Dark Energy Density Calculator Formula

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

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Formulas Used

Dark Energy Density

dark_energy_density = cosmological_constant * pow(2.998e8, 2) / (8 * pi * 6.674e-11)

Energy Density (GeV/m³)

dark_energy_density_gev = cosmological_constant * pow(2.998e8, 2) / (8 * pi * 6.674e-11) * pow(2.998e8, 2) / 1.602e-10

Variables

VariableDescriptionDefault
cosmological_constantCosmological Constant (Lambda)(1/m²)1.1056e-52

How It Works

Calculating Dark Energy Density

Dark energy drives the accelerating expansion of the universe. Its density is linked to the cosmological constant.

Formula

rho_Lambda = Lambda * c² / (8 pi G)

  • *Lambda* is the cosmological constant (~1.1 x 10⁻⁵² m⁻²)
  • *c* is the speed of light
  • *G* is the gravitational constant

    • The resulting density is extremely small but dominates the total energy budget of the cosmos.

    Worked Example

    Use the observed cosmological constant Lambda = 1.1056e-52 m⁻².

    cosmological_constant = 1.1056e-52
    1. 01rho = Lambda * c² / (8 pi G)
    2. 02c² = (2.998e8)² = 8.988e16
    3. 038 pi G = 8 * 3.14159 * 6.674e-11 = 1.676e-9
    4. 04rho = 1.1056e-52 * 8.988e16 / 1.676e-9
    5. 05rho ≈ 5.93e-27 kg/m³

    Ready to run the numbers?

    Open Dark Energy Density Calculator