Redshift Calculator

Redshift measures how much light has stretched, revealing how fast an object recedes.

How the Math Works

The redshift formula z = (λ_obs − λ_rest) ÷ λ_rest quantifies how much light from distant galaxies stretches to longer wavelengths as the universe expands. When a galaxy moves away from us, its emitted light (at λ_rest) appears at a longer observed wavelength (λ_obs). The ratio of this wavelength difference to the original λ_rest gives the dimensionless redshift value (z), which directly correlates with the galaxy's recession velocity and distance. A higher z means greater expansion and faster movement away from Earth.

Practical Applications

Astronomers use this calculator by inputting the observed wavelength of a spectral line (like hydrogen's H-alpha at 656.3 nm) and comparing it to its known rest wavelength. For instance, if a galaxy's H-alpha line appears at 720 nm, the redshift z = (720 - 656.3)/656.3 ≈ 0.098. This z value can then be paired with Hubble's Law (v = H₀ × d) to estimate the galaxy's distance or recession velocity, helping map cosmic structures and study the universe's expansion history.

Day-to-Day Use

While not used in daily tasks, redshift calculations help us comprehend our place in an evolving cosmos. By revealing how fast galaxies recede, they inform models of the universe's age, fate, and the scale of cosmic distances—like estimating the Milky Way's position in the expanding fabric of space. This knowledge fuels curiosity about astronomy, inspires STEM education, and connects everyday humans to the grand narrative of how stars, galaxies, and the universe itself came to be.

Worked example

Hydrogen 656.3 nm seen at 660 nm → z ≈ 0.0056, about 1690 km/s.

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