Gravitational Time Dilation Calculator

Calculate how gravity affects the passage of time using Einstein's general relativity. Compare time rates at different gravitational potentials.

TIME NEAR MASS
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Time Difference
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Dilation Factor
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Schwarzschild Radius
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Surface Gravity
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What Is Gravitational Time Dilation?

Gravitational time dilation is a prediction of Einstein's general relativity: clocks run slower in stronger gravitational fields. Time passes more slowly near massive objects compared to regions far from any mass. This effect has been confirmed experimentally with atomic clocks at different altitudes and is essential for GPS satellite accuracy.

The effect is proportional to the gravitational potential. On Earth's surface, clocks run about 0.7 parts per billion slower than in deep space. Near a black hole's event horizon, time dilation becomes extreme — time nearly stops relative to a distant observer.

Einstein's Formula

tnear = tfar × √(1 - rs/r)
rs = 2GM/c² (Schwarzschild radius)

Time Dilation Examples

LocationTime Slower By (per day)
Earth's surface vs space60 microseconds
GPS satellite vs surface45 microseconds faster
Sun's surface vs space~60 milliseconds
Neutron star surfaceHours

Frequently Asked Questions

How does GPS use gravitational time dilation?

GPS satellites orbit at 20,200 km altitude where gravity is weaker than on Earth's surface. Their clocks tick about 45 microseconds per day faster due to less gravitational time dilation. Without correcting for this relativistic effect, GPS positions would drift by about 10 km per day.

What happens at a black hole's event horizon?

At the Schwarzschild radius (event horizon), the time dilation factor becomes zero — time appears to stop completely from a distant observer's perspective. An infalling observer would not notice anything special at the horizon, but communication with the outside universe becomes impossible once inside.