Baryon Density Calculator Formula
Understand the math behind the baryon density calculator. Each variable explained with a worked example.
Formulas Used
Baryon Density Parameter
omega_b = baryon_density / critical_densityBaryon Fraction (%)
omega_b_pct = (baryon_density / critical_density) * 100Variables
| Variable | Description | Default |
|---|---|---|
baryon_density | Baryon Density(kg/m³) | 4.2e-28 |
critical_density | Critical 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.
- 01Omega_b = rho_b / rho_crit
- 02Omega_b = 4.2e-28 / 9.47e-27
- 03Omega_b ≈ 0.0443
- 04As a percentage: 4.43%
Frequently Asked Questions
What counts as baryonic matter?
All matter made of protons and neutrons: stars, planets, gas, dust, and diffuse intergalactic plasma. Electrons are included by convention.
Where is most of the baryonic matter?
Most is in the warm-hot intergalactic medium (WHIM) between galaxies. Only a small fraction is in stars and planets.
How is Omega_b measured?
Primarily from Big Bang nucleosynthesis abundances (deuterium, helium) and the acoustic peaks of the cosmic microwave background.
Ready to run the numbers?
Open Baryon Density Calculator