Turn redshift or velocity with distance into H0. See uncertainty and age estimates in seconds. Export clean tables with unit conversions for reports today.
| Case | Velocity (km/s) | Distance (Mpc) | H0 (km/s/Mpc) | h | Age (Gyr) ≈ 9.78/h |
|---|---|---|---|---|---|
| A | 7000 | 100 | 70 | 0.70 | 13.97 |
| B | 5000 | 75 | 66.67 | 0.6667 | 14.67 |
| C | 8200 | 110 | 74.55 | 0.7455 | 13.12 |
Hubble’s law (low redshift): v ≈ H0 · d
So the Hubble constant is:
H0 = v / d (units: km/s/Mpc when v is km/s and d is Mpc)
Redshift option:
Uncertainty propagation (optional):
σH0 / H0 = √[(σv/v)² + (σd/d)²], and the same relative error applies to the simple age estimate t ≈ 1/H0.
Use consistent units, and keep a record of assumptions.
The Hubble constant H0 links a galaxy’s recession speed to its proper distance in the nearby universe. It summarizes today’s cosmic expansion rate and sets the scale for distance–time conversions. In practice, H0 is reported in km/s/Mpc for direct comparison across surveys.
This calculator accepts velocity directly or derives it from redshift. For small z, the approximation v = c·z is convenient and widely used. At larger z, the relativistic Doppler option reduces bias from using a purely linear rule. Always ensure z corresponds to the same reference frame as your distance.
Distances appear in many forms: parsecs, kiloparsecs, megaparsecs, light‑years, and kilometers. Converting to Mpc keeps H0 in the standard cosmology unit. Internally, the calculator converts your chosen unit to Mpc before applying H0 = v/d. This avoids hidden scaling mistakes in reports.
Nearby galaxies have additional motions from local gravity, called peculiar velocities. These can be hundreds of km/s and may dominate over Hubble flow when distances are small. For improved estimates, prefer targets beyond the local volume, average over many objects, or use group/cluster means where random motions partially cancel.
Measurement errors matter because H0 depends on both velocity and distance. When you enter σv and σd, the calculator applies standard propagation: the fractional uncertainty in H0 is the quadrature sum of fractional uncertainties in v and d. This produces a practical ± value suitable for lab write‑ups.
A useful intuition is the “Hubble time” t ≈ 1/H0. The calculator reports this in gigayears and also shows the common approximation 9.78/h Gyr, where h = H0/100. This is not the exact universe age in ΛCDM, but it gives a clean scale for expansion timing.
Different methods can yield slightly different H0 values because of calibration choices, sample selection, and astrophysical systematics. Treat a single calculation as a measurement model, not a final truth. Compare against multiple objects, check residuals, and document whether your velocity came from spectra or assumptions about z.
After computing, export CSV for spreadsheets or PDF for quick sharing. Include the input distance unit, the redshift‑to‑velocity mode, and any uncertainties used. Recording these details prevents confusion when results are revisited later. Consistent formatting also helps compare datasets across instruments and observing campaigns.
Use km/s for velocity and Mpc for distance to get km/s/Mpc. If you choose other distance units, the calculator converts them to Mpc automatically before computing H0.
Use v = c·z for small redshifts where z is well below 0.1 and the linear relation is a good approximation. For higher z, select the relativistic option to reduce bias.
H0 depends on distance calibration, sample selection, local motions, and systematic effects in instruments and astrophysical models. Different methods can disagree slightly even with excellent statistics.
No. 1/H0 is a convenient timescale. The actual age depends on the full cosmological model and parameters like matter density and dark energy, so it can differ from the Hubble time.
It estimates σH0 using standard propagation: σH0/H0 = √[(σv/v)² + (σd/d)²]. If you also view the age scale, it applies the same fractional uncertainty to that estimate.
Very nearby objects can be dominated by peculiar velocities, making H0 noisy. Using more distant galaxies, clusters, or larger samples usually improves stability and reduces local motion bias.
Any method that yields a proper distance works, such as standard candles, surface brightness fluctuations, or calibrated redshift‑independent distances. The key is pairing it with a consistent recession velocity measurement.
Accurate inputs make better cosmology insights, always verify sources.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.