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Telescope calculator

Free telescope calculator: enter focal lengths and aperture to get magnification, field of view, exit pupil, Dawes’ limit and max useful power, with formulas.

Classroom activity Teaching with this lab?

Telescope calculatorInteractive model

Magnification40×

True field1.5°

Exit pupil2.5 mm

Dawes’ limit1.16″

Max useful power200×

Focal ratiof/10

Your experiment

Telescope focal length mm

Eyepiece focal length mm

Aperture mm

Eyepiece apparent field °

1,000 / 25 = 40×. Exit pupil: 100 mm / 40 = 2.5 mm. Approximate true field: 60° / 40 = 1.5°. Dawes’ limit: 116 / 100 = 1.16 arcseconds. Maximum useful power ≈ 2 × 100 = 200×; light grasp ≈ 204× a 7 mm eye pupil.

How it works

Magnification = telescope focal length / eyepiece focal length

Magnification depends on both telescope and eyepiece. Exit pupil describes the diameter of the light beam leaving the eyepiece. A wider true field lets you see more of the sky at once.

How to Calculate Telescope Magnification ↗

About this model
True field ≈ apparent field / magnification. Dawes’ limit estimates resolution for double stars; atmosphere, optics, and target contrast affect actual results. Never view the Sun without a purpose-built front-mounted solar filter.

Key formulas

Quantity	Formula	Note or example
Magnification	M = telescope focal length ÷ eyepiece focal length	1000 mm ÷ 25 mm = 40×
Exit pupil	exit pupil = aperture ÷ M	100 mm ÷ 40 = 2.5 mm
True field of view	TFOV ≈ apparent field ÷ M	60° ÷ 40 = 1.5°
Dawes’ limit	resolution ≈ 116 ÷ aperture (mm) arcseconds	116 ÷ 100 mm = 1.16″
Maximum useful magnification	≈ 2 × aperture in mm (50× per inch)	100 mm → about 200×
Focal ratio	f-number = focal length ÷ aperture	1000 ÷ 100 = f/10

Worked examples

Each row uses one of this lab’s presets and the same model as the interactive tool.

Example	Magnification	True field	Exit pupil	Dawes’ limit	Max useful power	Focal ratio
Wide view	20×	3.4°	4 mm	1.45″	160×	f/7.5
Lunar detail	120×	0.5°	1.25 mm	0.77″	300×	f/8
8-inch Dobsonian	48×	1.08°	4.17 mm	0.58″	400×	f/6

Keep wondering

Telescope calculator: common questions

Is higher magnification always better?

No. High power can make a view dimmer and amplify atmospheric blur. Aperture and observing conditions matter.

What does exit pupil mean?

It is the width of the light beam leaving the eyepiece, equal to aperture divided by magnification.

How do you calculate telescope magnification?

Divide the telescope’s focal length by the eyepiece’s focal length, in the same units. A 1,000 mm telescope with a 25 mm eyepiece magnifies 40×; a 10 mm eyepiece gives 100×.

What is the maximum useful magnification of a telescope?

A common rule of thumb is about twice the aperture in millimeters, or 50× per inch. A 100 mm telescope tops out near 200× in steady air; atmospheric turbulence often limits views to less.

What is Dawes’ limit?

An empirical estimate of the closest pair of equal stars a telescope can split: about 116 divided by the aperture in millimeters, in arcseconds. A 100 mm telescope resolves about 1.16″.

Your next discovery

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