Spectral redshift from wavelength
Redshift z measures the fractional change between an observed spectral wavelength and its laboratory rest wavelength. Longer observed wavelength gives positive z; shorter wavelength gives negative z.
The wavelength definition itself does not identify the physical cause or uniquely convert z into velocity or distance.
How to calculate redshift
- Select the unknown: Choose z, observed wavelength, or rest wavelength.
- Enter two values: Use the same wavelength unit for both wavelengths.
- Calculate: Generate the missing value.
Formula and variables
Observed and rest wavelengths must use the same unit.
z = (λobs − λ₀)/λ₀ = λobs/λ₀ − 1- z — Redshift
- Fractional wavelength change
- λobs — Observed wavelength
- Measured spectral-line wavelength (nm)
- λ₀ — Rest wavelength
- Laboratory wavelength (nm)
A ten-percent wavelength shift
A 500 nm rest line is observed at 550 nm.
- λobs
- 550 nm
- λ₀
- 500 nm
- z = (550−500)/500
Result: z = 0.1.
The line is redshifted to a wavelength 10% longer than its rest value.
Understanding your results
Redshift is not automatically velocity
At small Doppler shifts z approximates radial velocity divided by c, but relativistic and cosmological interpretations require appropriate models.
- z > 0 is redshift.
- −1 < z < 0 is blueshift by this wavelength definition.
Assumptions
- Both values identify the same spectral feature.
- Wavelengths use the same reference frame convention and unit.
Limitations
- Does not calculate velocity, cosmological distance, scale factor, or lookback time.
- Does not correct for instrument calibration or line identification.
Common mistakes
- Using different wavelength units.
- Reversing observed and rest wavelength.
- Treating every redshift as a classical Doppler velocity.
Practical use cases
Spectral-line analysis
Quantify the fractional displacement of a known line.
Frequently asked questions
Can redshift be negative?
Yes. A shorter observed wavelength gives a negative z, commonly called blueshift.
Does z = 1 mean the wavelength doubled?
Yes. Since λobs = λ₀(1+z), z = 1 gives twice the rest wavelength.
Sources and review
- Math of the Expanding Universe — NASA Jet Propulsion Laboratory. Accessed 2026-07-13.
Reviewed 2026-07-13.