Cosmic Age Calculator Formula

Understand the math behind the cosmic age calculator. Each variable explained with a worked example.

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Formulas Used

Hubble Time

hubble_time_s = 3.086e19 / hubble_constant

Hubble Time (Gyr)

hubble_time_gyr = 3.086e19 / hubble_constant / 3.156e16

Variables

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

How It Works

Estimating the Age of the Universe

The simplest age estimate comes from inverting the Hubble constant.

Formula

t_H = 1 / H0

Converting H0 from km/s/Mpc to 1/s requires dividing by 3.086 x 10¹⁹ km/Mpc. The result, about 14 Gyr for H0 = 70, is close to the accepted age of 13.8 Gyr because dark-energy acceleration partially compensates for the deceleration of matter.

Worked Example

H0 = 70 km/s/Mpc.

hubble_constant = 70
  1. 01t_H = 1 / H0 in SI
  2. 02H0 in 1/s = 70 / 3.086e19 = 2.269e-18 s⁻¹
  3. 03t_H = 1 / 2.269e-18 = 4.407e17 s
  4. 04t_H = 4.407e17 / 3.156e16 = 13.96 Gyr

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