Apparent Magnitude vs Distance Calculator
Calculate apparent magnitude change with distance using the inverse-square law and distance modulus.
Returns star brightness at any new distance.
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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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