Gravitational Redshift Calculator
Compute the gravitational redshift (z) of light climbing out of a gravitational well using Einstein's general relativity formula.
Use the Gravitational Redshift Calculator
Inputs
Formula: z = 1 / √(1 − 2GM/rc²) − 1
Select a preset or enter values to compute gravitational redshift.
Gravitational Redshift
Redshift Comparison — Common Objects
| Object | z | r / r_s |
|---|
Summary
Gravitational redshift is the increase in wavelength (and decrease in frequency) of light as it climbs out of a gravitational field, predicted by Einstein's general theory of relativity. A photon emitted near a massive object loses energy escaping the gravitational well; this energy loss appears as a longer (redder) wavelength to a distant observer. The redshift factor z is given by z = 1 / √(1 − 2GM / rc²) − 1, where G is the gravitational constant, M is the body's mass, r is the emission radius, and c is the speed of light.
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.