ONE FORMULA, ONE ANSWER
Gravitational Redshift Calculator
Calculate the gravitational wavelength shift between two static observers in exterior Schwarzschild spacetime. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Wavelength gravitational redshift z
Enter values and select Calculate.
z = √[(1−r_s/r_o)/(1−r_s/r_e)]−1; r_s=2GM/c²
Assumptions
Required: M>0 and r_e,r_o>r_s, with both positions in vacuum outside the material surface. Radius means Schwarzschild areal radius, not altitude or ruler-measured radial distance. A nonrotating uncharged spherical body and observers static at fixed radii are assumed. The convention is z=λ_o/λ_e−1; negative z is blueshift. For different radii, both positions require 1−r_s/r≥0.01 to protect numerical precision near the horizon. Excluded: Doppler and cosmological shifts, rotation and charge. Use a sufficiently large finite receiver radius to approximate infinity.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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