Cosmological Redshift Calculator

Redshift is the stretching of light to longer, redder wavelengths as a source recedes from us. For galaxies it grows with distance because the expanding universe stretches the light while it travels, so a larger z generally means a more distant object.

z equals the observed wavelength minus the rest wavelength, all divided by the rest wavelength. A z of 0.01 means the light was stretched by one percent. For the hydrogen-alpha line at 656.3 nm observed at 660 nm, that gives z of about 0.00563767.

This tool uses the non-relativistic Doppler approximation, v = c times z, with c near 299792 km/s. It is accurate at small z but overstates the true speed as z grows, so treat large-z velocities as rough estimates rather than physical speeds.

It is the recession velocity divided by the Hubble constant, v over H0. With H0 set to 70 km/s/Mpc, a velocity of 1690.13 km/s gives roughly 24.1447 megaparsecs. Changing the Hubble constant rescales the distance without changing z or velocity.

The Doppler approximation gives v = c at z = 1, shown here as 299792 km/s, but the correct relativistic treatment always keeps velocity below c. That is why this estimate is only reliable at low redshift, where the two formulas nearly agree.

There is no single agreed value. Measurements from the cosmic microwave background favor about 67 km/s/Mpc, while local distance-ladder methods favor roughly 73, a gap known as the Hubble tension. The tool defaults to 70 as a middle-ground round number you can override.

Both rest and observed wavelengths are entered in nanometres, and they must be positive. Because z is a ratio, the actual unit cancels out, so you can convert angstroms or micrometres to nanometres first and still get the same z.

Internally z is rounded to nine decimals and velocity to four, then each result is displayed to six significant figures, switching to scientific notation for very large or very small values. The distance depends on your chosen Hubble constant, so its precision is limited by how well H0 is known.

No. The redshift, velocity and distance are all computed locally in your browser, so the wavelengths or z values you enter stay on your device.