Gravitational Redshift Calculator

Frequently Asked Questions

What is the Schwarzschild radius?

The Schwarzschild radius is the distance from a mass at which the escape speed equals the speed of light. Light emitted at or below this radius cannot escape, which is why the emission radius must be larger.

Is gravitational redshift the same as Doppler shift?

No. Gravitational redshift comes from light climbing out of a gravity well, while Doppler shift comes from relative motion. This calculator gives only the static gravitational part.

How large is the Sun's gravitational redshift?

It is very small, only about two parts per million at the solar surface, because the Sun is far from being a compact object like a neutron star.

What is the gravitational redshift of a white dwarf like Sirius B?

White dwarfs are compact enough to show a clear shift. Sirius B packs roughly one solar mass into an Earth-sized radius, giving a measured gravitational redshift of about z ≈ 2.7 × 10⁻⁴ (roughly 80 km/s in velocity terms). Neutron stars are far denser and can reach z ≈ 0.2 or more at their surfaces, while a black hole's horizon corresponds to unbounded z.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Gravitational redshift is the stretching of light wavelengths as the light climbs out of a gravitational well. The deeper the well, the larger the shift. This calculator uses the Schwarzschild result, where the redshift z depends on the ratio of the Schwarzschild radius rₛ to the emitting radius r: 1 + z = 1 / √(1 − rₛ/r). For weak gravity (r much larger than rₛ), this reduces to z ≈ GM / (rc²). The Schwarzschild radius itself is rₛ = 2GM / c².

Worked Example

Suppose light is emitted close to a compact object, where the emitting radius r is 4/3 of the Schwarzschild radius, so rₛ/r = 0.75. Then 1 + z = 1 / √(1 − 0.75) = 1 / √0.25 = 1 / 0.5 = 2, which gives a redshift of z = 2 − 1 = 1. A redshift of 1 means the wavelength arrives stretched to twice its emitted value. By contrast, light from far above the body (r much larger than rₛ) would show only a tiny shift.

Reading The Result

A redshift of zero means no shift. As the emitting radius approaches the Schwarzschild radius, the redshift grows without bound, which corresponds to light being trapped at the event horizon of a black hole. For everyday bodies like Earth the shift is tiny but measurable with precise clocks.

Tips

The redshift grows sharply only very close to the Schwarzschild radius.

GPS satellites correct for this gravitational frequency shift (the same physics as the redshift here) so their onboard clocks stay in step with clocks on the ground.

Use the radius of emission, not the orbital distance, for surface light.

Gravitational Redshift Calculator

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