The star magnitude calculator uses the standard formula (limiting mag = 2 + 5 × log₁₀(aperture mm)) to find the faintest stars visible through your telescope. Toggle between mm and inches. Results include a comparison chart from naked-eye objects to Hubble.
Telescope Aperture
Limiting Magnitude
Magnitude Reference Table
| Instrument | Aperture | Limiting Mag. | Examples You Can See |
|---|---|---|---|
| Naked Eye | 7mm (pupil) | ~6.0 | Pleiades, Milky Way, ~9,000 stars |
| Binoculars 10×50 | 50mm | ~9.5 | 100,000s stars, M31 (Andromeda), globular clusters |
| 70mm Refractor | 70mm | ~11.1 | Planets, Moon, bright nebulae, ~200K stars |
| 4.5" (114mm) Reflector | 114mm | ~11.8 | Many nebulae, dim galaxies, Saturn's moons |
| 8" Dobsonian | 203mm | ~13.1 | Galaxy detail, dark nebulae, Pluto (with difficulty) |
| 12" SCT | 305mm | ~14.0 | Quasars, faint galaxy clusters |
| Your Telescope | 114mm | 11.8 | — |
| Hubble (2.4m) | 2400mm | ~31.5 | Earliest galaxies, objects 13.4 billion light-years away |
How to Use the Star Magnitude Calculator
Enter your telescope's aperture in millimeters or inches. The calculator immediately shows your limiting visual magnitude — the faintest stars you can theoretically detect under good dark sky conditions (Bortle 3–4).
The Limiting Magnitude Formula
The formula is: Limiting Magnitude = 2 + 5 × log₁₀(aperture in mm). This gives the approximate faintest stellar magnitude visible with careful averted vision (looking slightly to the side of the target). For direct vision, subtract about 0.5–1.0 magnitude. Under light-polluted skies, subtract 2–3 magnitudes.
Example: A 200mm telescope has limiting magnitude = 2 + 5 × log₁₀(200) = 2 + 5 × 2.301 = 2 + 11.5 = 13.5. Compare: the naked eye reaches about 6.0, binoculars about 9.5, and Hubble Space Telescope about 31.5.
How Light Pollution Affects Limiting Magnitude
The formula assumes transparent, dark skies. In city suburbs (Bortle 7–8), limiting naked-eye magnitude drops to 3–4, and your telescope's practical limiting magnitude decreases by about 2 magnitudes. A 200mm scope in a Bortle 7 sky behaves more like a 100mm scope in a dark Bortle 3 sky. For the deepest views, travel to dark sky sites or use narrowband emission filters.
FAQ
What is limiting magnitude?
Limiting magnitude is the faintest stellar magnitude visible through an instrument. Lower numbers mean brighter objects (the Sun is magnitude -27; the full Moon is -13). The limiting magnitude formula for a telescope is: 2 + 5 × log₁₀(aperture in mm). A 100mm telescope reaches about magnitude 12 under good conditions.
What is the magnitude scale?
Apparent magnitude is a logarithmic scale where each step of 1 magnitude is 2.512× brighter or dimmer (the fifth root of 100). A magnitude 1 star is 100 times brighter than a magnitude 6 star. Negative magnitudes are very bright objects — Venus reaches -4.6, Jupiter -2.9, and Sirius -1.5.
Does dark sky matter for limiting magnitude?
Yes, significantly. In light-polluted suburbs (Bortle 6–7), sky glow limits naked-eye visibility to about magnitude 3–4, reducing a telescope's effective limiting magnitude by 2–3 magnitudes compared to dark skies. The formula assumes reasonably dark skies (Bortle 4 or better).
Can aperture compensate for light pollution?
Partially. More aperture collects more light but also amplifies the sky background glow. A large telescope in a light-polluted area will still see fainter stars, but the contrast for nebulae and galaxies suffers more than for stars. Narrowband filters help for emission nebulae under light-polluted skies.
Is this tool free?
Yes, completely free with no signup required.