The relativity time dilation calculator computes all major effects of Einstein's special theory of relativity: Lorentz factor (γ), time dilation, length contraction, relativistic mass, and relativistic kinetic energy. Use the velocity slider to explore effects from 0 to 0.9999c, or select from pre-set scenarios including the ISS, fastest spacecraft, and classic "twin paradox" speeds.
Velocity Input
Optional: for time/length/mass calculations
Lorentz Factor (γ)
Lorentz Factor vs. Velocity
How to Use the Relativity Time Dilation Calculator
Einstein's special theory of relativity (1905) showed that time, length, and mass are not absolute — they depend on relative velocity. This calculator computes all these effects using the Lorentz factor γ = 1/√(1−v²/c²), where c = 299,792,458 m/s.
Step 1: Set the Velocity
Use the slider to set velocity as a fraction of c (the speed of light). You can also type a value directly in the fraction, m/s, or km/s fields — they update each other automatically. Use the presets to jump to common scenarios: the ISS (7.66 km/s = 0.00002558c), the fastest spacecraft ever (about 70 km/s), or relativistically significant speeds like 0.5c and 0.9c.
The Twin Paradox at 0.8c
At v=0.8c, γ = 1/√(1−0.64) = 1/√0.36 = 1/0.6 ≈ 1.667. If a traveler spends 1 year aboard a spacecraft at 0.8c (proper time t₀=1 year), Earth observers measure 1.667 years passing. The traveler returns home younger than their twin by 0.667 years. Enter t₀=31,557,600 seconds (1 year) to see this in seconds.
Length Contraction at 0.9c
A 100-meter spacecraft traveling at 0.9c (γ≈2.294) appears only 100/2.294 ≈ 43.6 meters long to a stationary observer. The crew aboard measures the full 100 meters. Enter L₀=100 to see the contracted length. This explains why cosmic ray muons, created at the top of the atmosphere (~15 km up), survive to reach Earth's surface despite having a short half-life — the atmosphere appears much shorter from the muon's reference frame.
FAQ
What is time dilation in special relativity?
Time dilation means that a moving clock runs slower than a stationary one. The moving observer experiences less time: t = γ × t₀, where γ (Lorentz factor) is always ≥ 1. At 0.9c, γ ≈ 2.29 — a 1-hour trip at 0.9c takes 2.29 hours as measured by a stationary observer, but only 1 hour for the traveler.
What is the Lorentz factor?
The Lorentz factor γ = 1/√(1 − v²/c²) quantifies all relativistic effects. At v=0, γ=1 (no effect). At v=0.5c, γ=1.155. At v=0.9c, γ=2.294. At v=0.99c, γ=7.089. The factor diverges to infinity as v approaches c, which is why nothing with mass can reach c — it would require infinite energy.
What is length contraction?
A moving object appears shorter along its direction of motion to a stationary observer. The contracted length is L = L₀/γ. At 0.9c (γ≈2.29), a 100 m spaceship appears 43.6 m long to a stationary observer. The traveler inside measures the full 100 m — length contraction is a relative effect between frames.
What is E=mc²?
E = mc² is the rest energy of a mass m at zero velocity. The full relativistic energy is E = γmc², which includes both rest energy and kinetic energy. Relativistic kinetic energy is KE = (γ−1)mc². At low speeds, (γ−1) ≈ v²/(2c²), so KE ≈ ½mv² — the classical formula. At 0.99c, relativistic KE is over 6 times the classical value.
Is this tool free?
Yes, completely free with no signup required. All calculations run locally in your browser.
Can anything travel faster than light?
No. As velocity approaches c, the Lorentz factor γ approaches infinity, meaning infinite energy would be required. This is a fundamental consequence of special relativity, not a practical engineering limitation. However, spacetime itself can expand faster than c — as in cosmic inflation — and this doesn't violate special relativity.