Special relativity and the Lorentz factor
Einstein's 1905 special relativity rests on two postulates: the laws of physics are the same in every inertial frame, and the speed of light c = 299 792 458 m/s (exact by definition, SI/NIST) is the same for all observers. Their consequence is the Lorentz factor γ = 1 / √(1 − v²/c²), which grows without bound as v → c and governs how time, length, momentum and energy transform between frames.
Time dilation and length contraction
A moving clock runs slow: an interval Δt₀ in the moving frame is observed as Δt = γ Δt₀. A moving object is shorter along its motion: L = L₀ / γ. Both effects are negligible at everyday speeds and become dramatic only as v approaches c — the reason muons created high in the atmosphere reach the ground before decaying.
How to use the calculator
Set the speed. The tool returns γ, the dilated time, the contracted length, the relativistic momentum p = γmv and the total energy E = γmc², so you can see how each quantity diverges as you approach the speed of light.
Note: this tool covers special relativity — uniform motion in flat spacetime, no gravity. Accelerating frames and gravitation require general relativity. Nothing with mass can reach c, because γ (and the energy) would become infinite.
Frequently asked questions
What is the Lorentz factor?
The Lorentz factor is gamma = 1 / sqrt(1 - v^2/c^2). It equals 1 at rest and grows toward infinity as the speed v approaches the speed of light c, scaling time dilation, length contraction and relativistic energy.
What is time dilation?
Time dilation is the slowing of a moving clock as seen from another frame: a proper time interval delta_t0 is observed as delta_t = gamma * delta_t0. It is only noticeable at speeds close to the speed of light.
What is length contraction?
A moving object is measured to be shorter along its direction of motion by the factor gamma: L = L0 / gamma, where L0 is the object's rest (proper) length. Perpendicular dimensions are unchanged.
Can anything travel faster than light?
No object with mass can reach or exceed the speed of light, because the Lorentz factor and the energy required both become infinite as the speed approaches c. Light itself always travels at c in vacuum.
References
- A. Einstein (1905), "Zur Elektrodynamik bewegter Körper" ("On the Electrodynamics of Moving Bodies"), Annalen der Physik 322(10):891–921.
- E. F. Taylor & J. A. Wheeler, Spacetime Physics, 2nd ed. (W. H. Freeman).
- Speed of light c = 299 792 458 m/s, exact by the SI definition of the metre (SI/NIST).