🚀 Special Relativity Calculator
Enter a speed as a fraction of light to get the Lorentz factor γ, plus time dilation, length contraction and relativistic energy.
Lorentz factor γ
1.6667
at 0.8c = 2.398e+8 m/s
Dilated time
1.6667 s
Contracted length
0.6 m
Kinetic energy
5.992e+16 J
Total energy
1.498e+17 J
The Lorentz factor γ = 1 ÷ √(1 − (v/c)²) governs special relativity. A moving clock runs slow (time dilation ×γ), a moving object shortens along its motion (length contraction ÷γ), and its kinetic energy is (γ−1)mc² — diverging from ½mv² as v approaches c. Nothing with mass can reach c, where γ → ∞. Speeds are entered as a fraction of the speed of light (299,792,458 m/s). 🔒 In your browser.
How the special relativity calculator works
Everything in special relativity flows from the Lorentz factor γ = 1 ÷ √(1 − (v/c)²). The tool computes γ from your speed, then applies it: a moving clock runs slow (dilated time = γ × proper time), a moving object contracts along its motion (contracted length = proper length ÷ γ), its relativistic kinetic energy is (γ − 1)mc² and its total energy is γmc².
Enter the speed as a fraction of the speed of light c (299,792,458 m/s) — 0.8 means 0.8c. The effects are negligible at everyday speeds (γ ≈ 1) and grow sharply as v approaches c, where γ → ∞ and energy would become infinite — which is why no object with mass can reach the speed of light.
Frequently asked questions
What is the Lorentz factor?
γ = 1 ÷ √(1 − (v/c)²), the factor by which time, length and energy are modified at speed v. It equals 1 at rest and grows without bound as v approaches the speed of light.
How do I calculate time dilation?
Multiply the proper time (measured in the moving frame) by γ: a moving clock ticks slower by that factor. At 0.8c, γ = 1.667, so 1 second aboard is 1.667 seconds to a stationary observer.
What is length contraction?
A moving object is shortened along its direction of motion by the factor γ: contracted length = proper length ÷ γ. At 0.8c a 1 m rod measures 0.6 m to a stationary observer.
Why can't anything travel faster than light?
As v approaches c, γ approaches infinity, so a mass's energy and momentum would become infinite — it would take infinite energy to get there. Only massless things (like light) travel at c.
What is relativistic kinetic energy?
KE = (γ − 1)mc². At low speeds this reduces to the familiar ½mv², but near light speed it grows far faster, diverging as v → c. The tool also shows the total energy γmc².