What this calculator does
Light from a receding source arrives stretched to longer wavelengths. The fractional stretch is called z, and measuring it against known spectral lines is how the motion of distant objects is determined.
The hydrogen-alpha line at 656.3 nm is the classic reference, because its rest wavelength is known exactly. Any shift away from that figure is a direct measurement of motion along the line of sight.
The formula
Redshift z is the change in wavelength divided by the emitted wavelength. Converting that to a velocity uses the relativistic Doppler relation rather than a simple proportion, since large redshifts correspond to speeds where relativity matters.
| Term | Meaning |
|---|---|
| Redshift (z) | The fractional increase in wavelength. Positive means receding; negative is a blueshift, meaning approach. |
| Rest wavelength | The wavelength the line would have if the source were stationary relative to the observer. |
| Relativistic Doppler | The correct velocity relation at high speed, which keeps velocities below the speed of light however large z becomes. |
The inputs explained
| Field | What to enter |
|---|---|
| Emitted (rest-frame) wavelength (nm) | The emitted or rest-frame wavelength in nanometres. Hydrogen-alpha is 656.3. |
| Observed wavelength (nm) | The observed wavelength in nanometres. Larger than the emitted value means a redshift. |
When to use it
Measuring a galaxy's recession
Comparing an observed spectral line against its laboratory wavelength gives z directly, and from that the velocity.
Detecting an approaching object
A blueshift, where the observed wavelength is shorter, indicates motion toward the observer.
Checking a published redshift
Astronomical sources quote z routinely, and recalculating from wavelengths confirms what it corresponds to.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What recession velocity does a given wavelength shift imply?
The same rest wavelength observed at increasing values.
| Observed wavelength | Redshift z | Recession velocity (relativistic) |
|---|---|---|
| 660 nm | 0.0056 | 1,685,366 m/s |
| 700 nm | 0.0666 | 19,298,598 m/s |
| 800 nm | 0.2190 | 58,593,370 m/s |
| 1000 nm | 0.5237 | 119,283,850 m/s |
Questions
Does redshift always mean the object is moving away?
For nearby objects, yes, it is ordinary Doppler motion. For distant galaxies the dominant cause is the expansion of space itself stretching the light in transit, which is cosmological redshift rather than motion through space.
Why not just multiply z by the speed of light?
That approximation is fine for small z but fails badly at large values, where it would give velocities above light speed. The relativistic relation keeps the result physically sensible however large z gets.
Can z exceed 1?
Yes, and the most distant observed objects have z well above 10. That does not mean faster than light: the relativistic relation maps any z, however large, onto a velocity below c.
What is a blueshift?
The opposite case, where the observed wavelength is shorter than the emitted one, indicating approach. The Andromeda galaxy is blueshifted because it is moving toward us.
For the sound equivalent of the same effect, see the Doppler effect calculator. For the photon energies involved, see the photon energy calculator.