🌌 Redshift Calculator
Calculate redshift, recessional velocity, and distance from wavelength measurements
Hα line redshifted: 656.47 nm (rest: 656.28 nm) | Use same units for both wavelengths
Hα line (rest): 656.28 nm | Lyman-α: 121.6 nm | Common: 656.28, 486.1, 434.0 nm
How to Use This Calculator
Enter Observed Wavelength
Input the wavelength of the spectral line as observed from Earth. This is typically measured from a galaxy's spectrum. For example, if the Hα line (normally 656.28 nm) is observed at 656.47 nm, enter 656.47.
Enter Rest Wavelength
Input the rest wavelength (laboratory wavelength) of the spectral line. This is the wavelength when the source is not moving relative to the observer. Common rest wavelengths: Hα = 656.28 nm, Hβ = 486.1 nm, Lyman-α = 121.6 nm. Make sure both wavelengths use the same units.
Calculate and Interpret
Click "Calculate" to determine the redshift (z), recessional velocity, and approximate distance. The calculator automatically uses relativistic formulas for large redshifts (z ≥ 0.1). Redshift measures how much the universe has expanded since the light was emitted.
Formula
z = (λ_observed - λ_rest) / λ_rest
(Redshift definition)
v ≈ cz (for z < 0.1)
(Non-relativistic)
v = c((1+z)²-1)/((1+z)²+1) (for z ≥ 0.1)
(Relativistic)
Where:
- z = Redshift (dimensionless)
- λ_observed = Observed wavelength (any unit)
- λ_rest = Rest wavelength (same unit as observed)
- v = Recessional velocity (km/s)
- c = Speed of light = 299,792.458 km/s
Example Calculation: Nearby Galaxy
Given:
- Observed Hα wavelength: 656.47 nm
- Rest Hα wavelength: 656.28 nm
Calculation:
z = (656.47 - 656.28) / 656.28
z = 0.19 / 656.28 = 0.000290
v ≈ cz = 299,792.458 × 0.000290 = 87 km/s
This galaxy is receding at about 87 km/s, typical for nearby galaxies.
Example Calculation: High Redshift (z = 2)
Given:
- z = 2 (from spectral measurement)
Calculation (relativistic):
v = c((1+z)²-1)/((1+z)²+1)
v = 299,792.458 × ((3)²-1)/((3)²+1)
v = 299,792.458 × 8/10 = 239,834 km/s
At high redshift, relativistic effects are significant. This object is receding at 80% the speed of light.
Key Insights:
- Redshift measures cosmic expansion, not just velocity
- For z < 0.1, non-relativistic approximation (v = cz) works well
- For z ≥ 0.1, relativistic formula is needed
- Redshift can be greater than 1 (objects receding faster than light's apparent speed)
- Redshift tells us how much the universe expanded since light was emitted
About the Redshift Calculator
The Redshift Calculator determines the redshift of astronomical objects from their observed and rest wavelengths. Redshift measures how much the universe has expanded since light was emitted, and it's the primary tool for measuring cosmic distances and understanding the expansion of the universe. Redshift is a fundamental concept in modern cosmology.
When to Use This Calculator
- Astronomical Observations: Convert measured wavelengths to redshift values
- Cosmology Research: Calculate distances and velocities from spectral data
- Educational Purposes: Understand redshift and cosmic expansion
- Astrophysics: Analyze galaxy spectra and determine distances
- Distance Measurements: Use redshift to estimate cosmic distances
Why Use Our Calculator?
- ✅ Accurate Formulas: Uses correct redshift definition and relativistic corrections
- ✅ Automatic Handling: Switches between non-relativistic and relativistic formulas
- ✅ Comprehensive Results: Shows redshift, velocity, and approximate distance
- ✅ Educational Tool: Learn about cosmic expansion and redshift
- ✅ Free to Use: No registration required
- ✅ Mobile Friendly: Works on all devices
Understanding Redshift
Redshift has two main causes:
- Doppler Redshift: From motion of source relative to observer (like sound Doppler effect)
- Cosmological Redshift: From expansion of space itself - this dominates for distant objects
- Gravitational Redshift: From gravity (general relativity) - typically small except near black holes
- Combined Effect: For distant galaxies, cosmological redshift dominates
- Measurement: Compare observed spectral lines to known rest wavelengths
Cosmological Redshift vs. Doppler Effect
- Doppler Effect: Wavelength shift from source motion through space (like sound)
- Cosmological Redshift: Wavelength stretch from expansion of space itself
- Key Difference: Space expands, stretching the wavelength as light travels
- For Distant Objects: Cosmological redshift dominates (z > 0.1)
- Interpretation: Redshift tells us how much the universe expanded since emission
Real-World Applications
- Distance Measurement: Redshift is used to estimate distances to galaxies
- Hubble's Law: v = Hâ‚€d relates redshift-derived velocity to distance
- Cosmic Expansion: Redshift measurements show universe is expanding
- Dark Energy: High-redshift supernovae revealed accelerating expansion
- Early Universe: High-redshift objects show us the universe when it was young
Tips for Using This Calculator
- Make sure both wavelengths use the same units (nm, Ã…, meters, etc.)
- For z < 0.1, the simple v = cz formula works well
- For z ≥ 0.1, relativistic effects are significant - the calculator handles this automatically
- Redshift can exceed 1 - objects can have z > 10 (very early universe)
- Distance estimates assume Hubble's Law with Hâ‚€ = 70 km/s/Mpc - actual distances may vary
Frequently Asked Questions
What is redshift?
Redshift (z) measures how much the wavelength of light has been stretched to longer wavelengths. It's defined as z = (λ_observed - λ_rest) / λ_rest, where λ_observed is the wavelength we measure and λ_rest is the wavelength when the source is at rest. For distant galaxies, redshift is primarily caused by the expansion of the universe.
How is redshift different from the Doppler effect?
The Doppler effect shifts wavelengths due to motion through space (like a moving car's sound). Cosmological redshift is different - it's caused by the expansion of space itself. As light travels through expanding space, the space stretches, stretching the light's wavelength. For nearby objects, Doppler effect dominates; for distant objects, cosmological redshift dominates.
Can redshift be greater than 1?
Yes! Redshift can be much greater than 1. The highest measured redshifts are around z ≈ 10-11 for the most distant galaxies. A redshift of z = 2 means the universe has expanded by a factor of 3 since that light was emitted (since 1+z = 3). The most distant objects we can see have z > 10, showing us the universe when it was very young.
How do astronomers measure redshift?
Astronomers measure redshift by observing spectral lines (like hydrogen lines) in a galaxy's spectrum and comparing them to known rest wavelengths. For example, the Hα line has a rest wavelength of 656.28 nm. If it's observed at 656.47 nm, the redshift is z = (656.47 - 656.28) / 656.28 = 0.00029. Modern telescopes can measure redshifts very accurately.
What does redshift tell us about distance?
Redshift is related to distance through Hubble's Law: v = H₀d, where v is recessional velocity (related to redshift) and d is distance. For small redshifts, v ≈ cz, so distance ≈ cz/H₀. However, for high redshifts, the relationship is more complex due to the universe's expansion history. Redshift is the primary tool for measuring cosmic distances.
Why is redshift important in cosmology?
Redshift is fundamental to cosmology because it measures cosmic expansion. It tells us how much the universe has expanded since light was emitted, allowing us to measure distances and understand the universe's history. High-redshift objects show us the early universe, and redshift measurements led to the discovery of dark energy and accelerating expansion. Redshift is the primary observable quantity in cosmology.