PHYSICS / SPECIAL RELATIVITY
Calculate length parallel to relative motion from proper length and speed fraction.
METHOD / WORKED EXAMPLE
Length contraction applies only along relative motion and compares a rest-frame proper length with simultaneous endpoint measurements in another inertial frame.
WORKED DEFAULT
For a 10 m proper length moving at 0.8c, sqrt(1 - beta squared) is 0.6, so the measured parallel length is 6 m, a difference of 4 m.
READ THE RESULT
The object is not compressed in its own rest frame. The shorter value arises from how the observing frame defines simultaneous positions of the moving front and rear endpoints.
ASSUMPTIONS AND LIMITS
Length is parallel to uniform relative motion, endpoints are measured simultaneously in the observing frame, and gravity is neglected.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
No in this standard special-relativity relation. Length contraction affects the component parallel to the relative velocity. Perpendicular dimensions are unchanged between the inertial frames. For an object or path at an angle, resolve the geometry into parallel and perpendicular components before interpreting a measured shape.
A length in one frame is the spatial separation of both endpoints measured at the same time in that frame. If the front and rear positions are recorded at different times while the object moves, their separation mixes motion with geometry and is not the frame's contracted length.
Not directly. A photograph records light arriving together, not endpoint positions measured simultaneously after correcting for light-travel time. Relativistic visual appearance can include aberration and timing effects. This calculator returns the coordinate length from the Lorentz relation, not a camera image or optical rendering of the moving object.
RELATED TOOLS
Use boundary
Scale the rest-frame proper length by the reciprocal Lorentz factor along the direction of motion. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
L = L0 sqrt(1 - beta^2)