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Relativistic Length, Proper Length & Speed

Solve special-relativistic length contraction along the direction of motion, including reverse proper-length and speed solutions.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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A 10 m proper length moving at 0.6c measures 8 m along its direction of motion.

L = L₀√(1 − v²/c²)

Enter these known values and leave the other values blank.

Proper length is measured in the object’s rest frame. The observed length uses simultaneous endpoint measurements in the observing inertial frame.
Only the dimension parallel to motion contracts. Both lengths must be positive and observed length cannot exceed proper length.
Relative speed is nonnegative and strictly below c. The inverse returns the speed magnitude, not a direction.

The observed length equals the proper length. A rest frame at exactly the speed of light is outside this model.

Bookify restricts the speed magnitude to 0 ≤ v < c and validates positive lengths with observed length no larger than proper length.