Cosmic Age Calculator Formula
Understand the math behind the cosmic age calculator. Each variable explained with a worked example.
Formulas Used
Hubble Time
hubble_time_s = 3.086e19 / hubble_constantHubble Time (Gyr)
hubble_time_gyr = 3.086e19 / hubble_constant / 3.156e16Variables
| Variable | Description | Default |
|---|---|---|
hubble_constant | Hubble 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.
- 01t_H = 1 / H0 in SI
- 02H0 in 1/s = 70 / 3.086e19 = 2.269e-18 s⁻¹
- 03t_H = 1 / 2.269e-18 = 4.407e17 s
- 04t_H = 4.407e17 / 3.156e16 = 13.96 Gyr
Frequently Asked Questions
Is the Hubble time the true age of the universe?
Not exactly. The Hubble time is an approximation. The true age depends on the full expansion history, including matter and dark energy contributions.
Why is the Hubble time close to the accepted age?
The decelerating effect of matter and the accelerating effect of dark energy roughly cancel, making 1/H0 a surprisingly good approximation.
What is the currently accepted age?
About 13.787 billion years, based on Planck satellite measurements of the cosmic microwave background.
Ready to run the numbers?
Open Cosmic Age Calculator