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Relativistic Length Contraction Calculator — result sheet
Calculate the length observed parallel to motion when an object travels at a chosen fraction of light speed.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: L = L₀√(1 − v²/c²), with β = v/c and γ = 1/√(1 − β²).
Length contraction applies to the dimension parallel to relative motion. The tool keeps proper length, contraction factor, Lorentz factor, and percent reduction visible so the visitor can see why everyday objects show no meaningful effect while relativistic speeds do.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Proper length — m; minimum 1.0E-6; maximum 1.0E+18
- Speed as a fraction of light speed — c; minimum 0; maximum 0.999999999999
Worked example
| Input | Value |
|---|---|
| Proper length | 10 |
| Speed as a fraction of light speed | 0.8 |
A 10 m proper length moving at 0.8c is observed as 6 m long, with γ = 1.6667.
Assumptions and limits
- Proper length is the length measured in the object's rest frame and the entered speed is relative to the observing frame.
- The motion is uniform and the reported dimension is parallel to the motion direction.
- The model is special relativity in flat spacetime and does not calculate acceleration, rotation, deformation, or transverse contraction.
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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