Enter the emitted wavelength and observed wavelength (or emitted and observed frequencies) of light from a distant astronomical object to calculate the redshift parameter z. You also get the recession velocity as a fraction of the speed of light, plus a breakdown of whether the object is redshifting or blueshifting.
Redshift Parameter (z)
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Shift Type
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Recession Velocity (v/c)
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Recession Velocity
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Wavelength Shift (Δλ)
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Redshift is a phenomenon where the spectral lines of electromagnetic radiation from distant stars or galaxies are shifted toward longer wavelengths (lower frequencies). It occurs because the source is moving away from the observer, causing the waves to 'stretch.' The term comes from the fact that longer visible-light wavelengths appear red (~700 nm).
The redshift parameter z quantifies how much a wavelength has been stretched. A z of 0 means no shift; z = 1 means the observed wavelength is twice the emitted wavelength. Higher z values correspond to objects farther away and moving faster from us due to the expansion of the universe.
Using wavelengths: z = (λ_observed − λ_emitted) / λ_emitted. Using frequencies: z = (f_emitted − f_observed) / f_observed. Both formulas yield the same z value for the same physical scenario.
Redshift (z > 0) occurs when an object is moving away from the observer, shifting light to longer (redder) wavelengths. Blueshift (z < 0) occurs when an object is approaching the observer, shifting light to shorter (bluer) wavelengths. Most distant galaxies exhibit redshift because the universe is expanding.
The three main causes are: (1) the relativistic Doppler effect, where the source moves away from the observer; (2) the expansion of the universe, which stretches the wavelength of photons as they travel through expanding space; and (3) gravitational redshift, where photons lose energy climbing out of a gravitational well.
For small redshifts (z << 1), recession velocity v ≈ z × c. For larger z values, the relativistic formula is used: v/c = ((z+1)² − 1) / ((z+1)² + 1), where c is the speed of light (~299,792.458 km/s). This calculator applies the relativistic formula for accuracy.
Yes. Because the speed of light is finite and the universe is expanding, the redshift of a galaxy is directly related to how far away it is and how long ago its light was emitted. Higher-z galaxies are seen as they were billions of years ago, making redshift one of astronomy's most powerful distance and age indicators.
Nearby galaxies like Andromeda show slight blueshifts (z ≈ −0.001). The Milky Way's neighboring galaxies have z values close to 0. Distant quasars can have z > 6, and the cosmic microwave background radiation has z ≈ 1100, representing light from just ~380,000 years after the Big Bang.