At speeds comparable to the speed of light c, time dilates (Δt = γ Δt₀), lengths contract (L = L₀/γ), and momentum and energy become relativistic: p = γ m₀ v, KE = (γ−1) m₀ c², E = γ m₀ c². Velocities add as w = (u+v)/(1+uv/c²). Classical limit when v ≪ c.
Relativity calculators
γ, length, time, momentum, energy, velocity addition
⚡ Relativity result
| Concept | Formula | Notes |
|---|---|---|
| Lorentz factor | γ = 1 / √(1 − v²/c²) | — |
| Length contraction | L = L₀ / γ | L₀ = proper length |
| Time dilation | Δt = γ Δt₀ | Δt₀ = proper time |
| Relativistic momentum | p = γ m₀ v | m₀ = rest mass |
| Relativistic kinetic energy | KE = (γ − 1) m₀ c² | — |
| Total energy | E = γ m₀ c² | Rest energy = m₀ c² |
| Mass-energy equivalence | E = m c² | — |
| Velocity addition | w = (u + v) / (1 + u v / c²) | Classical limit when v ≪ c |
About special relativity
Special relativity describes how space and time behave at speeds comparable to the speed of light c. The Lorentz factor γ = 1/√(1−v²/c²) appears in all key relations: length contraction L = L₀/γ (moving lengths shorten along the direction of motion), time dilation Δt = γ Δt₀ (moving clocks run slow), relativistic momentum p = γ m₀ v, and total energy E = γ m₀ c² with kinetic energy KE = (γ−1) m₀ c².
Velocity addition
Velocities do not add linearly. If a frame moves at v relative to the lab and an object moves at u in that frame, its speed in the lab is w = (u + v) / (1 + u v / c²). When u, v ≪ c, w ≈ u + v (classical).