Length Contraction Calculator
Calculate relativistic length contraction: L = L0 * sqrt(1 - v^2/c^2), the shortened length as seen by a stationary observer.
Contracted Length
43.602761 m
Contracted Length vs Proper Length (L0)
Formula
## Lorentz Length Contraction Objects moving at relativistic speeds appear shorter in the direction of motion. ### Formula **L = L0 * sqrt(1 - v^2/c^2) = L0 / gamma** - *L0* = proper length (measured at rest) - *v* = relative velocity Contraction occurs only along the direction of motion. Transverse dimensions are unaffected.
Esempio Risolto
A 100 m spaceship at 0.9c.
- 01beta = 0.9, gamma = 2.294
- 02L = L0 / gamma = 100 / 2.294
- 03L = 43.59 m
- 04The ship appears 56.4% shorter.
Domande Frequenti
Would a moving object look visually squished?
Not exactly. Due to the finite speed of light, a moving object appears rotated (Terrell rotation) rather than simply compressed. The contraction is real but the visual appearance is more complex.
Does the object actually shrink?
In the moving object's own frame, it is not contracted at all. Length contraction is a real physical effect of how different frames measure space, not an illusion.
At what speed is the contraction noticeable?
At 10% of c, contraction is only 0.5%. It becomes dramatic above 80% of c, where the length drops below 60% of the rest length.
Impara