Redshift Calculator

Calculate redshift values, radial velocities, and cosmic distances using Doppler effect and Hubble's law.

Determine the redshift (z) of astronomical objects, calculate their radial velocity, and estimate distances using cosmological principles and the expansion of the universe.

Examples

Click on any example to load it into the calculator.

Nearby Galaxy (M31)

Galaxy

Andromeda Galaxy showing blueshift due to approaching motion.

Observed Wavelength: 656.25 nm

Rest Wavelength: 656.28 nm

Distance: 0.78 Mpc

Hubble Constant: 70 km/s/Mpc

Distant Quasar

Quasar

High-redshift quasar showing significant cosmological redshift.

Observed Wavelength: 1312.56 nm

Rest Wavelength: 656.28 nm

Distance: 3000 Mpc

Hubble Constant: 70 km/s/Mpc

Type Ia Supernova

Supernova

Standard candle supernova used for distance measurements.

Observed Wavelength: 1312.56 nm

Rest Wavelength: 656.28 nm

Distance: 100 Mpc

Hubble Constant: 70 km/s/Mpc

Cosmic Microwave Background

Cosmic Microwave Background

Extreme redshift from the early universe.

Observed Wavelength: 1100000 nm

Rest Wavelength: 656.28 nm

Distance: 14000 Mpc

Hubble Constant: 70 km/s/Mpc

Other Titles
Understanding Redshift Calculator: A Comprehensive Guide
Explore the fundamental principles of cosmological redshift, Doppler effect, and how astronomers measure the expansion of the universe. This guide covers everything from basic wavelength measurements to complex cosmological calculations.

What is Redshift?

  • Doppler Effect
  • Cosmological Redshift
  • Gravitational Redshift
Redshift is one of the most fundamental concepts in modern astronomy and cosmology. It describes the phenomenon where light from distant objects appears shifted toward longer (redder) wavelengths compared to the same light emitted by a source at rest. This shift provides crucial information about the motion of astronomical objects and the expansion of the universe itself.
The Doppler Effect: Motion-Based Redshift
The Doppler effect occurs when a light source is moving relative to an observer. When an object moves away from us, its light waves are stretched, causing a redshift (z > 0). When an object moves toward us, its light waves are compressed, causing a blueshift (z < 0). This effect is most noticeable in nearby galaxies and stars where the motion is primarily due to gravitational interactions rather than cosmic expansion.
Cosmological Redshift: The Expansion of Space
Cosmological redshift is caused by the expansion of space itself. As light travels through the expanding universe, the space through which it propagates stretches, causing the wavelength of the light to increase. This effect becomes dominant for very distant objects and is the primary evidence for the Big Bang theory and the expanding universe.
Gravitational Redshift: Einstein's Prediction
Gravitational redshift occurs when light escapes from a strong gravitational field. According to Einstein's theory of general relativity, light loses energy as it climbs out of a gravitational well, causing its wavelength to increase. This effect is most significant near black holes and neutron stars, but can also be measured in the solar system.

Types of Redshift in Astronomy:

  • Doppler Redshift: Caused by relative motion between source and observer
  • Cosmological Redshift: Caused by the expansion of space-time
  • Gravitational Redshift: Caused by strong gravitational fields
  • Transverse Redshift: Caused by relativistic motion perpendicular to the line of sight

Step-by-Step Guide to Using the Calculator

  • Measuring Wavelengths
  • Inputting Data
  • Interpreting Results
Using the redshift calculator requires accurate wavelength measurements and understanding of the physical principles involved. Follow these steps to obtain reliable results.
1. Obtaining Accurate Wavelength Measurements
The most common method for measuring redshifts is spectroscopy. Astronomers use spectrographs to disperse light into its component wavelengths and identify specific spectral lines. The most frequently used lines include hydrogen Balmer lines (Hα at 656.28 nm, Hβ at 486.13 nm), calcium lines, and various metal lines. The accuracy of your redshift calculation depends entirely on the precision of these wavelength measurements.
2. Understanding the Redshift Formula
The fundamental redshift formula is z = (λobserved - λrest) / λrest, where λobserved is the measured wavelength and λ_rest is the rest wavelength of the same spectral line. For small redshifts (z < 0.1), the radial velocity can be approximated as v ≈ c × z, where c is the speed of light. For larger redshifts, relativistic corrections become important.
3. Inputting Data and Avoiding Common Errors
Ensure you're using the same units for both observed and rest wavelengths. Common units include nanometers (nm), angstroms (Å), and micrometers (μm). Double-check that you're comparing the same spectral line in both measurements. A common mistake is comparing different lines or using incorrect rest wavelengths.
4. Interpreting the Results
The redshift value z tells you how much the universe has expanded since the light was emitted. A redshift of z = 1 means the universe has expanded by a factor of 2 since that time. The radial velocity gives you the recessional velocity due to cosmic expansion, while the calculated distance provides an estimate based on Hubble's law.

Redshift Scale Reference:

  • z = 0.1: Universe expanded by 10%, distance ~400 Mpc
  • z = 1: Universe expanded by 100%, distance ~7 Gpc
  • z = 3: Universe expanded by 300%, distance ~11 Gpc
  • z = 1100: Cosmic Microwave Background, distance ~13.8 Gpc

Real-World Applications in Astronomy

  • Distance Measurements
  • Cosmology Research
  • Galaxy Evolution
Redshift measurements are fundamental to virtually every aspect of modern astronomy and cosmology, from mapping the local universe to understanding the earliest moments of cosmic history.
Measuring Cosmic Distances
Redshift is the primary method for measuring distances to galaxies and quasars. Hubble's law, v = H₀ × d, relates the recessional velocity (derived from redshift) to distance. While this relationship has uncertainties due to peculiar motions and the value of the Hubble constant, it provides the foundation for mapping the large-scale structure of the universe.
Studying Galaxy Evolution
By observing galaxies at different redshifts, astronomers can study how galaxies have evolved over cosmic time. Higher redshift corresponds to earlier times in the universe's history. This allows researchers to see how galaxy properties like size, color, star formation rate, and morphology have changed over billions of years.
Probing the Early Universe
The most distant objects we can observe have redshifts of z > 10, corresponding to times when the universe was less than 500 million years old. These observations provide crucial constraints on models of galaxy formation, reionization, and the nature of the first stars and black holes.

Common Misconceptions and Limitations

  • Redshift vs. Distance
  • Hubble's Law Limitations
  • Measurement Uncertainties
While redshift is a powerful tool, it's important to understand its limitations and avoid common misconceptions about what it tells us.
Misconception: Redshift Equals Distance
Redshift is not a direct measure of distance, but rather of the expansion of space between emission and observation. The relationship between redshift and distance depends on the cosmological model and the values of parameters like the Hubble constant, matter density, and dark energy density. At high redshifts, this relationship becomes highly non-linear.
Limitation: Peculiar Motions
Galaxies don't just move with the cosmic expansion; they also have peculiar motions due to gravitational interactions with nearby matter. These peculiar velocities can be hundreds or thousands of km/s, comparable to the recessional velocity for nearby galaxies. This makes redshift-based distance estimates uncertain for objects within about 100 Mpc.
Uncertainty: Hubble Constant Value
The value of the Hubble constant is still uncertain, with different measurement methods giving values between 67 and 74 km/s/Mpc. This uncertainty propagates into all distance calculations based on redshift. The tension between different measurement methods is one of the most active areas of research in cosmology.

Current Best Estimates:

  • Hubble Constant: 70.4 ± 1.4 km/s/Mpc (Planck 2018)
  • Matter Density: Ωm = 0.315 ± 0.007
  • Dark Energy Density: ΩΛ = 0.685 ± 0.007
  • Age of Universe: 13.787 ± 0.020 billion years

Mathematical Derivation and Advanced Concepts

  • Relativistic Redshift
  • Cosmological Models
  • Distance Measures
The full mathematical treatment of redshift involves general relativity and cosmology, but the basic principles can be understood with simpler physics.
Relativistic Doppler Effect
For objects moving at relativistic speeds, the simple formula v = c × z breaks down. The relativistic Doppler formula is z = √[(1 + β)/(1 - β)] - 1, where β = v/c. This correction becomes important for redshifts z > 0.1 and is essential for understanding the motion of jets from active galactic nuclei and gamma-ray bursts.
Cosmological Distance Measures
In cosmology, there are several different ways to define distance: luminosity distance (how bright an object appears), angular diameter distance (how large an object appears), and comoving distance (the distance that would be measured today). Each has a different relationship to redshift, and the choice depends on the specific application.
The Friedmann Equations
The relationship between redshift and distance is governed by the Friedmann equations, which describe how the scale factor of the universe evolves with time. These equations depend on the energy content of the universe (matter, radiation, dark energy) and their equations of state. Solving these equations numerically is how cosmologists calculate precise distance-redshift relationships.

Advanced Redshift Applications:

  • Baryon Acoustic Oscillations: Using redshift to measure cosmic expansion history
  • Weak Gravitational Lensing: Measuring dark matter distribution using redshift surveys
  • 21-cm Cosmology: Using neutral hydrogen redshift to probe the early universe
  • Gravitational Waves: Measuring redshift of merging black holes and neutron stars