Apparent Magnitude vs Distance Calculator
Calculate how a star changes in apparent brightness when moved to a new distance.
Uses the inverse-square law of light.
New Apparent Magnitude
How does a star change in brightness when its distance changes?
Since light follows the inverse-square law, moving an object twice as far away makes it appear four times dimmer. The magnitude system is logarithmic, so we use the formula:
m₂ = m₁ + 5 × log₁₀(d₂ / d₁)
Where:
- m₁ = known apparent magnitude at known distance d₁
- m₂ = apparent magnitude at new distance d₂
- d₁ and d₂ must be in the same units (km, AU, light-years, or parsecs all work)
The brightness ratio between two magnitudes:
F₁/F₂ = 10^((m₂ - m₁) / 2.5)
Real-world examples:
- The Sun at 1 AU has m = −26.74. At 10 AU (where Saturn orbits), it would be m ≈ −20.23 — still dazzlingly bright.
- Proxima Centauri (m = +11.1) is invisible to the naked eye. If moved to 1 AU, it would shine at about m ≈ −11 (brighter than the full Moon).
Key reference magnitudes:
- Venus at brightest: −4.9
- Full Moon: −12.7
- Sun: −26.74
- Faintest naked-eye stars: +6.5
- Hubble Space Telescope limit: about +31.5
The magnitude scale was originally defined so that a change of exactly 5 magnitudes equals a factor of exactly 100 in brightness.