Gravitational Redshift Calculator
Compute the observed frequency of light or electromagnetic radiation emitted near a massive object, accounting for gravitational redshift predicted by General Relativity. Essential for astrophysics, pulsar timing, and GPS system design.
Last updated: September 2026
Formula below · 2 sources (nasa.gov, Wikipedia) · Updated Sep 2026
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About this calculator
Gravitational redshift describes how light loses energy — and therefore drops in frequency — as it climbs out of a gravitational well. In the weak-field limit used here, the received frequency is f_obs = f_emit × (1 − ΔΦ/c²) for light climbing out, where ΔΦ is the gravitational potential difference between the receiver and the emitter (in m²/s², = GM/r₁ − GM/r₂ for a spherical mass) and c = 299,792,458 m/s; for light falling in, the sign flips and the light is blueshifted, f_obs = f_emit × (1 + ΔΦ/c²). The exact Schwarzschild result for light escaping to infinity from radius r is f_obs = f_emit × √(1 − 2GM/(rc²)), which reduces to the linear formula when GM/(rc²) ≪ 1; for neutron stars and black holes use the exact form. GPS satellite clocks gain about 45 µs/day from this effect because they sit higher in Earth's potential.
How to use
Example — a 1 GHz signal sent from Earth's surface to a distant receiver. The potential difference between the surface and infinity is ΔΦ = GM/R = 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶ ≈ 6.26×10⁷ m²/s². Enter Source Frequency = 1000000000, Gravitational Potential Difference = 62600000 and choose "Light climbing out (Redshift)". Fractional shift = ΔΦ/c² = 6.26×10⁷ / 8.988×10¹⁶ ≈ 6.96×10⁻¹⁰, so f_obs = 1,000,000,000 × (1 − 6.96×10⁻¹⁰) ≈ 999,999,999.3 Hz — a drop of 0.7 Hz. Choosing "Light falling in" gives 1,000,000,000.7 Hz instead.
Frequently asked questions
What is gravitational redshift and how is it different from Doppler redshift?
Gravitational redshift occurs because photons lose energy climbing out of a gravitational field — they do not slow down (light always travels at c) but their frequency decreases and wavelength increases, shifting them toward the red end of the spectrum. Doppler redshift, by contrast, arises from relative motion between source and observer and can be either a redshift (recession) or blueshift (approach). Gravitational redshift is a purely General Relativistic effect, confirmed by the Pound–Rebka experiment in 1959 and routinely measured in white dwarfs, neutron stars, and GPS satellites.
How does gravitational redshift affect GPS satellite clocks?
GPS satellites orbit at about 20,200 km altitude where Earth's gravitational field is weaker than at the surface. Clocks in a weaker gravitational field run faster (gravitational blueshift from the satellite's perspective). This causes satellite clocks to gain approximately 45.9 microseconds per day relative to ground clocks. Combined with the Special Relativistic time dilation of −7.2 µs/day due to their orbital speed, the net gain is about +38.4 µs/day. Without correcting for this, GPS position errors would accumulate at roughly 10 km per day, making the system useless for navigation.
What happens to light frequency when it falls into a gravitational field rather than escaping from it?
When light falls into a gravitational well — moving from a region of weaker gravity to stronger gravity — it gains energy and its frequency increases, a phenomenon called gravitational blueshift. This is the reverse of gravitational redshift. In the weak-field form used here, f_obs = f_emit × (1 + ΔΦ/c²) when the light falls through a potential difference ΔΦ. This effect has been confirmed experimentally and is precisely symmetric with the redshift case. It means a photon emitted far from a black hole and absorbed near it appears blueshifted to a local observer near the black hole.