What are apparent and absolute magnitude?
Astronomers rate the brightness of a star on the magnitude scale: apparent magnitude (m) is how bright it looks from Earth, and absolute magnitude (M) is how bright it would look from a standard distance of 10 parsecs (about 32.6 light-years). The gap between them, m − M = 5 log10(d ÷ 10 pc), is the distance modulus. This calculator solves that equation for whichever of m, M or the distance you do not know, with the working.
Two more jobs sit on the same page: the brightness ratio between two magnitudes, and the combined magnitude of several stars that blur into one point. Everything runs in your browser.
How to use the Apparent & Absolute Magnitude Calculator
- In the first block choose what to find: absolute magnitude, apparent magnitude or distance.
- Fill the other two fields. Distance can be in parsecs, light-years or astronomical units.
- Read the result and the worked substitution. Copy it if you need it for notes or homework.
- For a brightness comparison enter the two magnitudes in the second block; for a close pair or cluster, list the magnitudes in the third.
Apparent & Absolute Magnitude Calculator features
Three unknowns
Solve for M, for m or for the distance with the same distance-modulus equation.
Brightness ratio
Each step of 1 magnitude is a factor of 2.512; five steps are exactly 100.
Combined magnitude
Add the light of two or more stars and convert it back to a single magnitude.
Luminosity
The absolute magnitude is converted to luminosity compared with the Sun.
Reference values
A table of the Sun, Moon, Venus, Sirius, Vega and Polaris.
Formulas and a worked example
The magnitude scale is logarithmic and runs backwards: smaller numbers are brighter. A difference of 5 magnitudes is a factor of exactly 100 in brightness, so one magnitude is 1001/5 ≈ 2.512. The flux ratio is FA ÷ FB = 100.4 (mB − mA), the distance modulus is m − M = 5 log10(d ÷ 10 pc), and the combined magnitude of several stars is m = −2.5 log10 Σ 10−0.4 mi.
Example: Vega has m = 0.03 and lies at 7.68 pc. Then M = 0.03 − 5 log10(7.68 ÷ 10) ≈ 0.60. Sirius (−1.46) against Polaris (1.98) differs by 3.44 magnitudes, which is 100.4 × 3.44 ≈ 23.8 times brighter. Two equal stars of magnitude 3 together shine at 3 − 2.5 log10 2 ≈ 2.25, only 0.75 magnitudes brighter than one.
Reading the results
Magnitudes are also used for planets, the Moon and the Sun, but extended objects such as galaxies and nebulae have a surface brightness as well, which this calculator does not cover. For a quick feel for the scale: the faintest stars seen by eye under a dark sky are near magnitude 6, binoculars add about 3 to 4 magnitudes, and a small telescope about 10 to 13. The darker and clearer the sky, the fainter the limit.
A star with m = M sits exactly 10 pc away. If m is smaller than M the star is closer than 10 pc, and if it is larger the star is farther. The Sun has an apparent magnitude of about −26.74 but an absolute magnitude of only +4.83, a modest star. To change distances between parsecs, light-years and kilometres use the light-year converter; to see which stars your telescope can reach see the telescope resolution calculator, which also gives a limiting magnitude.
Limits of this calculator
- Interstellar dust dims and reddens starlight; the formula assumes none, so real distances found from m and M may come out too large.
- Magnitudes are in a single band (visual). Magnitudes in other filters or bolometric magnitudes differ by a correction.
- The luminosity relative to the Sun uses MSun = 4.83 in the visual band, so it is visual luminosity, not total energy output.
Apparent & Absolute Magnitude Calculator FAQ
How do I convert apparent magnitude to absolute magnitude?
Use M = m − 5 log10(d ÷ 10), with the distance d in parsecs. Choose “Absolute magnitude M” in the calculator and enter m and the distance.
What is the distance modulus?
The difference m − M. It equals 5 log10(d ÷ 10 pc), so a modulus of 5 means a distance of 100 parsecs.
How much brighter is magnitude 1 than magnitude 6?
Exactly 100 times, because five magnitudes are defined as a factor of 100.
Why do brighter stars have smaller or negative numbers?
The scale is historic: Hipparchus ranked the brightest stars first, and modern magnitudes keep that direction while extending it to negative values.
How do you add the magnitudes of two stars?
Add their fluxes, not their magnitudes: m = −2.5 log10(10−0.4 m1 + 10−0.4 m2).
What distance is 10 parsecs?
About 32.6 light-years or 3.086 × 1017 metres.