Einstein showed that clocks don't all tick at the same rate. How fast you move and how deep you sit in a gravity well both change it. Play with both effects below.
๐ Speed-Based Time Dilation
Special relativity: the faster you move relative to Earth, the slower your clock runs compared to Earth's.
% of light speed
1.000000000000
Lorentz Factor (ฮณ)
0 ns
Earth's clock gains, per year you travel
๐ณ๏ธ Gravity-Based Time Dilation
General relativity: the deeper you sit in a gravity well, the slower your clock runs compared to a clock far from any mass.
1.000000000000
Your Clock's Rate (dฯ/dt)
0 s
Lost per year, vs. deep space
๐The mass-independent black hole fact: the fractional time slowdown at a fixed multiple of the event horizon's radius is the same for a 10-solar-mass black hole and a 4-million-solar-mass one like Sagittarius A* at our galaxy's center. What differs enormously is the tidal force at that distance: near a small black hole you'd be stretched apart ("spaghettified") long before reaching the horizon; near a giant one, you could cross it alive and never notice.
๐ก Real-World Examples
๐งโ๐Scott Kelly's ISS year. Astronaut Scott Kelly spent 340 days aboard the ISS (~7.66 km/s / ~17,135 mph) while his identical twin Mark stayed on Earth. At that altitude, the ISS's speed dilates time more than its slightly weaker gravity speeds it up. Net effect, Scott came home about 5 milliseconds younger than his twin. Genuinely measured, not hypothetical.
๐ฐ๏ธGPS satellites. They orbit much higher (~20,200 km up) and slower than the ISS, so gravity wins instead: velocity dilation alone would lose about 7 microseconds/day, but weaker gravity up there gains about 45 microseconds/day, a net gain of roughly 38 microseconds/day. Engineers detune each satellite's clock before launch to cancel it out. Skip the correction and GPS positions would drift by about 10 km per day.
๐ The Physics
Special Relativity: Lorentz Factor
ฮณ = 1 / โ(1 โ vยฒ/cยฒ)
v = your speed, c = speed of light. If you experience ฯ years of travel at speed v, Earth experiences ฯยทฮณ years. This ignores the acceleration needed to turn around and come home, which adds further asymmetry in the classic "twin paradox."
General Relativity: Gravitational Time Dilation
dฯ/dt = โ(1 โ 2GM / (rcยฒ))
G = gravitational constant, M = mass of the body, r = your distance from its center, c = speed of light. This is the Schwarzschild solution for a non-rotating mass; 2GM/cยฒ is the Schwarzschild radius, the event horizon of a black hole of mass M.