Distance Modulus Calculator
Convert between an astronomical distance modulus and a physical distance in parsecs, kiloparsecs, megaparsecs, and light-years.
pc
From distance modulus μ = 10
- 1
Exponent (μ + 5) ÷ 5
(10 + 5) ÷ 5 = 3 - 2
Distance d = 10^exponent
10^3 = 1,000Each 5-magnitude increase in μ multiplies the distance by 10.
How does this calculator work?
The distance modulus μ = m − M relates apparent and absolute magnitude to distance: d_pc = 10^((μ + 5) / 5). Enter μ to get the distance, or a distance to get μ. Results appear in parsecs, kiloparsecs, megaparsecs, and light-years (1 pc = 3.2616 ly), assuming no dust extinction.
Formula
How this is calculated
The distance modulus μ is the difference between an object's apparent magnitude m and its absolute magnitude M. Because magnitudes are a logarithmic measure of brightness, this difference encodes how much an object has dimmed with distance. Enter either the distance modulus μ or a distance d in parsecs; the calculator solves for whichever value you leave blank.
The relationship comes from the inverse-square law of light: μ = 5·log10(d_pc) − 5, where d_pc is the distance in parsecs. Rearranging gives d_pc = 10^((μ + 5) / 5). A distance modulus of 0 corresponds to exactly 10 parsecs (the reference distance for absolute magnitude), μ = 5 to 100 pc, μ = 10 to 1000 pc, and so on — each 5 magnitudes multiply the distance by 10.
Distances are reported in parsecs, kiloparsecs (÷1000), megaparsecs (÷1,000,000), and light-years using 1 pc = 3.2616 ly. This formula assumes no interstellar extinction (dimming by dust); a real reddened object needs μ replaced by μ₀ = μ − A, the extinction-corrected modulus. Distances must be positive, so a distance input of zero or below is rejected.
Frequently asked questions
Zero. Absolute magnitude is defined as the apparent magnitude an object would have at exactly 10 parsecs, so at that distance m = M and μ = 0.
First convert to parsecs with d_pc = 10^((μ + 5) / 5), then multiply by 3.2616 light-years per parsec.
No. It uses the true distance modulus. If dust dims the object, subtract the extinction A in magnitudes from μ before computing the distance.
Also known as
TG we-Calculate Editorial Team. (2026). Distance Modulus Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/distance-modulus-calculator
TG we-Calculate Editorial Team. "Distance Modulus Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/distance-modulus-calculator.
TG we-Calculate Editorial Team, "Distance Modulus Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/distance-modulus-calculator
@misc{wecalculate_distance_modulus_calculator, title = {Distance Modulus Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/distance-modulus-calculator}}, year = {2026}, note = {TG we-Calculate} }
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