Age of the Universe from Hubble Constant

Hubble time is the simplest estimate for the age of the universe:

t_H = 1 / H₀

This assumes the universe has been expanding at a constant rate, which it has not.

Converting H₀ to SI units:

H₀ (1/s) = H₀ (km/s/Mpc) × 1000 / (3.0857 × 10²²)

1 Megaparsec = 3.0857 × 10²² meters.

ΛCDM correction: In the standard ΛCDM model (Lambda Cold Dark Matter, where Lambda is dark energy and CDM is cold dark matter), the universe’s expansion was decelerating early on (matter-dominated) and is now accelerating (dark energy dominated). Accounting for this, the actual age is:

t₀ ≈ 0.951 / H₀

That gives 13.80 billion years for H₀ = 67.4 km/s/Mpc, which matches what the cosmic microwave background says on its own.

Where does 0.951 come from? It is not a fudge factor. Integrate the expansion history of a flat universe with 31.5% matter and 68.5% dark energy, and the age comes out at 0.951 Hubble times. You will also see 0.964 quoted, which assumes 30% matter instead. On a 14.5 Gyr Hubble time the two differ by 0.19 Gyr, and that is enough to matter when the whole Hubble tension is a one-billion-year argument.

The Hubble tension: Different measurement methods give slightly different H₀ values:

• CMB-based (Cosmic Microwave Background, from Planck): H₀ = 67.4 ± 0.5 km/s/Mpc → t₀ ≈ 13.80 Gyr
• Distance ladder: H₀ = 73.0 ± 1.0 km/s/Mpc → t₀ ≈ 12.74 Gyr

This ~5σ discrepancy between local and early-universe measurements is one of the biggest unsolved problems in cosmology. It may indicate new physics (dark energy evolving over time, additional light particles, etc.) or systematic measurement errors.

For context:

• Solar System age: ~4.57 billion years
• First stars formed: ~200–400 million years after Big Bang
• Milky Way formation: ~1 billion years after Big Bang
• Oldest observed galaxies: z ≈ 10 is about 470 million years after the Big Bang, and the current record holder JADES-GS-z14-0 at z ≈ 14.3 is about 290 million years

Those last two numbers are worth pausing on, because they are the reason the age of the universe stopped being an armchair question. JWST is finding galaxies at 290 million years that are brighter and more massive than the models expected to exist that early. Nobody thinks that breaks the 13.8-billion-year figure, but it does put pressure on how fast the first structures could assemble, and a shorter universe would squeeze that window further. The distance-ladder value of 73 km/s/Mpc would leave only 12.7 billion years to fit everything into.