Baryon Density Calculator Formula

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

Use the Baryon Density Calculator

Formulas Used

Baryon Density Parameter

omega_b = baryon_density / critical_density

Baryon Fraction (%)

omega_b_pct = (baryon_density / critical_density) * 100

Variables

VariableDescriptionDefault
baryon_densityBaryon Density(kg/m³)4.2e-28
critical_densityCritical Density(kg/m³)9.47e-27

How It Works

Baryon Density Parameter

Ordinary (baryonic) matter—protons, neutrons, electrons—makes up only a small fraction of the universe.

Formula

Omega_b = rho_b / rho_crit

Current measurements give Omega_b about 0.049, meaning only roughly 5% of the total energy budget is ordinary matter.

Worked Example

rho_b = 4.2e-28 kg/m³, rho_crit = 9.47e-27 kg/m³.

baryon_density = 4.2e-28critical_density = 9.47e-27
  1. 01Omega_b = rho_b / rho_crit
  2. 02Omega_b = 4.2e-28 / 9.47e-27
  3. 03Omega_b ≈ 0.0443
  4. 04As a percentage: 4.43%

Ready to run the numbers?

Open Baryon Density Calculator