In physics, the Lorentz transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frame of reference. It reflects the surprising fact that observers moving at different velocities report different distances, passage of time, and in some cases even different orderings of events. The Lorentz transformation was the result of attempts by the eponymous Hendrik Lorentz and others to explain observed properties of light propagating in what was presumed to be the luminiferous aether; Albert Einstein later reinterpreted the transformation as a statement about the nature of space and time themselves and derived it from the postulates of relativity.

In classical physics (Galilean relativity), the only conversion believed necessary was x' = x − vt, describing how the origin of one observer's coordinate system slides through space with respect to the other's, at speed v and along the x-axis of each frame. According to special relativity, this is only a good approximation at much smaller speeds than the speed of light, and in general the result is not just an offsetting of the x coordinates; lengths and times are distorted as well.

If space is homogeneous, then the Lorentz transformation must be a linear transformation. Also, since relativity postulates that the speed of light is the same for all observers, it must preserve the spacetime interval between any two events in Minkowski space. The Lorentz transformations describe only the transformations in which the event at x = 0, t = 0 is left fixed, so they can be considered as a rotation of Minkowski space. The more general set of transformations that also includes translations is known as the Poincaré group.

Henri Poincaré named the Lorentz transformations after the Dutch physicist and mathematician Hendrik Lorentz (1853–1928) in 1905. They form the mathematical basis for Albert Einstein's theory of special relativity. They were derived by Joseph Larmor in 1897, and Lorentz (1899, 1904). In 1905 Einstein derived them under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame.