iCosmos › Distance modulus calculator

Distance modulus calculator

The difference between apparent and absolute magnitude at redshift z: μ = m − M.

The interactive calculator loads here: change the redshift and the cosmological parameters (Ω_m, Ω_Λ, Ω_r, w₀, w_a, H₀) and the result and plot update instantly.

What it is

The distance modulus expresses the luminosity distance on the astronomical magnitude scale. If you know a source’s absolute magnitude M, its apparent magnitude is m = M + μ.

Supernova cosmology works in exactly this form: the Hubble diagram plots μ against z, and different cosmologies predict different curves.

Formula

• μ = m − M = 5 log₁₀(D_L / 10 pc) = 5 log₁₀(D_L / Mpc) + 25

Worked example

In the classic model (Ω_m = 0.3, Ω_Λ = 0.7, H₀ = 70 km s⁻¹ Mpc⁻¹), μ(z = 1) = 44.10 mag (D_L = 6,607.66 Mpc) and μ(z = 0.1) = 38.32 mag.

A Type Ia supernova with peak absolute magnitude M ≈ −19.3 (B band, for H₀ ≈ 70) would therefore appear at about m ≈ 24.8 at z = 1, before K-corrections.

Common questions

Does the distance modulus include extinction or K-corrections?

No. It is the purely cosmological distance modulus. Dust extinction and the K-correction for the filter and spectrum must be added separately.

Related calculators

• Luminosity distance calculator
• Redshift to distance calculator
• Angular diameter distance calculator
• The full iCosmos cosmology calculator

About iCosmos

iCosmos was created by Mihran Vardanyan. Mihran Vardanyan is a cosmologist who earned his DPhil in cosmology at the University of Oxford, supervised by Joseph Silk and Roberto Trotta. He developed iCosmos during his research years at Oxford Astrophysics, where his work applied Bayesian model selection to the curvature and size of the Universe.

How to cite: Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.