Gravitational Redshift Calculator

About this calculator

This calculator uses the weak-field approximation of gravitational redshift, z ≈ G·M/(r·c²), derived from the Schwarzschild metric of general relativity for the case where the gravitational field is not extreme (far from a black hole's event horizon). It describes how light climbing out of a gravitational well loses energy and shifts to longer (redder) wavelengths, because a photon's frequency, as measured by a distant observer, depends on how deep in the gravity well it was emitted.

Astrophysicists use this formula to predict the redshift of light from white dwarfs and neutron stars, where the effect is measurable, and it's the same physics behind the tiny but critical clock corrections applied to GPS satellites, whose onboard clocks run fast relative to ground clocks because they sit higher in Earth's gravitational field. Physics students studying general relativity use it as an accessible entry point before tackling the full Schwarzschild formula.