED refractor | Moderately wide | Mid range eyepieces are fine | General purpose |
| f/7 to f/8 | Long refractor, 6 inch Dobsonian | Moderate | Simple Plossls work well | Planets and doubles |
| f/10 | Schmidt-Cassegrain | Narrow | Any eyepiece looks good | Planets, small deep sky |
| f/12 to f/15 | Maksutov-Cassegrain, long achromat | Very narrow | Anything works, long eyepieces needed | Planets, double stars, the Moon |
Does a faster telescope really collect light faster?
For extended objects, yes. For stars, no. That single distinction resolves almost every argument you will read about focal ratio.
A nebula or a galaxy is an extended object: it covers real area on the sky, so its light spreads over real area on the sensor. Halving the focal length concentrates the same collected photons into a quarter of the area, so each square millimetre of sensor receives four times the light per second. This is why an f/5 telescope reaches a given signal level on the Orion Nebula four times faster than an f/10 telescope of the same aperture, and it is the entire reason fast astrographs exist.
A star is a point source. Its light lands in a tiny spot whose size is set by the optics and the atmosphere, not by the focal ratio, so the total photons in that spot depend only on how much aperture collected them. An f/10 telescope and an f/5 telescope of the same aperture record the same star at the same rate. This is why photometrists and double star observers care about aperture and ignore focal ratio entirely.
| Focal ratio | Relative exposure for extended objects | Relative exposure for stars, same aperture |
|---|---|---|
| f/2.8 | 0.31x | 1.0x |
| f/4 | 0.64x | 1.0x |
| f/5 | 1.00x | 1.0x |
| f/6 | 1.44x | 1.0x |
| f/7 | 1.96x | 1.0x |
| f/10 | 4.00x | 1.0x |
| f/15 | 9.00x | 1.0x |
The practical reading of that table: if you image nebulae and galaxies, a fast telescope buys you real time and a slow one costs you real time. If you image planets, or measure stars, or observe visually, the focal ratio is a description of the telescope rather than a measure of its speed.
What does focal ratio mean for visual observing?
Far less than for imaging, and what it does mean is mostly about eyepieces and field width rather than about brightness. Two telescopes of the same aperture at the same magnification show the same image brightness regardless of focal ratio, because magnification is what sets exit pupil and exit pupil is what sets brightness.
What the focal ratio does decide visually is the widest field you can reach and how good your eyepieces have to be. The longest useful eyepiece is roughly 7 times the focal ratio in millimetres, because beyond that the exit pupil exceeds the roughly 7 mm of a dark adapted pupil and the surplus light is wasted. At f/5 that is a 35 mm eyepiece; at f/10 it is a 70 mm eyepiece, which does not exist in a usable form, which is why long telescopes cannot deliver wide fields at all.
On the eyepiece side, a fast telescope sends a steeply converging light cone into the eyepiece and simple designs cannot correct it across the whole field. A Plossl that is sharp to the edge at f/10 can look visibly soft in the outer third at f/4.7. Fast Newtonians additionally show coma, which stretches stars near the field edge into small comet shapes, and a coma corrector is the fix. Slow telescopes have neither problem, which is one reason a long refractor can look so good with cheap eyepieces.
Should you use a Barlow or a reducer?
Both are cheap ways to change the character of a telescope without buying another one.
A 2x Barlow doubles the effective focal length and therefore doubles the f number, turning an f/5 telescope into an f/10 for as long as it is in the light path. Visually it doubles the magnification of every eyepiece you own, which is why a Barlow is usually a better second purchase than a third eyepiece: two eyepieces plus a Barlow gives four focal lengths. For planetary imaging it is close to essential, because planetary cameras have small pixels and need a long effective focal length to sample the disc properly.
A focal reducer works the other way, shortening the effective focal length to widen the field and shorten exposures on extended objects. A 0.63x reducer on an f/10 Schmidt-Cassegrain gives about f/6.3, which cuts exposure time on a nebula by roughly 2.5 times and widens the frame by the same factor. Reducers are fussier than Barlows: they require a specific spacing between the reducer and the sensor, usually 55 mm for a camera flattener, and getting it wrong produces elongated stars in the corners that look exactly like a tracking fault.
| Telescope | Native | With 0.63x reducer | With 2x Barlow | With 3x Barlow |
|---|---|---|---|---|
| 203 mm, 2032 mm SCT | f/10 | f/6.3 | f/20 | f/30 |
| 203 mm, 1200 mm Dobsonian | f/5.9 | f/3.7 | f/11.8 | f/17.7 |
| 130 mm, 650 mm reflector | f/5.0 | f/3.2 | f/10.0 | f/15.0 |
| 80 mm, 600 mm ED refractor | f/7.5 | f/4.7 | f/15.0 | f/22.5 |
| 127 mm, 1500 mm Maksutov | f/11.8 | f/7.4 | f/23.6 | f/35.4 |
What focal ratio should you buy?
Start from what you want to do, not from the number.
- Wide field deep sky imaging wants f/4 to f/6 and a short focal length. An 80 mm ED doublet at f/7 with a flattener is the standard entry, and a faster astrograph shortens exposures further at the cost of far tighter tolerances.
- Planetary imaging and high magnification visual wants f/10 or slower, or a faster telescope with a good Barlow. A Schmidt-Cassegrain at f/10 reaches planetary magnifications with comfortable long eyepieces.
- General visual observing is happiest between f/5 and f/8, which is where most Dobsonians and most beginner reflectors sit. It gives a usable wide field without demanding premium eyepieces.
- Absolute portability pushes toward slow catadioptrics, because folding a long focal length into a short tube is exactly what those designs do.
One thing focal ratio never tells you is how much a telescope can see. That is aperture, and it is worth repeating because the f number looks like a quality score and is not one. Work out what aperture your targets need with the telescope size calculator, then use the focal ratio to choose between the instruments that meet it.
Related tools and charts
Frequently asked questions
How do you calculate focal ratio?
Divide the focal length by the aperture, using the same units for both. A telescope with a 1200 mm focal length and a 203 mm aperture is 1200 divided by 203, which is f/5.9. A 900 mm focal length on an 80 mm aperture is f/11.25. The result is written with an f and a slash, and it has no units because it is a ratio.
Is a lower focal ratio better?
For imaging extended objects, yes, because a faster ratio delivers more photons per square millimetre of sensor per second and shortens the exposures. For visual observing it is close to irrelevant, since aperture and eyepiece choice decide what you see. Fast optics also demand better eyepieces, tighter collimation and usually a coma corrector, so the speed is not free.
Does focal ratio affect how bright stars look?
No, and this is the exception that causes most of the confusion. Stars are point sources, so all their light lands in one small spot regardless of focal ratio, and their brightness on the sensor depends only on aperture. Nebulae and galaxies are extended, so their light spreads across an area that focal ratio does change. This is why the f ratio rule works for nebulae and fails for stars.
What focal ratio is best for planets?
Something slow, typically f/10 to f/20, because planets need magnification rather than a wide field and slow optics reach high magnification with comfortable long eyepieces. Schmidt-Cassegrains at f/10 and Maksutovs at f/12 to f/15 are popular planetary instruments for exactly this reason. A fast Newtonian reaches the same magnification, but needs very short eyepieces or a Barlow to get there.
What does a focal reducer do?
It shortens the effective focal length, which lowers the focal ratio and widens the field. A 0.63x reducer on an f/10 Schmidt-Cassegrain gives roughly f/6.3, cutting exposure times for extended objects by about 2.5 times and widening the frame by the same factor. The cost is that reducers introduce their own aberrations at the edges and require a specific spacing to the sensor to work correctly.
Why do fast telescopes need better eyepieces?
Because the light cone leaving a fast telescope arrives at a steeper angle, and simple eyepiece designs cannot bring the steep off axis rays to the same focus as the central ones. A Plossl that looks sharp to the edge at f/10 can show noticeably soft outer field at f/4.7. Fast Newtonians also show coma, an optical effect that stretches stars near the field edge into small comet shapes.
How we choose: we compare published manufacturer specifications, optical figures we can verify, and reviews from owners who have used the equipment under real skies. We do not test gear in person. Never point any telescope, finder or binocular at the Sun without a certified full-aperture solar filter fitted over the front of the instrument.
Recording your own eyepieces, exit pupils and sessions? The Observing & Astrophotography Planner is the paid version of these pages: 8 printable worksheets you fill in with your own numbers, plus the full PDF, $29.