--- title: "Gravitational Time Dilation Calculator - Relativity Clock Effect" description: "Calculate gravitational time dilation with the Schwarzschild formula or compare clock rates at different altitudes above Earth." image: "https://onlineminitools.com/tools/gravitational-time-dilation-calculator/logo.svg" --- ### Report Help us improve this tool # Gravitational Time Dilation Calculator Calculate gravitational time dilation with the Schwarzschild formula or compare clock rates at different altitudes above Earth. O M T ## What Is Gravitational Time Dilation? Gravitational time dilation is a prediction of Einstein's general relativity: clocks run slower in stronger gravitational fields. The effect is tiny in everyday life but measurable with atomic clocks on Earth and essential for GPS satellites, which orbit farther from Earth's mass and tick slightly faster than clocks on the ground. ## The Schwarzschild Time Dilation Formula For a stationary clock at distance \(r\) from the center of a spherical mass \(M\): $$\Delta t' = \Delta t \sqrt{1 - \frac{2GM}{rc^2}}$$ Here \(\Delta t\) is proper time far from gravity, \(\Delta t'\) is elapsed time near the mass, \(G\) is the gravitational constant, and \(c\) is the speed of light. The ratio approaches zero as \(r\) approaches the Schwarzschild radius \(2GM/c^2\). ## Altitude Comparison on Earth Comparing sea level to an altitude \(h\) uses Earth's mass and radius \(R\). Evaluate the square-root factor at \(r = R\) and at \(r = R + h\). GPS orbits at roughly 400 km and gain about 45 microseconds per day relative to sea level before velocity corrections are applied. Related tools: [Earth Orbit Calculator](https://onlineminitools.com/earth-orbit-calculator) and [Black Hole Calculator](https://onlineminitools.com/black-hole-calculator). ## Frequently Asked Questions **Is gravitational time dilation real?** Yes. Experiments with atomic clocks on aircraft and satellites confirm it. Hafele and Keating flew clocks around the world in 1971 and measured the predicted shift. **How much slower is time on Earth's surface?** Compared to a clock far from gravity, Earth's surface clocks lose about 67 microseconds per year. The difference between sea level and orbit is smaller but still matters for GPS. **What is the Schwarzschild radius?** It is \(2GM/c^2\), the radius of a non-rotating black hole event horizon. Inside that radius the dilation formula breaks down. **Does speed also affect time?** Yes. Special relativity adds velocity time dilation. Fast-moving clocks tick slower. GPS must correct for both gravity and orbital speed. **Can humans feel time dilation?** No. The effect is far too small at everyday speeds and altitudes. 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Experiments with atomic clocks on aircraft and satellites confirm it. Hafele and Keating flew clocks around the world in 1971 and measured the predicted shift." } }, { "@type": "Question", "name": "How much slower is time on Earth's surface?", "acceptedAnswer": { "@type": "Answer", "text": "Compared to a clock far from gravity, Earth's surface clocks lose about 67 microseconds per year. The difference between sea level and orbit is smaller but still matters for GPS." } }, { "@type": "Question", "name": "What is the Schwarzschild radius?", "acceptedAnswer": { "@type": "Answer", "text": "It is \\(2GM/c^2\\), the radius of a non-rotating black hole event horizon. Inside that radius the dilation formula breaks down." } }, { "@type": "Question", "name": "Does speed also affect time?", "acceptedAnswer": { "@type": "Answer", "text": "Yes. Special relativity adds velocity time dilation. Fast-moving clocks tick slower. GPS must correct for both gravity and orbital speed." } }, { "@type": "Question", "name": "Can humans feel time dilation?", "acceptedAnswer": { "@type": "Answer", "text": "No. The effect is far too small at everyday speeds and altitudes. It becomes dramatic only near very massive objects or black holes." } } ] } ```