Doppler Redshift Calculator
Cosmological redshift measures how much light from distant objects has been stretched by the expansion of the universe. Redshift z = 1 means the universe has expanded to twice its size since the light was emitted.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Redshift | z | z = Δλ/λ = v/c (small v) | — |
| Relativistic | z | z = √((1+v/c)/(1−v/c)) − 1 | — |
| Distance (Hubble) | d | d = cz/H0 | Mpc |
| Lookback Time | t | ~z/H0 (approx, low z) | Gyr |
Step-by-Step Examples
H-alpha normally at 656 nm, observed at 700 nm.
- z = (700-656)/656 = 44/656 = 0.067
- v = c * z = 0.067 * 3e5 = 20,100 km/s
- d = v/H0 = 20,100/70 = 287 Mpc
Known redshift z=3 (observed wavelengths 4x rest).
- v = c*((4^2-1)/(4^2+1)) = c*15/17 = 0.882c
- d = c*z/H0 = 3e5*3/70 = 12,857 Mpc
Cosmic Microwave Background: rest T=3000 K (recombination), observed T=2.725 K.
- z = 3000/2.725 - 1 = 1100
- Universe has expanded 1101x since recombination ~380,000 years after Big Bang
Real-World Applications
Common Mistakes to Avoid
z = v/c only valid for v << c. Use z = sqrt((1+v/c)/(1-v/c)) - 1 for relativistic recession.
Cosmological redshift is from space expanding, not object motion. True velocity is defined differently. For small z, cz gives recession velocity.
d = cz/H0 valid only for z < 0.1. For larger z, full cosmological model needed, depending on dark energy equation of state.
Frequently Asked Questions
Related Physics Calculators
Formula Explorer connections
Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.