Hubble Time Calculator Formula

Understand the math behind the hubble time calculator. Each variable explained with a worked example.

Use the Hubble Time Calculator

Formulas Used

Hubble Time

hubble_time_s = 3.086e19 / hubble_constant

Hubble Time (Gyr)

hubble_time_gyr = 3.086e19 / hubble_constant / 3.156e16

Hubble Radius

hubble_radius_mpc = 2.998e5 / hubble_constant

Variables

VariableDescriptionDefault
hubble_constantHubble Constant (H0)(km/s/Mpc)70

How It Works

The Hubble Time

The Hubble time is the reciprocal of the Hubble constant, giving the time scale of the present expansion.

Formula

t_H = 1 / H0

To convert, note that 1 km/s/Mpc = 1 / (3.086 x 10¹⁹ s).

The Hubble radius c / H0 defines the distance at which the recession velocity equals the speed of light.

Worked Example

H0 = 70 km/s/Mpc.

hubble_constant = 70
  1. 01t_H = 3.086e19 / H0
  2. 02t_H = 3.086e19 / 70 = 4.409e17 s
  3. 03In Gyr: 4.409e17 / 3.156e16 = 13.97 Gyr
  4. 04Hubble radius = c / H0 = 299800 / 70 ≈ 4283 Mpc

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