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Distance modulus · magnitudes · 1/r^2

Distance modulus & stellar magnitude calculator

Solve distance, apparent magnitude, or absolute magnitude from the distance modulus m - M = 5 log10(d/10 pc) and see how brightness changes with distance.

All calculations stay in your browser; units are converted to parsec internally.

How to use (3 steps)

  1. Choose what to solve for: apparent m, absolute M, or distance d.
  2. Enter the other two values and pick the distance unit (pc, ly, kpc, Mpc).
  3. Press Compute to get the result, brightness ratios, graph, and narrated steps. Copy URL shares the same setup.

Sample values (m=10, M=5) are preloaded and calculated automatically so you see a result on first view.

Inputs

Example: 10.0
Example: 5.0
Pick the display unit for the solved distance.
Processed locally. The base unit is parsec (1 pc = 3.26156 ly).

Results

Values are recomputed with the same formula to keep them consistent.

1/r^2 brightness graph

The inverse-square law means 10x farther gives roughly 1/100 the brightness.

Calculation steps

    FAQ

    What is the distance modulus?

    The distance modulus is \u03bc = m - M. It links brightness and distance with \u03bc = 5 log10(d/10 pc), letting you solve distance from magnitudes or vice versa.

    Why does brightness drop with 1/d^2?

    Light spreads over a sphere, so flux (brightness per unit area) scales as 1/d^2. If distance grows by 10x, brightness drops to about 1/100.

    Can I enter negative magnitudes or very large distances?

    Yes. The formulas accept negative magnitudes and very large distances. The result is an idealized, textbook-level estimate that ignores extinction or cosmology.

    What do the units pc, ly, kpc, and Mpc mean?

    One parsec (pc) is about 3.26 light-years (ly). A kiloparsec (kpc) is 1000 pc, and a megaparsec (Mpc) is 1,000,000 pc. This calculator converts your chosen unit to parsecs internally before applying the distance modulus formula.