Gravitational Time Dilation
Calculate time dilation caused by gravity using Einstein general relativity formula t = t₀ × √(1 − 2GM/rc²) for Earth Sun Jupiter black holes and other massive objects with interactive charts.
About This Calculator
The Gravitational Time Dilation Calculator lets you explore how gravity warps time as predicted by Einstein's general theory of relativity. Simply select a celestial body — Earth, Sun, Jupiter, Mars, Saturn, or the Moon — or enter custom mass and distance values, then specify a time interval to see how much time actually passes near the massive object compared to a distant observer.
The calculation uses the gravitational time dilation formula t' = t × √(1 − 2GM/rc²), where G is the gravitational constant (6.6743 × 10⁻¹¹ N·m²/kg²), M is the mass of the gravitating body in kilograms, r is the distance from the center of mass in meters, and c is the speed of light (299,792,458 m/s). The results show the dilated time, the dimensionless dilation factor, the time lost per year, and the Schwarzschild radius of the body. If the entered distance falls within the event horizon, the calculator warns that time dilation becomes infinite.
Regional Notes
Global: Gravitational time dilation is a universal relativistic effect independent of location on Earth. The same physics applies everywhere — the formulas use SI units (kg, km, seconds) recognized worldwide.
GPS and Satellite Applications: GPS satellites orbiting at approximately 20,200 km altitude experience both gravitational time dilation (time runs faster due to weaker gravity) and special relativistic time dilation (time runs slower due to orbital velocity). GPS receivers must apply relativistic corrections of about 38 microseconds per day to maintain positional accuracy. This calculator can estimate the gravitational component by entering the satellite altitude distance from Earth center.
Experimental Verification: The Hafele-Keating experiment (1971) and the Gravity Probe A mission (1976) confirmed gravitational time dilation predictions with high precision. Modern atomic clocks at different elevations show measurable time differences — a clock at 1 meter higher altitude gains about 10⁻¹⁶ seconds per second due to reduced gravity.
Frequently Asked Questions
What is gravitational time dilation?
Gravitational time dilation is a phenomenon predicted by Einstein general theory of relativity where time passes slower in stronger gravitational fields. The closer you are to a massive object the slower time runs relative to a distant observer.
How do you calculate gravitational time dilation?
Use the formula t' = t × √(1 − 2GM/rc²) where G is the gravitational constant M is the mass of the object r is the distance from its center and c is the speed of light. Enter the mass radius and time interval into the calculator to get the dilated time.
How much time dilation occurs on Earth surface?
Gravitational time dilation on Earth surface is very small about 22 milliseconds per year. Clocks at sea level tick slightly slower than clocks at high altitude because gravity is stronger at lower elevations.
Is time dilation real and has it been proven?
Yes time dilation is real and experimentally confirmed. The Hafele-Keating experiment in 1971 flew atomic clocks around the world and showed time differences matching relativity predictions. GPS satellites must correct for both gravitational and velocity time dilation daily.
What is the time dilation on the Sun compared to Earth?
Time passes about 67 seconds slower per year on the Sun surface compared to Earth due to the Sun much stronger gravity. The dilation factor depends on the mass and radius of the celestial body.
What happens to time at a black hole event horizon?
At the Schwarzschild radius event horizon of a black hole the time dilation factor becomes infinite. To a distant observer an object falling into the black hole appears to slow down and freeze at the event horizon never crossing it.
Does this calculator work for any celestial object?
Yes the calculator works for any massive object. You can select from presets Earth Sun Moon Mars Jupiter Saturn or enter custom mass and radius values. It also shows the Schwarzschild radius to help identify when an object is within its event horizon.
What is the Schwarzschild radius?
The Schwarzschild radius is the distance from a massive object center at which the escape velocity equals the speed of light marking the event horizon of a black hole. It is calculated as Rs = 2GM/c². If you enter a distance smaller than this the calculator warns that you are inside the event horizon.