Magnitude-Distance Calculator
The distance modulus is the astronomer's ruler for objects too far away to measure by parallax. The formula m - M = 5 log10(d) - 5 connects apparent magnitude m, absolute magnitude M, and distance d in parsecs. Given any two of these three quantities, you can solve for the third. Enter apparent and absolute magnitude to find the distance, or enter the distance modulus directly to find the distance. The calculator also converts parsecs to light-years for ease of interpretation.
Distance modulus formula
mu = m - M = 5 * log10(d) - 5
d (pc) = 10^((m - M + 5) / 5)
Where mu is the distance modulus, m is apparent magnitude, M is absolute magnitude, d is distance in parsecs, and log10 is the base-10 logarithm. One parsec = 3.2616 light-years. A distance modulus of 0 corresponds to 10 pc; mu = 5 to 100 pc; mu = 10 to 1,000 pc.
Standard candle reference objects
Sun: M = 4.74, at 1 AU giving m = -26.74. Sirius: M = 1.43, m = -1.46, d = 2.64 pc. The Andromeda Galaxy's distance is measured using Cepheid variables (M known from period-luminosity law), giving d = about 770 kpc (m - M = about 24.4). Type Ia supernovae reach M = about -19.3, used to measure distances to billions of light-years.
Magnitude-distance: frequently asked questions
What is the distance modulus?
The distance modulus is mu = m - M, where m is apparent magnitude (how bright an object looks) and M is absolute magnitude (how bright it would look at 10 parsecs). The distance d in parsecs is found from d = 10 to the power of (mu/5 + 1).
What is apparent magnitude?
Apparent magnitude m measures how bright an object appears from Earth. The scale is logarithmic and reversed: brighter objects have lower (or negative) magnitudes. The Sun is m = -26.74, the full Moon m = -12.6, Venus at brightest m = -4.9, and the faintest naked-eye stars are around m = 6.5.
What is absolute magnitude?
Absolute magnitude M is the apparent magnitude an object would have if it were exactly 10 parsecs from Earth. The Sun's absolute magnitude is M = 4.74. Supernovae can reach M = -19, making them visible across billions of light-years.
How accurate is this method for measuring distances?
The distance modulus is accurate if you know M precisely, which requires using standard candles (objects with known intrinsic brightness). Cepheid variable stars and Type Ia supernovae are the most important standard candles used by astronomers.
What is a parsec?
A parsec (pc) is the distance at which 1 AU subtends an angle of 1 arcsecond. One parsec equals approximately 3.0857 x 10 to the 16th meters, or about 3.2616 light-years. The nearest star, Proxima Centauri, is about 1.30 parsecs away.
Official sources
- USNO Astronomical Almanac Online: aa.usno.navy.mil.
- NASA IPAC Extragalactic Database distance reference: ned.ipac.caltech.edu.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.