Relativistic Doppler Effect Calculator
Find the relativistic Doppler shift in observed frequency for a source moving directly toward or away from you at relativistic speed.
📡 What is the Relativistic Doppler Effect Calculator?
This relativistic Doppler effect calculator finds the observed frequency of light or radio waves from a source moving directly toward or away from you at relativistic speed. Enter the source frequency and β=v/c, choose approaching or receding, and it returns the observed frequency and (for receding) the redshift z.
f_obs = f_source√((1∓β)/(1±β)) is the exact relativistic formula, correctly including the extra time-dilation factor beyond the classical (sound-wave) Doppler effect.
This is the exact formula astronomers use to measure recession velocities of galaxies and quasars from their observed spectral redshift, the foundational evidence for the expanding universe.
This calculator is useful for special relativity, astrophysics, and particle physics students studying frequency shift, redshift, and blueshift.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Slowly receding source
Example 2 - Approaching source (blueshift)
Example 3 - Fast receding source, exact z=2
❓ Frequently Asked Questions
🔗 Related Calculators
What is the relativistic Doppler effect?
The relativistic Doppler effect is the shift in observed frequency (or wavelength) of light or other radiation from a source moving at a significant fraction of the speed of light, correctly accounting for both the classical wave-compression effect and relativistic time dilation.
What is the formula for the relativistic Doppler effect?
For a source receding directly away: f_obs = f_source√((1−β)/(1+β)). For a source approaching directly: f_obs = f_source√((1+β)/(1−β)), where β=v/c is the source's speed as a fraction of light speed.
How is the relativistic Doppler effect different from the classical Doppler effect?
The classical (sound-wave-style) Doppler formula only accounts for the wave being compressed or stretched by relative motion. The relativistic formula adds an extra factor from time dilation, which is why even purely transverse motion (perpendicular to the line of sight) still produces a frequency shift relativistically, something the classical formula predicts as zero.
What is redshift z and how does it relate to this calculator?
Redshift z is defined by 1+z = f_source/f_obs (equivalently, observed wavelength = (1+z) times source wavelength). For a receding source, z is always positive; this calculator computes z directly in receding mode.
What is a real-world example that gives a nice round redshift value?
At β=0.8 (80% of the speed of light) receding, the relativistic Doppler formula gives an observed frequency of exactly one-third the source frequency, corresponding to a redshift of exactly z=2, a clean textbook benchmark for checking the formula.
How is the relativistic Doppler effect used in astronomy?
It is the primary tool for measuring how fast distant galaxies and quasars are receding from Earth, by comparing observed spectral line wavelengths to their known laboratory (rest-frame) wavelengths. This measurement, applied across many galaxies, provided the original observational evidence for the expanding universe (Hubble's law).
What happens when β approaches 1 for a receding source?
As β approaches 1 (the source's speed approaches the speed of light), the observed frequency ratio √((1−β)/(1+β)) approaches zero, meaning the observed frequency drops toward zero (infinite redshift), reflecting the extreme time dilation of a source moving at nearly light speed.
Does the relativistic Doppler formula apply to sound waves?
No, the relativistic Doppler formula specifically applies to electromagnetic waves (light, radio, etc.) traveling at the invariant speed c. Sound waves travel through a medium at a fixed speed relative to that medium, so they follow the classical (non-relativistic) Doppler formula, which behaves quite differently at high source speeds.
Is there a difference between the source moving and the observer moving?
For purely relative radial motion, no, only the relative velocity β between source and observer matters, exactly consistent with the principle of relativity (there is no absolute rest frame to distinguish which one is 'really' moving).
Can this calculator be used for blueshift as well as redshift?
Yes, select the approaching mode for a source moving toward the observer, which produces a higher observed frequency than the source frequency (blueshift), the mirror image of the receding (redshift) case.