Radial Velocity from Doppler Shift Calculator

Enter an observed wavelength and the corresponding laboratory rest wavelength in the same unit. The result includes velocity in meters per second and kilometers per second, along with the absolute and fractional wavelength shifts. A positive result indicates redshift and recession, while a negative result indicates blueshift and approach. It is designed for quick astronomy checks where the measured speed is small compared with the speed of light.

Choose matching observed and rest wavelengths

Start with a spectral feature that you can identify reliably in both the measured spectrum and a laboratory reference. Enter its observed central wavelength as observed_wavelength and its unshifted laboratory value as rest_wavelength. Both numbers must use the same wavelength unit. Nanometers, angstroms, micrometers, or meters all work because the calculation uses their ratio, but mixing units produces a meaningless velocity. The rest wavelength must be strictly positive, and both inputs must be finite numbers. For the best scientific result, derive the observed line center from a fitted profile rather than selecting a single noisy pixel. Also check whether the quoted laboratory wavelength is measured in air or vacuum, since combining an air wavelength with a vacuum measurement introduces a systematic offset. This calculator treats the submitted values as exact inputs; it does not estimate measurement uncertainty, resolve blended features, or correct the spectrum for instrumental calibration. Those preparation steps belong in the data-reduction workflow before the two wavelengths are supplied here.

Understand the Doppler calculation and its sign

The calculator first finds the wavelength shift by subtracting the rest wavelength from the observed wavelength. It then divides that shift by the rest wavelength to obtain the dimensionless fractional shift, often written as z for small velocities. Finally, it multiplies the fraction by the exact speed of light, 299,792,458 meters per second. The implemented relation is v = c times (observed wavelength minus rest wavelength) divided by rest wavelength. When the observed wavelength is longer, the shift and velocity are positive: the source is redshifted and receding along the line of sight. When it is shorter, both are negative: the source is blueshifted and approaching. Equal wavelengths return zero velocity. The result is radial velocity only, meaning the component directed toward or away from the observer. It says nothing about motion across the sky. Output includes meters per second for precision, kilometers per second for familiar astronomical reporting, and both intermediate shifts so the calculation can be checked or recorded.

Know when the non-relativistic approximation is appropriate

This capability deliberately uses the classical, non-relativistic Doppler formula. It is useful when the magnitude of the radial velocity is small relative to the speed of light, which covers many stellar, planetary, binary-star, and nearby-galaxy measurements. As the fractional wavelength shift grows, the classical approximation increasingly differs from the special-relativistic Doppler relation. For high-velocity jets, quasars, distant galaxies, or any case where relativistic accuracy matters, use a relativistic calculation and consider the appropriate cosmological redshift model instead. The number returned here is also only as reliable as the wavelength calibration and line identification. Earth’s rotation and orbit, observatory location, source coordinates, observation time, gravitational shifts, and motion relative to a chosen reference frame can all require separate corrections. No barycentric, heliocentric, or local-standard-of-rest correction is applied. Treat the output as the direct velocity implied by the two submitted wavelengths under the stated approximation. For automated use, the same deterministic calculation is available through the API for $0.002 per request.