Distance Modulus & Absolute Magnitude Calculator

How it works

m − M = 5·log₁₀(d / 10 pc) + A; d = 10^((m − M − A)/5 + 1) pc; A = m − M − 5·log₁₀(d / 10 pc); A_V = R_V × E(B−V); d = 1000 / parallax(mas) pc; L/L☉ = 10^(0.4·(M☉ − M)) with M☉ = 4.83 (V); σd/d ≈ 0.461 σ(m − M)

Apparent magnitude is how bright a star looks; absolute magnitude is how bright it would look from 10 parsecs — a true luminosity. The difference, the distance modulus, depends only on distance (five magnitudes per factor of ten) plus any dimming by interstellar dust, the extinction A. Pick what to solve for: the absolute magnitude from a measured brightness and distance, the distance from a known absolute magnitude (the standard-candle method used with Cepheids and Type Ia supernovae), the apparent magnitude an object would have at a given distance, or the extinction when all three are known. Distance can be entered in parsecs, light-years, kpc, Mpc or AU, or as a Gaia-style parallax, and extinction directly or from the colour excess E(B−V). Because the scale is logarithmic, a small magnitude error becomes a sizeable distance error — about 4.6% per 0.1 mag — which the uncertainty field shows. The table places the same object at familiar distances, from 10 pc out to the Virgo Cluster, and says what you would need to see it.

Worked example

Betelgeuse: m = 0.42, d = 168 pc → M = 0.42 − 5 × log₁₀(16.8) = 0.42 − 6.13 = −5.71, about 16,400 times the Sun’s visual luminosity, with a parallax of 5.95 mas. Supernova 1987A peaked at m = 2.8 in the Large Magellanic Cloud (m − M = 18.5), so M = 2.8 − 18.5 = −15.7. A ±0.1 mag error on the modulus moves a distance by about ±4.6%.

Sources: Distance modulus — Wikipedia · IAU 2015 Resolution B2 — zero points for absolute and apparent bolometric magnitudes

Frequently asked questions