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Special-Relativistic Time Dilation — result sheet
Calculate proper elapsed time from a coordinate-time interval and a subluminal speed using the special-relativistic inertial-clock relation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Proper time tau = coordinate time t x sqrt(1 - (v/c)^2), using the exact SI speed of light c = 299792458 m/s.
This special-relativity calculator converts a coordinate-time interval in one inertial frame into the proper time along a clock moving at a constant entered speed. It reports proper time and the coordinate-minus-proper difference, explicitly separating those quantities from the input coordinate time.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coordinate time interval — s; Finite nonnegative time measured in the selected inertial frame.; minimum 0; maximum 1000000000000
- Speed — m/s; Finite nonnegative speed strictly below c = 299792458 m/s.; minimum 0; maximum 299792457.999
Worked example
| Input | Value |
|---|---|
| Coordinate time interval | 10 |
| Speed | 179875474.8 |
At 0.6c, 10 s of coordinate time corresponds to 8 s of proper time; the difference is 2 s.
Assumptions and limits
- Coordinate time is a finite nonnegative interval in seconds and speed is a finite nonnegative magnitude in metres per second.
- The speed is constant and strictly below the exact SI speed of light, c = 299792458 m/s; the relation is the inertial special-relativistic time-dilation equation.
- Acceleration history, gravitational time dilation, clock construction, synchronization procedure, signal delay, and navigation or mission conclusions 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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