Case 1
- Observed wavelength
- 660nm
- Rest wavelength
- 656.3nm
0.005638
Open with these valuesRedshift Calculator
0.005638
Result: 0.005638Redshift z is how much a spectral line has been stretched: the observed wavelength minus the rest wavelength, divided by the rest wavelength. Any wavelength unit works as long as both use the same one, because z is a ratio. A negative z is a blueshift — the source is approaching.
Worked examples
Case 2
- Observed wavelength
- 434nm
- Rest wavelength
- 410nm
0.058537
Open with these valuesCase 3
- Observed wavelength
- 243.2nm
- Rest wavelength
- 121.6nm
1.000000
Open with these valuesHow it's calculated
z = (λ_obs − λ_rest) ÷ λ_rest
- StepEnter the wavelength of the line as you measured it.
- StepEnter the wavelength of the same line at rest in the lab.
- StepUse the same unit for both — the unit cancels out.
- ResultRead z: positive is a redshift, negative a blueshift.
Reference table
| Observed, rest (nm) | Line | Redshift z |
|---|---|---|
| 656.3, 656.3 | Hα, no shift at all | 0 |
| 650, 656.3 | Hα, blueshift — source approaching | -0.009599 |
| 660, 656.3 | Hα, slight recession | 0.005638 |
| 434, 410 | Hγ | 0.058537 |
| 600, 500 | — | 0.2 |
| 243.2, 121.6 | Lyman α, wavelength doubled | 1 |
Questions
How do I calculate redshift?
Subtract the rest wavelength from the observed wavelength, then divide by the rest wavelength: z = (λ_observed − λ_rest) / λ_rest. A hydrogen-alpha line shifted from 656.3 nm to 660 nm gives about 0.005638.
What is redshift?
Redshift is the stretching of light to longer, redder wavelengths when a source moves away from us. It is written as z, a dimensionless number, and the larger z is, the more the light has been stretched.
Does it matter which wavelength unit I use?
No, as long as both wavelengths use the same unit. Redshift z is a ratio of two wavelengths, so the unit cancels out. Nanometres, ångströms and micrometres all work; just never mix them between the two fields.
How do I turn redshift into a recession velocity?
For small z the recession velocity is roughly v ≈ c × z, with c the speed of light. That approximation is only good well below z of about 0.1: at z = 1 it would give exactly the speed of light, which is wrong, and the relativistic Doppler formula is needed instead. This calculator therefore returns z itself, which is exact.
What is the difference between redshift and blueshift?
A positive z means the observed wavelength is longer than the rest wavelength and the source is moving away. A negative z means it is shorter and the source is approaching, like the Andromeda galaxy heading toward the Milky Way.
Sources and last check
Information, not professional advice.