What is gravitational redshift?

Gravitational redshift is the stretching of light wavelength as a photon escapes a gravitational field. A photon emitted at radius r from a mass M arrives at infinity with a longer wavelength than it had at emission. The fractional shift is z = Δλ / λ_emit.

What formula does this calculator use?

z = 1 / √(1 − 2GM / rc²) − 1, derived from the Schwarzschild metric of general relativity. G = 6.674 × 10⁻¹¹ N·m²/kg² and c = 2.998 × 10⁸ m/s.

What is the Schwarzschild radius?

The Schwarzschild radius (r_s = 2GM / c²) is the radius at which gravitational redshift becomes infinite — light cannot escape and the formula's denominator reaches zero. It is the event horizon radius for a black hole.

Can the result be negative (blueshift)?

This calculator assumes light is emitted at radius r and observed at infinity. z is always ≥ 0 for that geometry. A negative z (blueshift) occurs when light falls toward a mass, which is the reverse scenario.

How large is the gravitational redshift for Earth?

For Earth, z ≈ 6.96 × 10⁻¹⁰ at the surface — extremely small. GPS satellites, however, must correct for this effect (and time dilation) to maintain centimeter-level positioning accuracy.

What happens when the emission radius equals the Schwarzschild radius?

The denominator 1 − 2GM/rc² reaches zero, making z → ∞. This is the event horizon of a black hole. The calculator warns you when r / r_s < 1.001.

Gravitational Redshift Calculator

Name: Gravitational Redshift Calculator
Availability: InStock
Author: Nham Vu

Compute the gravitational redshift (z) of light climbing out of a gravitational well using Einstein's general relativity formula.

Inputs

Body Preset

Mass (kg) e.g. 1.989e30

Emission Radius (m) from center

Emitted Wavelength (nm) optional, e.g. 656 for H-alpha

Formula: z = 1 / √(1 − 2GM/rc²) − 1

Select a preset or enter values to compute gravitational redshift.

Redshift Comparison — Common Objects

Object	z	r / r_s

Copied!

Summary

Compute the gravitational redshift (z) of light climbing out of a gravitational well using Einstein's general relativity formula.

How it works

Select a celestial body preset or choose Custom to enter your own mass and radius.
Optionally enter the emitted wavelength (in nm) to see the observed wavelength.
The tool computes the Schwarzschild radius to show how close the emission point is to the event horizon.
The redshift factor z is calculated using z = 1 / √(1 − 2GM / rc²) − 1.
The observed wavelength is displayed as λ_obs = λ_emit × (1 + z).
If z is negative, the light is blueshifted (photon falling into a well).

Use cases

Calculate the gravitational redshift of light leaving the surface of a neutron star.
Verify the equivalence principle in a GR physics course.
Estimate how much GPS satellite clocks gain per day due to weaker gravity.
Explore how close a body must be to its Schwarzschild radius before z becomes extreme.
Compare redshift factors across planets, stars, and compact objects.
Study the boundary where gravitational redshift approaches infinity (event horizon).
Determine the observed wavelength of a laser beam fired from a white dwarf surface.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu