Time Dilation Calculator

At a glance:Time dilation is one of the most famous predictions of special relativity (Einstein, 1905): a moving clock runs slower than one at rest. The relation is Δt=γ·Δτ, where Δτ is the proper time (the time measured by a clock moving with the object — e.g. your own ageing on a spaceship), Δt is the time measured by a stationary observer (people on Earth), γ=1/√(1−v²/c²) is the Lorentz factor and v is the relative speed. Because γ≥1, Δt≥Δτ: the moving observer's clock ticks less. Example: v=0.8c → γ=1/√(1−0.64)=1.667; if you spend Δτ=1 year on the ship, people on Earth see Δt=1.667 years pass — the classic twin paradox (the travelling twin ages less). Physical meaning: time is not absolute; it depends on the observer's motion — high-speed travel literally slows your clock. At v≪c, γ≈1 and the effect is negligible (GPS satellites at ~3.9 km/s show ~7 µs/day, corrected continuously); as v→c, γ→∞ and time nearly stops. History: Einstein's 1905 special relativity built on the Michelson–Morley experiment (1887) and Lorentz's transformation; time dilation was verified by muon-decay atmospheric measurements and is now standard in particle accelerators and GPS. Applications: (1) the twin paradox and thought experiments; (2) GPS — satellite and ground clocks must be synchronised with relativistic correction; (3) particle accelerators — fast particles live longer (muons reach the ground); (4) cosmic-ray muon lifetime extension; (5) understanding the light-speed limit. Notes: (1) v must be below c; (2) Δτ is the moving frame's own time, Δt the stationary frame's; (3) this is symmetric for inertial frames (each sees the other's clock slow — resolved in the twin paradox by the turnaround acceleration).