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Cosmology Suite Calculator

Complete cosmology calculations. Hubble's law, cosmic distances, Big Bang timeline, dark matter/energy, CMB analysis, and black hole physics.

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How to Use This Calculator
  1. Use the Hubble module to enter a redshift (z) and Hubble constant to compute recession velocity and comoving distance.
  2. Switch to the Composition tab and enter Ω_matter, Ω_dark matter, and Ω_Lambda to see the pie chart of cosmic energy budget and the Universe Fate.
  3. In the CMB section, input the CMB temperature (2.725 K default) to see peak wavelength (mm) and photon density.
  4. Use the Black Hole tab to enter black hole mass and spin parameter to compute Schwarzschild radius, Hawking temperature, and ISCO.
  5. Cross-reference the Universe Age (Gyr) and Matter-Λ Equality redshift outputs to place cosmological events on a timeline.

What each input means

Calculation Type
Calculation mode to use.
Redshift (z)
Observed redshift of object
Hubble Constant (km/s/Mpc)
H₀ ≈ 70 km/s/Mpc
Time After Big Bang (years)
Enter time in years
Scale Factor (a)
a = 1 today, a = 0 at Big Bang
CMB Temperature (K)
Measured: 2.72548 ± 0.00057 K
Dipole Amplitude (mK)
Due to Solar System motion
Fluctuation Level (μK)
Primary anisotropies
Black Hole Mass (M☉)
In solar masses
Spin Parameter (a/M)
0 = Schwarzschild, 1 = extremal Kerr

How this is calculated

Formula

v = H₀d (Hubble) | r_s = 2GM/c² | T_H = ℏc³/(8πGMk_B)

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Calculation Type = 0, Redshift (z) = 0.1, Hubble Constant (km/s/Mpc) = 70, Ωm (Matter Density) = 0.3 = 16 input(s) provided
  2. Calculate Recession Velocity
    Recession Velocity
    29979.2458 = 29979.2458
  3. Calculate Comoving Distance
    Comoving Distance
    1.3648144186670264 = 1.3648144186670264
  4. Calculate Luminosity Distance
    Luminosity Distance
    1.501295860533729 = 1.501295860533729
  5. Calculate Lookback Time
    Lookback Time
    1.3013070119190429 = 1.3013070119190429

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.

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