Astronomy calculators
Explore telescope, astrophotography, orbital and stellar tools.
Which calculator should I use?
| Your question | Use this tool | Key formula |
|---|---|---|
| How strong is this eyepiece in my telescope? | Telescope magnification | Magnification = telescope focal length ÷ eyepiece focal length |
| How much sky will I see? | Field of view | True field = apparent field ÷ magnification |
| Is the beam of light too wide for my eye? | Exit pupil | Exit pupil = aperture ÷ magnification |
| How fast is my optical system? | Focal ratio | f-ratio = focal length ÷ aperture |
| Can I split this double star? | Resolution | Dawes limit = 116 ÷ aperture (mm) |
| How faint a star can I reach? | Limiting magnitude | Gain ≈ 5 log₁₀(aperture ÷ 7 mm) |
| How much more light than my eye? | Light gathering | (aperture ÷ 7 mm)² |
| Will my camera oversample the sky? | Pixel scale | 206.265 × pixel size (µm) ÷ focal length (mm) |
| How large does it look? | Angular size | θ = 2 arctan(size ÷ 2 distance) |
| How bright is it really? | Magnitudes | m − M = 5 log₁₀(d ÷ 10 pc) |
| How long does a signal take? | Light travel time | t = distance ÷ 299,792.458 km/s |
| How long is one orbit? | Orbital period | T = 2π √(a³ ÷ μ) |
| How fast must it move? | Orbital velocity | v = √(μ ÷ r) |
| What speed leaves the planet? | Escape velocity | v = √(2μ ÷ r) |
| Could liquid water exist there? | Habitable zone | 0.95–1.67 × √L AU (conservative) |
| What would I weigh there? | Weight on planets | Weight = mass × local gravity |
| Which unit is this distance in? | Distance converter | 1 ly = 63,241 AU = 0.3066 pc |
Units and constants used across the tools
| Quantity | Value | Used for |
|---|---|---|
| Speed of light | 299,792.458 km/s | Light travel time, distance conversion |
| Astronomical unit | 149,597,870.7 km | Planet distances, habitable zone |
| Earth GM (μ) | 398,600.4418 km³/s² | Orbital period and velocity around Earth |
| Sun GM (μ) | 1.32712440018 × 10¹¹ km³/s² | Heliocentric orbits |
| Jupiter GM (μ) | 1.26686534 × 10⁸ km³/s² | Orbits around Jupiter |
| Earth mean radius | 6,371 km | Altitude to orbital radius |
| Arcseconds per radian | 206,265 | Angular size, pixel scale |
| Dark-adapted eye pupil | about 7 mm (younger adults) | Light gathering, exit pupil |
How to use calculators with the rest of the site
A calculator explains the arithmetic behind something you can observe. Check the Night Sky Tonight page to see what is worth looking at, use the exit-pupil and field-of-view tools to pick an eyepiece for it, then use the satellite directory or deep-space trackers to put the same physics to work: the orbital period tool explains why the ISS circles Earth in about 92 minutes, and the light-travel-time tool explains the signal delay shown on the Voyager and JWST pages.
Accuracy, assumptions and how the numbers are produced
All calculations run in your browser from standard textbook formulas. Optical results assume ideal optics and typical eye properties; orbital results assume a two-body circular orbit; the habitable zone is a simplified educational estimate. Use specialist software for operational mission design or professional observatory planning.