Calculate distance modulus, distance in parsecs, or parallax to distance using μ, kpc, Mpc, ly, km, arcseconds, mas, or μas values.

Infer distance from μ = m − M after correcting extinction.

Use extinction-corrected distance modulus in a matching magnitude band. Simple inverse parallax is for positive, well-measured stellar parallaxes.

Distance Modulus Formula

The following formula is used to calculate a distance modulus.

m − M = 5 × log10(r / 10)
  • Where m-M is the distance modulus
  • r is the positive distance from the observer to the object in parsecs

To calculate a distance modulus, take the base-10 logarithm of the distance in parsecs divided by 10, then multiply by 5.

What is a distance modulus?

Definition:

Distance modulus is the difference between apparent magnitude m (corrected for extinction) and absolute magnitude M in the same band. It relates to distance through μ = 5 log₁₀(r/10 pc).

Distance modulus is used to understand the distance of extragalactic objects that are extremely far away in relative terms.

How to calculate distance modulus?

Example problem:

The following example outlines how to calculate a distance modulus.

First, determine the distance from the observer to the object in parsecs. For this example, the object is 25 parsecs away.

Next, use the formula above to calculate the distance modulus.

m − M = 5*log10(r/10)

m − M = 5*log10(25/10)

m-M = 1.9897