Hubble Time Calculator Formula
Understand the math behind the hubble time 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 / 3.156e16Hubble Radius
hubble_radius_mpc = 2.998e5 / hubble_constantVariables
| Variable | Description | Default |
|---|---|---|
hubble_constant | Hubble 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.
- 01t_H = 3.086e19 / H0
- 02t_H = 3.086e19 / 70 = 4.409e17 s
- 03In Gyr: 4.409e17 / 3.156e16 = 13.97 Gyr
- 04Hubble radius = c / H0 = 299800 / 70 ≈ 4283 Mpc
Frequently Asked Questions
What is the Hubble radius?
The Hubble radius (or Hubble sphere) is the distance at which the recession velocity equals the speed of light: d_H = c / H0.
Is the Hubble time constant?
No. As the universe evolves the Hubble parameter changes, so the Hubble time changes too. The Hubble constant is its present-day value.
How does the Hubble time relate to the age of the universe?
For a matter-dominated universe the age is about 2/3 of the Hubble time. With dark energy the age is close to the Hubble time.
Ready to run the numbers?
Open Hubble Time Calculator