Enter any 2 values (apparent magnitude, stellar parallax, or absolute magnitude) into the Calculator. The calculator will evaluate the missing value. If you use parallax, make sure the selected unit (arcsec/mas/µas) matches your input.
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Absolute Magnitude Formula
The calculator uses three formulas, one per mode.
Absolute mode solves for absolute magnitude from apparent magnitude and distance:
M = m - 5*log10(d) + 5
Apparent mode rearranges the same distance modulus to solve for apparent magnitude:
m = M + 5*log10(d) - 5
Luminosity mode converts absolute magnitude to a luminosity ratio against the Sun:
L/Lsun = 10^((Msun - M) / 2.5)
- M = absolute magnitude (visual, on the bolometric-free Vega system)
- m = apparent magnitude as seen from Earth
- d = distance to the object in parsecs
- Msun = absolute magnitude of the Sun, fixed at 4.83
- Lsun = solar luminosity, 3.828 × 10^26 W
Assumptions: distances are converted to parsecs internally. Light-years use 1 pc = 3.261563777 ly. AU uses 1 pc = 206264.806247 AU. Parallax in arcseconds gives d = 1/p, and parallax in milliarcseconds gives d = 1000/p. The formulas assume no interstellar extinction. If the line of sight passes through dust, the true absolute magnitude is brighter than the result by the extinction A in magnitudes.
The Absolute mode takes what you measure (m) and how far the object is, and returns the intrinsic brightness M. The Apparent mode does the reverse: given the intrinsic M and a distance, it predicts how bright the object will look. The Luminosity mode skips distance entirely and converts M directly to a power output, expressed both as a multiple of the Sun and in watts.
Reference Tables
Absolute magnitudes of familiar objects for sanity-checking your inputs:
| Object | Absolute Magnitude (M) | L / Lsun |
|---|---|---|
| Sun | +4.83 | 1 |
| Sirius A | +1.42 | ~23 |
| Vega | +0.58 | ~50 |
| Betelgeuse | −5.85 | ~17,000 |
| Rigel | −7.84 | ~110,000 |
| Proxima Centauri | +15.60 | ~0.0017 |
| Type Ia supernova (peak) | −19.3 | ~5 × 10^9 |
Distance modulus (m − M) for common distances:
| Distance | In parsecs | m − M |
|---|---|---|
| 10 pc (reference) | 10 | 0.00 |
| 100 pc | 100 | 5.00 |
| 1 kpc | 1,000 | 10.00 |
| Galactic center | ~8,200 | ~14.57 |
| LMC | ~50,000 | ~18.49 |
| Andromeda (M31) | ~7.78 × 10^5 | ~24.45 |
Worked Examples and FAQ
Example 1: Find the absolute magnitude of Sirius. Sirius has m = −1.46 and lies 2.64 pc away. Plug into M = m − 5·log10(d) + 5:
M = −1.46 − 5·log10(2.64) + 5 = −1.46 − 2.107 + 5 = +1.43. That matches the catalog value to within rounding.
Example 2: Predict the apparent magnitude of the Sun from 10 pc. By definition, m = M = +4.83. From 10 pc the Sun would be a faint naked-eye star.
Example 3: Convert M = +4.83 to luminosity. L/Lsun = 10^((4.83 − 4.83)/2.5) = 10^0 = 1. The Sun outputs 1 solar luminosity, as expected.
Example 4: A star has absolute magnitude −2.0. How does it compare to the Sun? L/Lsun = 10^((4.83 − (−2.0))/2.5) = 10^2.732 ≈ 540. The star is roughly 540 times more luminous than the Sun.
Why is 10 parsecs the reference distance? It is a convention. Placing every object at 10 pc removes distance from the comparison, so two stars with the same M put out the same visible-light power.
What if I only have parallax? Use the parallax options in the unit dropdown. Distance in parsecs equals 1 divided by parallax in arcseconds, or 1000 divided by parallax in milliarcseconds. Gaia data is usually in mas.
Why do extinction and reddening matter? Dust between you and the star absorbs and scatters light, making m larger (fainter) than it would otherwise be. If you ignore extinction, the M you compute will be too faint. Subtract the extinction A from m before using the formula when accuracy matters.
Is this visual or bolometric magnitude? The calculator uses the standard visual-band convention with Msun = 4.83. For bolometric work, use Mbol,sun = 4.74 and apply a bolometric correction to the star's M.
Can I use this for galaxies or quasars? Yes for nearby galaxies where Euclidean distance applies. For high-redshift sources you need the distance modulus based on luminosity distance, which includes cosmological terms not handled here.
