The focal ratio: what it changes, and what it does not

The arithmetic

The focal ratio (also called the f-number) is the instrument's focal length divided by its aperture, both in millimetres. It has no unit, and it follows from the other two: it tells you nothing they do not, but it tells you faster.

• 76/300 tabletop Newtonian: 300 ÷ 76 = f/3.9.
• 130/650 tabletop Dobsonian: 650 ÷ 130 = f/5.
• 200/1200 Dobsonian: 1,200 ÷ 200 = f/6.
• 150/1200 Dobsonian: 1,200 ÷ 150 = f/8.
• 70/900 refractor: 900 ÷ 70 = f/12.9.

An f/5 is not brighter at the eyepiece

In photography, a lens 'open to f/2' is called fast, and the idea has drifted over to telescopes. At the eyepiece it does not hold. What the eye receives depends on the aperture, which gathers the light, and on the exit pupil, which says over what area it is spread.

Nor does the focal ratio set the maximum useful magnification: the aperture does, at about twice its value in millimetres. A 130 mm f/5 and a 130 mm f/8 both top out around 260× on 130 mm, an exit pupil of 0.5 mm; the f/5 just needs a shorter eyepiece to get there.

The exit pupil, explained →

What it changes: the eyepiece you need

The exit pupil also equals the eyepiece focal length divided by the focal ratio. That is the most practical use of the number: it tells you, without working out a magnification, what an eyepiece will do on your instrument.

• A 10 mm gives a 2 mm exit pupil at f/5, 1.25 mm at f/8, and 0.78 mm at f/12.9.
• A 25 mm gives 5 mm at f/5, 3.1 mm at f/8, and 1.9 mm at f/12.9.
• For a 1 mm exit pupil, the eyepiece focal length in millimetres equals the focal ratio: 5 mm on an f/5, 8 mm on an f/8.

Which eyepiece to buy first →

What it changes: the field

The widest true field a tube can show depends on its focal length, and so, at a given aperture, on its focal ratio. It equals the diameter of the eyepiece's field stop divided by the telescope's focal length. A 31.75 mm focuser passes, at most, a field stop of about 27 mm.

That is the real strength of a short focal ratio: the wide field, for finding things, for big clusters, for the Milky Way. To go beyond it on a long focal ratio you need a 50.8 mm focuser and more expensive eyepieces.

What it asks of you

• A short Newtonian, around f/4 or f/5, shows stars as little comets at the edge of the field (coma), and asks for more careful collimation than an f/8.
• A short achromatic refractor shows more violet fringing around bright objects than a long one of the same aperture.
• A long focal ratio is bulkier at the same aperture: a Newtonian's tube is roughly as long as its focal length, about 1.2 m for a 150/1200 and 65 cm for a 130/650.

Collimating a Newtonian →

In photography, it is another story

On a sensor, the illumination from an extended object follows the inverse square of the focal ratio. That is where 'fast' and 'slow' mean something: an f/5 instrument piles up a nebula's light on each pixel four times as fast as an f/10.

For visual observing, keep the questions in order: aperture first, then the mount, then the focal ratio, which will tell you which eyepieces to buy.

Questions people ask