Matter Density Parameter Calculator Formula

Understand the math behind the matter density parameter calculator. Each variable explained with a worked example.

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Formulas Used

Matter Density Parameter (Omega_m)

omega_m = matter_density / critical_density

As Percentage

omega_m_pct = (matter_density / critical_density) * 100

Variables

VariableDescriptionDefault
matter_densityMatter Density (rho_m)(kg/m³)2.65e-27
critical_densityCritical Density (rho_crit)(kg/m³)9.47e-27

How It Works

How the Matter Density Parameter Is Found

The density parameter Omega_m tells us the fraction of the universe's critical density that is in the form of matter.

Formula

Omega_m = rho_m / rho_crit

  • *rho_m* is the average matter density
  • *rho_crit* is the critical density

    • If Omega_total = 1 the universe is geometrically flat. Current measurements give Omega_m about 0.31.

    Worked Example

    With rho_m = 2.65e-27 kg/m³ and rho_crit = 9.47e-27 kg/m³.

    matter_density = 2.65e-27critical_density = 9.47e-27
    1. 01Omega_m = rho_m / rho_crit
    2. 02Omega_m = 2.65e-27 / 9.47e-27
    3. 03Omega_m ≈ 0.2799

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