Last updated: 2026-06-16

Gravitational Redshift

Gravitational redshift is the lengthening of the wavelength of light as it escapes a gravitational field. Predicted by Einstein's general theory of relativity, it is closely tied to gravitational time dilation: light emitted deep in a gravity well is observed at a lower frequency, and hence a longer wavelength, by someone far away.

This calculator takes the mass $M$ of a body, the radius $r$ at which light is emitted, and the emitted wavelength $\lambda_e$, and returns the redshift $z$, the observed wavelength $\lambda_o$, and the shift factor 1 + z.

How gravitational redshift works

Clocks run slower in stronger gravity. A wave emitted at radius $r$ oscillates at a fixed rate in its local frame, but a distant observer — whose own clock runs faster — counts those oscillations as arriving more slowly. A lower frequency means a longer wavelength, so the light is shifted toward the red. No relative motion is involved; the shift comes entirely from the difference in gravitational potential between emission and observation.

The size of the shift depends on the ratio of the Schwarzschild radius $2GM/c^2$ to the emission radius $r$.

Formula

For weak fields, where $2GM/rc^2 \ll 1$, this reduces to $z \approx GM/rc^2$. As $r$ approaches the Schwarzschild radius the redshift grows without bound.

Worked example

Sunlight at $\lambda_e = 500\ \text{nm}$ leaving the Sun's surface: $M = 1.989 \times 10^{30}\ \text{kg}$, $r = 6.9634 \times 10^8\ \text{m}$.

Step 1 — Schwarzschild ratio:

Step 2 — Redshift:

Step 3 — Observed wavelength:

The shift is tiny — about one part in 470 000 — but real, and it has been measured in the Sun's spectrum. Enter these values in the calculator to reproduce the result.

Redshift at different field strengths

Real-world relevance

Gravitational redshift was first confirmed in the laboratory by the Pound–Rebka experiment in 1959, which measured a shift of a few parts in 10¹⁵ over a 22-metre tower. It has since been detected in the spectra of the Sun and white dwarfs such as Sirius B, and in stars orbiting the black hole at the centre of the Milky Way. The same physics underlies the clock corrections that keep GPS accurate.

Limitation: static, non-rotating mass

This calculator uses the Schwarzschild metric for a spherical, non-rotating, uncharged mass, and requires the emission radius to lie outside the Schwarzschild radius $2GM/c^2$. Doppler shifts from relative motion and cosmological redshift from the expansion of the universe are separate effects not included here.