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Calcimator

Redshift Calculator

Calculate cosmological redshift, recessional velocity, distance, and lookback time using Hubble's law.

Inputs

nm
nm
km/s

Results

Redshift (z)

0

Velocity from Redshift

0 km/s

Distance

142.86 Mpc

Lookback Time

0.14 billion years

Relativistic Redshift0.033932
Distance0.14 Gly
How to Use This Calculator
  1. Enter the Observed Wavelength (nm) of the spectral line measured in the spectrum of the galaxy or quasar.
  2. Enter the Rest Wavelength (nm) — the lab-frame wavelength of the same line; H-alpha is 656.3 nm.
  3. The Redshift (z) is computed automatically from (λ_obs − λ_rest) / λ_rest.
  4. Alternatively, enter a Recessional Velocity (km/s) to compute the corresponding redshift from velocity.
  5. Read Distance (Mpc and Gly) and Lookback Time (billion years) to place the object in cosmic context.

How the result changes with Rest Wavelength

Rest WavelengthRedshift (z)Velocity from RedshiftDistance
1,090-0.39789-119,284.39 km/s142.86 Mpc
3,565-0.815905-244,602.05 km/s142.86 Mpc
6,535-0.899572-269,684.76 km/s142.86 Mpc
9,010-0.927159-277,955.19 km/s142.86 Mpc

What each input means

Observed Wavelength
Observed wavelength of spectral line
Rest Wavelength
Rest wavelength of spectral line (e.g., H-alpha = 656.3 nm)
Recessional Velocity
Recessional velocity of object

How this is calculated

Formula

z = (λ_obs - λ_rest) / λ_rest

Worked example, using the default values

  1. Identify Input Parameters
    Observed Wavelength = 656.3, Rest Wavelength = 656.3, Recessional Velocity = 10000 = 3 input(s) provided
  2. Calculate Redshift
    Redshift
    0 = 0
  3. Calculate Velocity from Redshift
    Velocity from Redshift
    0 = 0
  4. Calculate Distance
    Distance
    142.86 = 142.86
  5. Calculate Relativistic Redshift
    Relativistic Redshift
    0.033932 = 0.033932
  6. Calculate Distance
    Distance
    0.14 = 0.14

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