Doppler Shift Calculator
Calculate light Doppler shift / redshift using Δλ/λ = v_r/c and relativistic formula.
What Is Doppler Shift Calculator?
This calculator implements Calculate light Doppler shift / redshift using Δλ/λ = v_r/c and relativistic formula. — a core relationship in physics.
The formula follows from fundamental principles and applies across a wide range of physical scenarios.
Pay attention to units and sign conventions when using these calculations in practice.
Results are valid within the stated assumptions; real systems may deviate at extremes.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Redshift z | z = Δλ/λ = (λ_obs−λ_emit)/λ_emit | Dimensionless |
| Classical velocity | v_r = z·c | For z << 1 |
| Relativistic (exact) | z+1 = √((1+β)/(1−β)) | β = v/c |
| Recession speed | v = c·z (approx) | km/s = z × 3×10⁵ km/s |
| Hubble Law | v = H₀d; z ≈ H₀d/c | H₀ ≈ 70 km/s/Mpc |
| Blueshift | z < 0 (λ_obs < λ_emit) | Approaching object |
3 Worked Examples
H-alpha (656.3 nm) observed at 660 nm.
- z = (660−656.3)/656.3 = 0.00564
- v = 0.00564 × 3×10⁵ = 1,692 km/s
- d = v/H₀ = 1692/70 = 24.2 Mpc ≈ 79 million ly
z = 3.0.
- v = c × [(z+1)²−1]/[(z+1)²+1] = c × (15/17) = 0.882c
- Relativistic formula needed at high z
Sirius: H-alpha at 656.24 nm (rest: 656.28 nm).
- z = (656.24−656.28)/656.28 = −6.1×10⁻⁵
- v = −6.1×10⁻⁵ × 3×10⁵ = −18.3 km/s (approaching)
Real-World Applications
Common Mistakes to Avoid
SI units.
Correct variant.
Ideal conditions.
Check conventions.
Check squaring.
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.