What do the numbers on my binoculars mean?
Binoculars are named by two numbers: 10×50 means 10 times magnification and 50 mm objective lenses. From those two figures and the field of view printed on the barrel, this binocular calculator works out the exit pupil, the field of view in metres at 1,000 m, the twilight factor and a relative brightness figure, so you can compare pairs for stargazing, birding or dusk use.
It is quick, free and runs in your browser; nothing is sent anywhere.
How to use the Binocular Calculator
- Enter the magnification and the lens diameter (10 and 50 for 10×50).
- Enter the field of view from the barrel, either in degrees or as metres at 1,000 m (or leave it empty).
- Set your eye pupil if you want brightness limited by it; the default is 7 mm.
- Read the results and compare with the common models in the table.
Binocular Calculator features
Field of view
Degrees to metres at 1,000 m and back, plus the apparent field of view.
Exit pupil
Lens diameter ÷ magnification, checked against your eye pupil.
Twilight factor
The square root of magnification × lens diameter, a measure of detail at dusk.
Comparison table
Seven popular sizes from 8×42 to 20×80 side by side.
Formulas and a worked example
Exit pupil = D ÷ M. Twilight factor = √(M × D). Field at 1,000 m = 1000 × tan(field angle), which is about 17.45 m per degree. Relative brightness = exit pupil², limited by your eye pupil. Apparent field = 2 × atan(M × tan(real field ÷ 2)), following ISO 14132.
Example: 10×50 binoculars with a 6.5° field have a 50 ÷ 10 = 5 mm exit pupil, a twilight factor of √500 = 22.4, a relative brightness of 25 and a field of 1000 × tan 6.5° ≈ 114 m at 1,000 m.
Choosing for astronomy
For stargazing an exit pupil of 4–7 mm suits a dark-adapted eye, but an older eye opens to only 5 mm or less, so 7×50 wastes light for many people. A 10×50 or 8×42 is a good starting point; above about 12× you will want a tripod. See the exit pupil calculator for eye pupil by age, and the telescope resolution calculator for how aperture sets the faintest stars you can see.
Limits
- Brightness here is geometric. Real transmission depends on glass and coatings, which can matter more than the numbers.
- The twilight factor is a rule of thumb for detail in poor light, not a measured score.
- Field of view figures printed on the barrel are the maker’s claim; check against a known distance if it matters.
- The limiting magnitude is a rough formula for a steadily held pair under dark sky.
Binocular Calculator FAQ
What does 10×50 mean on binoculars?
Ten times magnification with 50 mm diameter objective lenses.
How do I convert degrees of field of view to metres at 1,000 m?
Multiply the degrees by about 17.45, or calculate 1000 × tan(angle) for an exact figure. 6.5° is roughly 114 m.
What is the twilight factor?
The square root of the magnification times the lens diameter. A higher value suggests better detail in dim light.
What is a good exit pupil for binoculars?
About 5 mm for night use, and 2–4 mm for daytime. It should not exceed your own pupil.
Are bigger binoculars always better for stargazing?
Not always. Larger lenses gather more light but weigh more and shake more, and above about 12× most people need a tripod. A steady 10×50 often shows more than a shaky 15×70.
What is relative brightness?
The exit pupil squared, a quick way to compare the light reaching the eye between two pairs, capped at the size of your pupil.
How faint a star can binoculars show?
About magnitude 11 for 50 mm binoculars under a dark sky with a steady hold, using an approximate formula.