Binoculars Range Calculator

With this binoculars range calculator, you can find the distance to the object if you know its height.

Range at which a 1.7 m object fills the field14.969 mthe principle behind a ranging reticle

Magnification10×100 mm ÷ 10 mm

Focal ratiof/2.38objective focal length ÷ aperture

Aperture area1,385.44 mm²13.854 cm² — πd²/4, and this is what collects the light

Exit pupil4.2 mmcomfortable for visual use

Light gathering against a 7 mm eye36×as the SQUARE of aperture — this, not magnification, is what lets a telescope see faint objects

Diffraction-limited resolution3.2953 arcseconds1.22λ/D — no magnification can improve on this

Dawes limit2.7619 arcsecondsthe empirical double-star limit, close to but not identical with the Rayleigh figure

Maximum useful magnification84×about 2× the aperture in mm — beyond this you magnify the diffraction pattern itself and gain nothing, which is why "500× telescope" claims are meaningless without a large aperture

You are at11.9% of that limitwithin the useful range

Faintest star visible10.82 magnitudea rough visual limit for this aperture

True field of view6.5°390 arcminutes — the Moon is about 31 arcminutes across, so it fits in this field

Field width at 1 km113.5682 m

With a 5 mm eyepiece20×halving the eyepiece focal length doubles the magnification, and halves the exit pupil and the field of view with it

The formula

M = f_obj ÷ f_eye; true field = apparent field ÷ M

Aperture, not magnification

A telescope's magnification is just the ratio of two focal lengths, and it can be changed for the price of an eyepiece. What cannot be changed is the aperture, and that is what determines both how much light is collected — as the square of diameter — and how fine a detail can be resolved. Advertisements quoting huge magnifications on small apertures are selling a meaningless number.

Useful magnification tops out at roughly twice the aperture in millimetres. Beyond that you are magnifying the diffraction pattern rather than the object: the image grows larger, dimmer and no more detailed. A 200 mm telescope is genuinely useful to about 400×, and atmospheric turbulence usually limits it further.

Exit pupil is the diameter of the light cone leaving the eyepiece, and it should roughly match the eye's pupil. Larger and light spills past the iris and is wasted; much smaller and the view is dim and the eye's own imperfections become visible. Around 2 to 5 mm is comfortable for most observing.

True field of view is the apparent field of the eyepiece divided by the magnification, so higher power always means a narrower view. The Moon spans about half a degree, which is a useful yardstick for judging whether a given combination will frame it.