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Schwarzschild Gravitational Time Dilation — result sheet
Estimate the proper time elapsed near a spherical nonrotating mass compared with a distant coordinate-time interval.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: τ = t√(1 − rₛ/r), with rₛ = 2GM/c²; valid only outside the Schwarzschild radius for a stationary clock.
The Schwarzschild factor compares the proper time of an ideal stationary clock at radius r with a coordinate-time interval measured far from an isolated spherical mass. The result approaches the distant interval as gravity weakens and is not a model of orbital motion.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Central mass — kg; minimum 1.0E-6; maximum 1.0E+35
- Distance from center — m; minimum 1.0E-6; maximum 1.0E+18
- Distant coordinate-time interval — s; minimum 0; maximum 1.0E+15
Worked example
| Input | Value |
|---|---|
| Central mass | 5.9722E+24 |
| Distance from center | 6771000 |
| Distant coordinate-time interval | 3600 |
Proper time about 3,599.99 s for a 3,600 s distant interval
Assumptions and limits
- The central body is spherical, nonrotating, isolated, and described by the Schwarzschild solution.
- The clock is stationary at the entered radius and the radius is strictly outside the Schwarzschild radius.
- Rotation, tides, orbital velocity, acceleration, atmosphere, clock engineering, and survivability are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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