Redshift Calculator
Calculate the cosmological redshift z from observed and emitted wavelengths using z = (λobs − λemit) / λemit. Free online astrophysics calculator with velocity conversion and charts.
About This Calculator
The Redshift Calculator computes the cosmological redshift parameter z from the observed and emitted wavelengths (or frequencies) of spectral lines. Redshift is one of the most important concepts in astronomy and astrophysics — it tells us how fast a celestial object is moving away from Earth and, by extension, how far away it is. This calculator is designed for astronomy students, astrophysics researchers, and amateur stargazers who need to quickly determine the redshift of a galaxy, quasar, or supernova from spectral data.
The calculator uses the fundamental redshift formula z = (λobs − λemit) / λemit where λobs is the observed wavelength and λemit is the emitted (rest) wavelength. For frequency inputs, the equivalent formula z = (femit − fobs) / fobs is used. The recession velocity is approximated as v = z × c where c = 299,792 km/s is the speed of light. Common rest wavelengths include the hydrogen Balmer series: H-alpha at 656.3 nm, H-beta at 486.1 nm, and H-gamma at 434.1 nm.
About Redshift in Astronomy
The discovery of cosmological redshift by Edwin Hubble in 1929 revolutionized our understanding of the universe. Hubble observed that galaxies farther from Earth have higher redshifts, establishing the linear relationship known as Hubble Law: v = H₀ × d where H₀ is the Hubble constant (~70 km/s/Mpc). This led to the realization that the universe is expanding — one of the cornerstones of the Big Bang theory. The James Webb Space Telescope has recently pushed redshift observations to z ~ 14, revealing galaxies from the first few hundred million years after the Big Bang.
Using the Calculator
Enter the rest wavelength (or frequency) of a known spectral line and the observed wavelength (or frequency) from your astronomical data. The calculator will instantly compute the redshift parameter z, the recession velocity in km/s, and whether the light is redshifted or blueshifted. The comparison chart visualizes the wavelength shift, and the breakdown table shows all intermediate values for educational purposes.
Frequently Asked Questions
What is redshift in astronomy?
Redshift is a phenomenon where light from distant galaxies is stretched to longer wavelengths due to the expansion of the universe. It is measured by the dimensionless parameter z = (λobserved − λemitted) / λemitted. A higher z means the object is farther away and moving away faster.
How is redshift calculated?
Redshift z is calculated using the formula z = (λobs − λemit) / λemit where λobs is the observed wavelength and λemit is the emitted rest wavelength. For example the H-alpha line at 656.3 nm observed at 820 nm gives z = 0.249.
What is the difference between redshift and blueshift?
Redshift occurs when light is stretched to longer wavelengths as an object moves away from the observer resulting in a positive z value. Blueshift occurs when light is compressed to shorter wavelengths as an object moves toward the observer resulting in a negative z value.
What causes cosmological redshift?
Cosmological redshift is caused by the expansion of the universe stretching the wavelength of light as it travels through space. This is different from the Doppler effect which is caused by the relative motion of objects. The further a galaxy is the more its light is redshifted described by Hubble law v = H₀ × d.
How do you convert redshift to velocity?
For low redshifts z less than 0.1 the recession velocity is approximated by v = z × c where c is the speed of light 299792 km per second. For higher redshifts the relativistic formula must be used. This calculator uses the simple approximation v = z × c which is accurate for most practical purposes.
What is the highest redshift ever observed?
The highest confirmed galaxy redshift as of 2024 is z approximately 14.3 for JADES-GS-z14-0 observed by the James Webb Space Telescope. This means we are seeing the galaxy as it was about 290 million years after the Big Bang.
What is blueshift and when does it occur?
Blueshift is the opposite of redshift where light waves are compressed to shorter wavelengths as an object moves toward the observer. It is common in our local group of galaxies for example the Andromeda Galaxy is blueshifted as it is moving toward the Milky Way.
How do astronomers measure redshift?
Astronomers measure redshift by comparing the observed wavelength of known spectral lines such as the hydrogen H-alpha line at 656.3 nm to their laboratory rest wavelengths. The shift in wavelength directly gives the redshift parameter z using the standard formula.