Gravitational Time Dilation Calculator
Time runs slower deeper in a gravitational field. This calculator uses the Schwarzschild solution of general relativity to find how much slower a clock ticks at a given distance from a mass, compared to a clock far away. Enter the mass and the radial distance to get the time dilation factor, the fractional slowdown, and the elapsed time a distant observer would record for one second of local time. The gravitational constant and the speed of light default to their CODATA values and remain editable.
Gravitational time dilation formula
factor = sqrt(1 - (2 * G * M) / (r * c^2))
slowdown = 1 - factor
Schwarzschild radius r_s = (2 * G * M) / c^2
The factor is the rate of a local static clock relative to a clock at infinity. If r is at or below the Schwarzschild radius, no static observer exists and the calculator flags it.
Worked example
At Earth's surface (M = 5.972e24 kg, r = 6,371,000 m), the factor is sqrt(1 - (2 * 6.674e-11 * 5.972e24) / (6,371,000 * 299,792,458^2)) = 0.9999999993. The slowdown is about 6.96e-10, meaning Earth's surface clock loses roughly that fraction of a second per second relative to a distant clock. The Schwarzschild radius of Earth is about 8.87e-3 metres.
Gravitational time dilation: frequently asked questions
What is gravitational time dilation?
Gravitational time dilation is the slowing of time in a gravitational field predicted by general relativity. A clock deep in a gravity well, closer to a massive body, ticks slower than a clock far away. The effect is real and measurable: GPS satellite clocks must be corrected for it to keep the system accurate.
What is the Schwarzschild time dilation factor?
Outside a non-rotating spherical mass, the rate of a clock at radius r relative to a distant observer is the square root of (1 minus 2GM divided by r times c squared). Here G is the gravitational constant, M the mass, r the radial distance, and c the speed of light. The factor is below 1, so the local clock runs slow.
What happens at the Schwarzschild radius?
When r equals 2GM divided by c squared, the Schwarzschild radius, the dilation factor reaches zero: to a distant observer, time appears to stop at the event horizon of a black hole. Inside that radius the formula no longer describes a static observer. This calculator reports when your radius is at or below the Schwarzschild radius.
Sources
- Gravitational constant G: NIST CODATA, Newtonian constant of gravitation.
- Speed of light c: NIST CODATA, speed of light in vacuum (299,792,458 m/s, exact).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.