Redshift Calculator

Calculate cosmological redshift z from observed and emitted wavelengths, or from recession velocity. Includes relativistic Doppler, look-back time, and scale factor.

nm
nm
Redshift z
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Scale Factor a —
Recession Velocity (low-z approx) —
Extended More scenarios, charts & detailed breakdown ▾
nm
nm
Redshift z
—
Scale Factor a —
Velocity (low-z) —
Professional Full parameters & maximum detail ▾
nm
nm

Redshift & Expansion

Cosmological Redshift z —
Scale Factor a = 1/(1+z) —

Velocity & Time

Velocity (relativistic) —
Look-back Time (H₀=70 approx) —

Gravitational

Gravitational Redshift —

How to Use This Calculator

  1. Enter the observed wavelength and emitted wavelength to compute redshift z.
  2. Use From Velocity tab for low-z approximation (z ≈ v/c) or relativistic Doppler.
  3. Use Relativistic Doppler tab for high velocities.
  4. Professional tier adds scale factor, look-back time estimate, and gravitational redshift.

Formula

z = (λ_obs − λ_em) / λ_em

Low-z from velocity: z ≈ v/c

Relativistic: z = √((1+v/c)/(1−v/c)) − 1

Scale factor: a = 1/(1+z)

Example

Hydrogen Lyman-α emitted at 121.6 nm, observed at 243.2 nm: z = (243.2 − 121.6) / 121.6 = 1.0. Universe was half its current size when emitted.

Frequently Asked Questions

  • Redshift z = (λ_obs − λ_em) / λ_em, where λ_obs is the observed wavelength and λ_em is the emitted wavelength. A positive z means the source is receding (light is stretched to longer/redder wavelengths).
  • z = 1 means observed wavelength is twice the emitted wavelength. The universe has expanded to twice its size since that light was emitted. Light travel time for z=1 is approximately 7.9 billion years.
  • The JWST has detected galaxies at z ≈ 14–16, corresponding to the universe being only ~280–340 million years old. The cosmic microwave background (CMB) has z ≈ 1100.
  • Scale factor a = 1/(1+z). It tells you how large the universe was relative to today when the light was emitted. At z=1, a=0.5 meaning the universe was half its current size.
  • Gravitational redshift occurs when light climbs out of a gravitational field: z_grav = 1/√(1 − r_s/r) − 1, where r_s is the Schwarzschild radius. Near a black hole this becomes extreme.

Related Calculators

🌠 Hubble Law Calculator ⚫ Schwarzschild Radius Calculator ✨ Light-Year Converter 🔭 Parsec Calculator
Sources & References (5) ▾
  1. NASA Astrophysics Data System — NASA ADS
  2. Hubble Space Telescope Archives — Redshift — STScI / HubbleSite
  3. JWST Data Releases — High-z Galaxies — STScI / JWST
  4. ESA Planck — Cosmological Parameters — ESA Planck
  5. OpenStax Astronomy, Ch. 27: The Big Bang — OpenStax