Time Dilation Calculator (Special Relativity)

Time Dilation — Einstein’s Special Theory of Relativity

One of the most counterintuitive predictions of Einstein’s Special Theory of Relativity (1905) is that time passes more slowly for a moving observer than for a stationary one. This effect — called time dilation — has been experimentally confirmed many times.

Lorentz Factor (γ) The Lorentz factor is the key dimensionless quantity in special relativity: γ = 1 / √(1 − v²/c²) = 1 / √(1 − β²)

Where:

• v = velocity of the moving object
• c = speed of light = 2.998 × 10⁸ m/s
• β = v/c (velocity as a fraction of the speed of light)

At low speeds (v « c), γ ≈ 1 and effects are negligible. As v → c, γ → ∞.

Time Dilation Formula Δt’ = γ × Δt

Where:

• Δt = proper time (time measured in the moving frame: on the moving clock)
• Δt’ = coordinate time (time measured by the stationary observer)
• A moving clock ticks SLOWER as seen by a stationary observer.

The Twin Paradox If one twin travels at high speed to a distant star and returns, they will be younger than the twin who stayed on Earth. This is not a paradox — the traveling twin experienced true acceleration, making the situations non-symmetric.

Length Contraction Moving objects also appear shorter along the direction of motion: L = L₀ / γ

Real-World Confirmation

• GPS satellites: move at 3.87 km/s, causing clocks to run slower by 7 μs/day (special relativity). General relativity adds another +45 μs/day (gravity). Without correction, GPS would drift ~10 km per day.
• Hafele-Keating experiment (1971): atomic clocks flown around the world confirmed time dilation within 10% of relativistic predictions.
• Muon lifetime: cosmic ray muons travel at 0.9999c and survive long enough to reach the ground: a journey that would take far longer than their laboratory lifetime without time dilation.