Hubble Law Calculator

In 1929, Edwin Hubble noticed something odd about the handful of galaxies whose distances and spectra had been measured: the farther away a galaxy was, the faster it appeared to be receding from us. Plot one against the other and the points fall — roughly, for anything reasonably nearby — on a straight line through the origin.

The formula

Here $d$ is a galaxy’s distance, $v$ is its recession velocity (read off its redshift), and $H_0$ — the Hubble constant — is the slope of that line: how fast the relationship between distance and velocity scales, in kilometers per second per megaparsec. It is simultaneously one of the simplest equations in cosmology and, because of exactly how that slope gets measured, one of the most argued-over numbers in the field.

The Hubble tension

$H_0$ isn’t a single agreed-upon number. Measurements built from the “distance ladder” — Cepheid variable stars and Type Ia supernovae in relatively nearby galaxies — tend to land around 73 km/s/Mpc. Measurements derived from the cosmic microwave background, run through the standard cosmological model, tend to land closer to 67 km/s/Mpc. The gap between them is small in absolute terms but statistically stubborn, and nobody has definitively shown which side (if either) has an unaccounted-for systematic error. This calculator doesn’t take a side — it just lets you slide $H_0$ across the range these methods actually produce (60–80 km/s/Mpc) so you can see how much of a difference it makes for any particular galaxy.

Reading the Hubble diagram

The chart is the whole point of the tool: distance on the x-axis, recession velocity on the y-axis, the line $v = H_0 d$ drawn for whatever $H_0$ you’ve picked, and your current distance/velocity pair marked as a dot that always sits exactly on that line — because under this linear model, that’s all a distance/velocity pair is. Drag $H_0$ and watch the line’s slope change while the dot rides along with it.

Solving in either direction

Use the toggle to pick which quantity you know:

• Distance → velocity — enter a distance in megaparsecs (or million light-years) and read off the predicted recession velocity, shown in km/s and as a fraction of the speed of light.
• Velocity → distance — enter an observed recession velocity and read off the implied distance. This direction is closer to how the relation is actually used in practice: redshift is what a spectrum directly gives you, and Hubble’s law is what turns that into a distance estimate.

Where this stops being valid

This is deliberately a linear, low-redshift tool, and it says so plainly rather than quietly producing a number that looks precise but isn’t. The straight-line $v = H_0 d$ relation is the correctly-truncated, first-order approximation to something more complicated: the full FLRW (Friedmann–Lemaître–Robertson–Walker) cosmological distance–redshift relation. That fuller relation accounts for the universe’s expansion history — how much of the cosmos is matter ($\Omega_m$ ) versus dark energy ($\Omega_\Lambda$ ) — and it also has to distinguish between several genuinely different notions of “distance” (comoving distance, luminosity distance, angular-diameter distance) that all collapse into one obvious quantity only in the nearby limit.

Concretely: the linear approximation is reasonable out to distances of roughly a few hundred megaparsecs, corresponding to redshifts $z$ ≲ 0.1-ish, and correspondingly to recession velocities that are a small fraction of the speed of light. Push it further — the way you’d have to for genuinely distant galaxies, let alone the redshifts at which quasars or the cosmic microwave background are observed — and $v = H_0 d$ stops meaningfully applying at all. This calculator will warn you as your input’s implied velocity climbs past about 10% of $c$ , and flag it more strongly past 20% of $c$ ; it intentionally does not attempt to compute a “distance” beyond that point, because doing so with this formula would just be wrong.

The presets

The Local Group, Virgo Cluster, and Coma Cluster entries are illustrative, self-consistent stand-ins (chosen to satisfy $v = H_0 d$ at $H_0$ ≈ 70 km/s/Mpc) rather than a specific literature citation — real measured distances and velocities for these clusters vary across sources and methods. They’re there to give the diagram a physically reasonable sense of scale, from “practically next door” to “a meaningful fraction of the way to where the linear approximation starts to strain.”