What is the Redshift Calculator?
Calculate cosmological redshift from rest and observed wavelengths, or convert between redshift and recession velocity with this free redshift calculator. Get Hubble distance, scale factor, and relativistic velocity. Includes H-alpha, Lyman-alpha, and quasar presets. Runs entirely in your browser with no signup.
How to use the Redshift Calculator
- Choose Wavelength, Redshift, or Velocity mode.
- Enter rest and observed wavelengths, redshift z, or recession velocity.
- Set the Hubble constant H₀ (default 70 km/s/Mpc) for distance estimates.
- Click Calculate to get z, velocity, scale factor, and Hubble distance.
- Copy results and step-by-step formulas.
Common use cases
- Computing redshift from a shifted H-alpha spectral line
- Finding recession velocity for a galaxy with z = 0.5
- Estimating Hubble distance for a quasar at z = 6
Frequently asked questions
- How is redshift calculated from wavelength?
- z = (λ_observed − λ_rest) / λ_rest. A positive z means the source is redshifted (receding); a negative z is a blueshift (approaching).
- What is the relativistic velocity formula?
- For radial motion, v = c × ((1+z)² − 1) / ((1+z)² + 1). At low z this approximates the classical v ≈ cz.
- What is Hubble distance?
- Using Hubble's law v ≈ H₀d, distance d ≈ cz/H₀. With H₀ = 70 km/s/Mpc and z = 0.1, d ≈ 428 Mpc. This is a low-redshift approximation.
- What does the scale factor mean?
- The cosmological scale factor a = 1/(1+z). A redshift of z = 1 means the universe was half its current size when the light was emitted.
