Backyard OrbitTelescope, eyepiece & night sky calculators

Telescope magnification & eyepiece calculator

Magnification, exit pupil, true field, the useful range of magnification, resolving power and the faintest stars for your telescope and eyepieces, in millimetres or inches. Every formula is named below.

Magnification48×25 mm eyepiece
Exit pupil4.17 mmfits your 7 mm pupil
True field1.08°65′ · 2.1 full-Moon widths
Telescope
= 7.87 in
Aperture unit

I know the
= 47.2 in · f/6

Eyepiece

Your eye and sky

Max useful400×rule of thumb: 2× per mm (≈50× per inch)
Min useful29×eyepieces over 42 mm waste light
Resolution0.58″Dawes · Rayleigh 0.69″
Faintest stars13.5–14.0approx., Bortle 5 sky
Focal length1,200 mmf/6 · 47.2 in
Light grasp816×your 7 mm pupil's light

200 mm (7.87 in) f/6 at 48×: low to medium power (6.1× per inch), showing 1.08° of sky, about 2.1 times the width of the full Moon.

Never aim a telescope or its finder at the Sun without a proper solar filter covering the front of the telescope; cap or remove the finder.

Your eyepiece set

All your eyepieces at once on the telescope above (with its Barlow, if any). Edit the sizes, add or remove eyepieces; the set is remembered on this device.

EyepieceApparent fieldMagnificationExit pupilTrue fieldWhere it sitsRemove
mm°37.5×5.33 mm1.39° (83′)Low to medium power
mm°48×4.17 mm1.08° (65′)Low to medium power
mm°80×2.50 mm0.65° (39′)Low to medium power
mm°120×1.67 mm0.43° (26′)Low to medium power
mm°200×1.00 mm0.33° (20′)Planetary range (20–30× per inch)

What the numbers mean

Magnification is the telescope's focal length divided by the eyepiece's (a 1200 mm telescope with a 25 mm eyepiece gives 48×). A Barlow lens multiplies it. If you only know the f-ratio, the focal length is aperture × f-ratio: a 200 mm f/6 has a 1200 mm focal length.

The exit pupil is the beam of light leaving the eyepiece: aperture ÷ magnification. If it is wider than the pupil of your eye, some of the light the telescope collects is wasted, which sets the lowest useful magnification. Below about 0.5 mm the view turns dim and soft, which matches the usual top limit of about 2× per millimetre of aperture (50× per inch). On most nights the air limits you well before that.

The true field is how much sky you see. Dividing the eyepiece's apparent field by the magnification gives a good estimate; if you know the eyepiece's field-stop diameter, field stop ÷ focal length × 57.3 gives the exact figure.

Resolution is the closest pair of equal stars the aperture can split: 116″ ÷ aperture in mm (Dawes) or 138″ ÷ aperture (Rayleigh, for yellow-green light). The faintest stars figure starts from what John Bortle reported for a 12.5-inch telescope under each class of sky and scales it to your aperture. Treat it as a rough guide: eyesight, experience and steady air all change it.

Sources

More tools for the backyard

See what fits in the eyepiece, choose binoculars, rate your sky and plan meteor nights.

Questions

How do I work out my telescope's magnification?

Divide the telescope's focal length by the eyepiece's focal length. A 1200 mm telescope with a 25 mm eyepiece gives 48×, and with a 10 mm eyepiece 120×. A 2× Barlow doubles both. Swapping eyepieces is how you change magnification: the telescope itself has no fixed "power".

What is the highest magnification my telescope can use?

The usual rule of thumb is about 2× per millimetre of aperture, or 50× per inch: 400× for a 200 mm telescope. Beyond that the exit pupil drops below 0.5 mm and the image gets dim and blurry. Tele Vue notes that the atmosphere usually limits planetary viewing to about 300× whatever the telescope, and Nagler puts the planetary sweet spot at 20–30× per inch.

What is exit pupil, and why does it matter?

It is the width of the beam of light leaving the eyepiece: aperture divided by magnification, or eyepiece focal length divided by the f-ratio. If it is wider than your eye's pupil, part of the light misses your eye, so there is no point going lower in magnification. Dark-adapted pupils are often quoted as 7 mm, but they shrink with age: a 2024 study measured about 0.4 mm less per decade of age.

What is the difference between apparent field and true field?

The apparent field is how wide the circle of view looks when you put your eye to the eyepiece, a property of the eyepiece design (often 50° to 82°). The true field is the patch of sky inside that circle. Dividing apparent field by magnification estimates it; the field-stop method is exact when the maker publishes the field-stop diameter.

What does the f-ratio of a telescope mean?

It is the focal length divided by the aperture: a 200 mm telescope with a 1200 mm focal length is f/6. With a given eyepiece, a lower f-ratio gives less magnification, a wider true field and a larger exit pupil, because exit pupil = eyepiece focal length ÷ f-ratio.