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Absolute Magnitude Calculator

Enter apparent magnitude and distance to get the absolute magnitude.

How it is calculated

M = m − 5 × log10(d ÷ 10), where m is the apparent magnitude (as observed), d is the distance in parsecs and M is the absolute magnitude, the brightness the star would show at 10 parsecs. The tool also reports the distance modulus, m − M = 5 × log10(d ÷ 10). Distance must be above zero; the apparent magnitude can be negative (very bright objects). Both numbers are rounded to two decimals. At exactly 10 pc the modulus is 0 and M equals m. Lower magnitudes mean brighter objects. The formula ignores dust that dims starlight (interstellar extinction), so for distant stars in dusty regions M comes out too faint.

Worked example

A star with apparent magnitude 8.2 lies 250 parsecs away. d ÷ 10 = 25, and log10(25) = 1.3979. Distance modulus = 5 × 1.3979 = 6.99. Absolute magnitude = 8.2 − 6.99 = 1.21. Seen from 10 parsecs the star would look much brighter, about magnitude 1.2.

Try this example →

Common mistakes

  • Entering the distance in light-years. One parsec is about 3.26 light-years, so a distance of 815 light-years should be typed as about 250.
  • Entering the distance in kilometres, AU or in thousands of parsecs (kpc); the field is parsecs only.
  • Expecting a higher number to mean a brighter star. The magnitude scale runs backwards: M = −2 is brighter than M = +5.
  • Using the natural logarithm; the formula needs the base-10 logarithm, which the tool uses.
  • Ignoring interstellar dust. The tool does not apply an extinction correction, so the result describes the observed dimming plus distance only.

About this calculator

Absolute magnitude (M) is the apparent brightness a star would have if placed at a standard distance of exactly 10 parsecs from Earth, which lets astronomers compare the true, intrinsic luminosity of stars regardless of how far away they actually are. It's computed from the star's observed apparent magnitude (m) and its distance d in parsecs using the distance modulus relation: M = m − 5·log10(d/10), equivalently written as M = m − 5·log10(d) + 5.

Because the magnitude scale is logarithmic and inverted (lower numbers mean brighter objects), a star that looks faint only because it's far away will have a much brighter — more negative — absolute magnitude than its apparent magnitude suggests. This calculation underlies the cosmic distance ladder: once a star or supernova's absolute magnitude is known or assumed (as with Cepheid variables and Type Ia supernovae, both “standard candles”), the same formula can be rearranged to solve for distance instead, which is how astronomers measure distances well beyond what parallax can reach.

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