Analyze observed wavelength, redshift, frequency, and gamma precisely. Enter rest wavelength and speed inputs clearly. Plot trends, export values, and compare classical estimates fast.
This calculator uses the line-of-sight relativistic Doppler wavelength relation.
The graph shows observed wavelength versus beta for approaching and receding motion using the current rest wavelength.
For line-of-sight motion, let β = v / c.
For a receding source:
λobs = λrest × √((1 + β) / (1 - β))
For an approaching source:
λobs = λrest × √((1 - β) / (1 + β))
The redshift is:
z = (λobs / λrest) - 1
The Lorentz factor is:
γ = 1 / √(1 - β²)
The observed frequency follows from:
f = c / λ
The calculator also compares the exact relativistic value with the low-speed classical approximation.
| Spectral line | Rest wavelength | Beta | Direction | Observed wavelength | Redshift z |
|---|---|---|---|---|---|
| Hydrogen H-alpha | 656.28 nm | 0.1 | Receding | 725.5448 nm | 0.105542 |
| Hydrogen H-beta | 486.13 nm | 0.2 | Approaching | 396.9235 nm | -0.183503 |
| Lyman-alpha | 121.57 nm | 0.35 | Receding | 175.201 nm | 0.441153 |
| Sodium D line | 589.29 nm | 0.05 | Approaching | 560.5266 nm | -0.04881 |
The relativistic Doppler effect describes how motion changes the wavelength of light measured by an observer. When a source moves away, the observed wavelength stretches and creates a redshift. When a source moves toward the observer, the wavelength compresses and creates a blueshift.
At low speeds, a classical estimate can be useful. At higher speeds, relativity becomes necessary because time dilation changes the result. That is why this calculator reports both the exact relativistic wavelength and a classical comparison value. The difference between them grows as the speed approaches the speed of light.
This tool is useful for astronomy, spectroscopy, and physics education. You can test how emission lines shift for stars, galaxies, fast-moving plasmas, or thought experiments in special relativity. The calculator also reports redshift, observed frequency, beta, and gamma, which makes it easier to interpret motion from measured wavelengths.
Because the formula here is for line-of-sight motion, it is best used when the source moves directly toward or directly away from the observer. For angled motion, a more general relativistic Doppler treatment is needed. For radial motion, however, this calculator gives a fast and reliable way to analyze wavelength change.
It computes the observed wavelength from a rest wavelength and a relativistic speed. It also shows redshift, frequency, beta, gamma, and a classical comparison.
Use it whenever the source speed is a meaningful fraction of light speed. At high speeds, classical formulas become inaccurate because time dilation matters.
Approaching motion compresses the incoming wave pattern. The observer receives wave crests closer together, so the measured wavelength becomes shorter.
Receding motion stretches the spacing between received wave crests. That makes the observed wavelength longer and produces a redshift.
Beta is the speed ratio v/c. A beta of 0.20 means the source moves at twenty percent of the speed of light.
Redshift z measures the fractional wavelength change. Positive z indicates redshift, while negative z indicates blueshift.
Yes. The calculator accepts meters, centimeters, millimeters, micrometers, nanometers, and angstroms, then keeps the displayed result in your selected unit.
No. This version is designed for direct line-of-sight motion only. Angled motion requires a more general relativistic Doppler relation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.