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Redshift To Distance Calculator

Work out redshift to distance instantly with clear inputs, formula shown and shareable results.

About Redshift To Distance Calculator

For nearby galaxies, Hubble's law inverted gives distance as cz/H0. A redshift of 0.05 corresponds to 14,990 km/s and, at H0 = 70, a distance of 214 Mpc - about 700 million light years. Above z of roughly 0.1 the relativistic Doppler expression is used, and beyond z of 1 a full cosmological model is required.

Formulas

Hubble distance

d = v / H0, with v = cz for small z

Relativistic velocity

v = c((1+z)^2 - 1) / ((1+z)^2 + 1)

Worked example

With the default values below, Redshift To Distance Calculator returns Distance of 214.14. Change any input above and every figure here is recalculated in your browser.

Inputs used

Redshift zminimum 0
0.05
Hubble constantminimum 0 km/s/Mpc
70 km/s/Mpc

Results

Distance
214.14 Mpc
Recession Velocity
14,989.6 km/s
Distance In Light Years
6.9842 × 10⁸
Approximate Light Travel Time
0.698 Gyr

Step by step

  1. 1Values used
  2. 2Hubble distance
  3. 3Relativistic velocity
  4. 4Distance= 214.14 Mpc
  5. 5Recession Velocity= 14,989.6 km/s
  6. 6Distance In Light Years= 698,423,000.0000
  7. 7Approximate Light Travel Time= 0.698 Gyr

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does the simple formula fail at high redshift?

Because cz exceeds the speed of light above z = 1, and because expansion history matters over billions of years.

Which distance does this give?

Roughly the light travel distance for small z. At high redshift comoving, luminosity and angular diameter distances all differ substantially.

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