Redshift Calculator: Measure the Expanding Universe
Calculate cosmological redshift, distances, and recession velocities. Understand how light stretches across expanding space and reveals the universe’s history.
Redshift is one of the most powerful tools in astronomy—the stretching of light wavelengths as objects move away from us in our expanding universe. When Edwin Hubble discovered in 1929 that distant galaxies show redshifted light, he revealed that the universe itself is expanding. Our Redshift Calculator helps you convert between redshift values (z), distances (in megaparsecs and light-years), recession velocities, and lookback times—essentially letting you measure how far back in cosmic history you’re looking when you observe a distant galaxy.
The mathematics of redshift reveals profound truths about spacetime. For nearby objects, redshift follows the simple Doppler formula: z = v/c (where v is recession velocity and c is light speed). But for distant galaxies, we must account for the expansion of space itself during the light’s journey. The relationship involves Hubble’s Law (v = H₀d) and cosmological parameters like the Hubble constant (currently ~70 km/s/Mpc). At extreme distances, relativistic effects and dark energy dominate, requiring the full machinery of general relativity and the ΛCDM cosmological model.
Redshift observations transformed our understanding of the cosmos. The Hubble Space Telescope has measured redshifts beyond z = 11, revealing galaxies as they appeared just 400 million years after the Big Bang. The James Webb Space Telescope pushes even further, potentially reaching z ≈ 20. Each increase in z takes us deeper into cosmic history, toward the first stars and the era when the universe transitioned from opaque to transparent—the epoch captured in the cosmic microwave background at z ≈ 1,100.
Calculate Cosmic Distances from Redshift
Enter redshift value to find distance, recession velocity, and lookback time
Red Shift Distance Calculator
Calculate cosmic distances from redshift values using latest cosmological parameters
Calculate Distance from Redshift
Famous Redshift Objects
Click any object to calculate its distance
Understanding Redshift
What is Redshift?
Redshift (z) measures how much light from an object has been stretched to longer (redder) wavelengths. It's caused by the expansion of space itself. A galaxy with z=1 had its light wavelength doubled during its journey to us.
Types of Distance
Comoving Distance: Where object is NOW (accounts for expansion)
Light-travel Distance: How far light traveled
Lookback Time: How long ago we see it
Proper Distance: Current actual distance
Hubble's Law
For nearby objects (z < 0.1), distance is proportional to recession velocity: v = H₀ × d. Beyond this, we need full cosmological calculations accounting for dark energy and matter density.
H₀ = 67.4 km/s/Mpc
Expansion of Space
The universe expands, stretching light waves. Objects don't move through space - space itself grows. Distant galaxies can recede faster than light because space expansion has no speed limit. Only motion through space is limited to c.
Lookback Time
Lookback time tells us when the light left. z=1 means we see the object as it was 7.7 billion years ago. z=11 shows universe at 400 million years old. We're looking back in time as we look out in space.
Measuring Redshift
Astronomers identify spectral lines (hydrogen, oxygen) in galaxy light and measure how shifted they are. Each element has unique fingerprint. Shift tells us both velocity (Doppler) and cosmic expansion (cosmological redshift).
Cosmological Parameters
Hubble Constant (H₀)
Expansion rate of universe today. Measured by Planck satellite using CMB. There's tension with local measurements (~73 km/s/Mpc).
Dark Energy (ΩΛ)
Mysterious force causing accelerating expansion. Einstein's cosmological constant. Dominates universe evolution today.
Dark Matter (Ωₘ)
Invisible matter detected by gravity. About 26.5% dark matter, 5% normal matter. Slows expansion through gravity.
Age of Universe
Time since Big Bang. Calculated from expansion rate and cosmic composition. Most precisely measured by Planck satellite.
Flat Universe (Ωₖ)
Universe appears geometrically flat. Parallel lines stay parallel forever. Critical density exactly balanced.
Observable Radius
Current distance to objects whose light is just reaching us. Larger than 13.8 Gly because space expanded while light traveled.
Cosmic History by Redshift
Compare Two Redshifts
Advanced: Custom Cosmology
Modify cosmological parameters (for experts)
How to Use the Redshift Calculator
1. Enter Redshift Value
Input the observed redshift (z) of a galaxy or object. Examples: z = 0.1 (nearby galaxies), z = 1 (halfway back in time), z = 6 (early universe), z = 1100 (cosmic microwave background). Or select from famous objects like quasars and high-z galaxies.
2. View Calculated Distances
See both comoving distance (accounting for expansion) and proper distance (actual separation now) in megaparsecs, light-years, and kilometers. Understand how space expansion affects measurements across cosmic scales.
3. Explore Lookback Time
Discover when the light you’re observing was emitted—the lookback time. See the universe’s age at that moment, and understand you’re viewing cosmic history, not just spatial distance. Higher z = further back in time.
Why Calculate Redshift?
🌌 Map the Universe
Convert spectroscopic measurements into actual distances and times. Essential for creating 3D maps of galaxy distributions and understanding large-scale cosmic structure. Explore distances further with our Time to Universe Edge Calculator.
⏰ Time Machine
Higher redshift = further back in cosmic history. Observe galaxy evolution, star formation rates, and universe conditions billions of years ago. Compare with our Cosmic Calendar to contextualize these epochs.
🔭 Test Cosmology
Redshift measurements constrain the Hubble constant, dark energy density, and universe geometry. Essential data for the ΛCDM standard model of cosmology. Learn more with our Light Speed Journey Simulator.
📊 Educational Value
Perfect for astronomy students learning observational techniques and cosmological distance measures. Understand the “cosmic distance ladder” and how astronomers measure the unmeasurable. Extend learning with Deep Time Visualizer.
The Physics of Redshift
Redshift Formula
z = (λobserved – λemitted) / λemitted = Δλ/λ₀. For nearby objects: z ≈ v/c (Doppler). For cosmological distances, z relates to scale factor: 1 + z = anow/athen, showing universe expansion since light emission.
Hubble’s Law
v = H₀d where v is recession velocity, H₀ ≈ 70 km/s/Mpc is Hubble constant, and d is distance. Valid for z < 0.1. At higher z, must account for dark energy and matter density using integral distance formulas from general relativity.
Lookback Time
Time elapsed since light emission. Calculated by integrating dt = -dz/[H₀(1+z)√(Ωm(1+z)³ + ΩΛ)] over redshift. At z = 1, lookback ≈ 7.7 Gyr. At z = 1100 (CMB), we see universe at 380,000 years old.
Frequently Asked Questions
What causes cosmological redshift?
Cosmological redshift is caused by the expansion of space itself, not by galaxies moving through space. As space expands during a photon’s journey, its wavelength stretches proportionally—making blue light become red, red become infrared, etc. This is fundamentally different from Doppler shift (motion through space). The wavelength increase equals the factor by which the universe expanded: λnow/λthen = anow/athen = 1 + z.
How do astronomers measure redshift?
Astronomers use spectroscopy to spread light into wavelengths, revealing absorption/emission lines from elements (hydrogen, oxygen, etc.). These lines appear at known laboratory wavelengths. By measuring how far these lines shift toward red (longer wavelengths), we calculate z = Δλ/λ₀. Modern telescopes can measure redshifts to incredible precision—JWST and VLT have found galaxies at z > 13.
What’s the difference between comoving and proper distance?
Proper distance is the actual separation between us and a galaxy right now, accounting for all expansion that occurred. Comoving distance removes expansion effects—it’s the distance the galaxy was when light was emitted, adjusted to “current” universe scale. For z = 1, comoving ≈ 3.4 Gpc, but proper ≈ 6.8 Gpc because space doubled during the 7.7 billion year journey. Proper distance always equals comoving × (1 + z).
Can redshift exceed z = 1?
Absolutely! There’s no upper limit to cosmological redshift. z = 1 means wavelengths doubled (universe doubled in size). z = 10 means 11× expansion. The cosmic microwave background has z ≈ 1100, meaning the universe expanded 1100× since that light was emitted 13.8 billion years ago. JWST has found galaxies at z > 13. Theoretically, we could observe up to z ≈ 1600 if neutrino detectors become sensitive enough.
Related Cosmology & Distance Tools
Explore more ways to measure and understand cosmic distances:
- Time to Universe Edge Calculator – Journey to observable universe boundaries
- Light Speed Journey Simulator – Travel the cosmos at light speed
- Cosmic Calendar Converter – Map universe history to a year
- Deep Time Visualizer – Comprehend cosmic and geological time
- Interstellar Travel Calculator – Calculate interstellar journey times
- Time Dilation Calculator – Relativistic time effects
Scientific References & Further Reading
- Hubble’s Law – Wikipedia comprehensive overview
- The Hubble Constant – NASA LAMBDA educational resource
- Hubble Space Telescope – NASA’s redshift observations
- James Webb Space Telescope – Observing high-z galaxies
- Very Large Telescope – ESO’s spectroscopic capabilities
- Planck 2018 Results: Cosmological Parameters – Precision cosmology
- JWST High-Redshift Galaxies – Nature journal discoveries
- Introduction to Redshift – Astrobites educational guide