Apparent Magnitude Calculator
How bright a star appears from a given distance, from its absolute magnitude — with its luminosity in Suns, the distance modulus, and how far away it would still be visible to the naked eye.
Absolute magnitude is how bright a star would look from 10 parsecs; apparent magnitude is how bright it looks from where you are.
How the apparent magnitude calculator works
Absolute magnitude is how bright a star would look from 10 parsecs; apparent magnitude is how bright it looks from where you are. The difference — the distance modulus — is 5 log of distance over 10 parsecs, because brightness falls with the square of distance and the magnitude scale is logarithmic.
The scale runs backwards: five magnitudes is a factor of 100 in brightness, and smaller numbers are brighter. The Sun is −26.7 from here and 4.83 from 10 parsecs — an ordinary star.
Formula: m = M + 5 log₁₀(d / 10 pc); L / L☉ = 10^(0.4 (4.83 − M))
Worked examples
| Inputs | Apparent magnitude m | Note |
|---|---|---|
| The Sun from 10 parsecs | 4.83 | magnitude 4.83, just an ordinary star |
| The Sun from Earth | -26.742 | −26.7 |
| Rigel at 260 pc | -0.725 | still bright |
FAQFrequently asked questions
What is the difference between apparent and absolute magnitude?
Apparent is how bright a star looks from Earth; absolute is how bright it would look from a standard 10 parsecs. The gap between them is the distance.
Why do smaller magnitudes mean brighter?
Hipparchus ranked the brightest stars "first magnitude" and the faintest "sixth". The modern scale kept the direction and made five magnitudes exactly a hundredfold.
What is the distance modulus?
m minus M, equal to 5 log of the distance in parsecs minus 5. Measure both magnitudes and you have the distance — the basis of standard-candle astronomy.
What is the naked-eye limit?
About magnitude 6 under a truly dark sky, 4 in the suburbs, 2 or 3 in a city. Enter yours to see what is visible.
Does this account for dust?
No — interstellar extinction dims distant stars beyond the inverse-square law. For nearby stars it is negligible; across the galactic plane it can be several magnitudes.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- NASA — the US space agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).