Time Dilation Calculator
Calculate time dilation using Einstein relativity formula Δt' = Δt/√(1−v²/c²). Enter proper time and velocity as fraction of c to compute dilated time, Lorentz factor, and time difference with interactive physics charts.
About This Calculator
This Time Dilation Calculator helps physics students, educators, and enthusiasts explore Einstein's theory of special relativity by computing how time slows down for objects moving at relativistic speeds. Enter the proper time experienced by a moving observer and their velocity as a fraction of the speed of light to calculate the dilated time as measured by a stationary observer. The results include the Lorentz factor γ, the equivalent velocity in meters per second, and the time difference between the two reference frames.
The calculation uses Einstein's time dilation formula: Δt' = Δt / √(1 − v²/c²), where Δt is the proper time, v is the observer velocity, c = 299,792,458 m/s is the speed of light, and Δt' is the relative time. The Lorentz factor γ = 1/√(1 − v²/c²) quantifies the degree of relativistic time dilation. At low speeds (v ≪ c), γ is approximately 1, and time dilation is negligible. As v approaches c, γ increases dramatically, approaching infinity at the speed of light. The interactive Lorentz factor chart visualizes how γ changes across the velocity range from rest to the entered velocity, helping users understand the nonlinear nature of relativistic effects.
About the Physics: Special relativity, published by Albert Einstein in 1905, revolutionized our understanding of space and time. The theory establishes that the laws of physics are the same in all inertial reference frames and that the speed of light is constant regardless of the observer's motion. Time dilation, length contraction, and relativity of simultaneity are direct consequences of these two postulates. This calculator focuses specifically on time dilation — one of the most counterintuitive yet experimentally confirmed predictions of relativity. Real-world applications include GPS satellite corrections, particle accelerator experiments, and cosmic ray muon observations, all of which demonstrate that time dilation is a real physical phenomenon, not merely a theoretical curiosity.
Frequently Asked Questions
What is time dilation?
Time dilation is the difference in elapsed time measured by two observers who are moving relative to each other. According to Einstein's special relativity, the faster an object moves through space, the slower time passes for that object relative to a stationary observer. This effect becomes significant only at speeds close to the speed of light.
How does the time dilation formula work?
The time dilation formula is Δt' = Δt / √(1 − v²/c²), where Δt is the proper time measured by the moving observer, v is the velocity of the observer, c is the speed of light (299,792,458 m/s), and Δt' is the dilated time measured by a stationary observer. The denominator √(1 − v²/c²) is the Lorentz factor γ, which determines how much time slows down.
What is the Lorentz factor?
The Lorentz factor γ = 1/√(1 − v²/c²) is a key quantity in special relativity that describes how much time dilation, length contraction, and relativistic mass increase occur. At everyday speeds, γ is approximately 1, meaning relativistic effects are negligible. At 50% of light speed, γ ≈ 1.155. At 90% of light speed, γ ≈ 2.294. As velocity approaches the speed of light, γ approaches infinity.
At what speed does time dilation become noticeable?
Time dilation effects become noticeable at speeds above 10% of light speed (approximately 30,000 km/s). At 10% of c, time slows by about 0.5%. At 50% of c, time slows by about 13.4%. At 86.6% of c, time runs at half the rate. At 99.99% of c, one year for the traveler equals about 70.7 years for an observer on Earth.
Does time dilation affect GPS satellites?
Yes, GPS satellites experience both special relativistic time dilation (due to their orbital velocity of about 14,000 km/h) and general relativistic gravitational time dilation (due to weaker gravity at altitude). The combined effect causes GPS satellite clocks to gain about 38 microseconds per day relative to Earth clocks. GPS systems must correct for this relativistic effect to maintain positional accuracy.
What is the twin paradox?
The twin paradox is a thought experiment where one twin travels at near-light speed in a spaceship while the other remains on Earth. When the traveling twin returns, they find the Earth-bound twin has aged much more. This is not actually a paradox because the traveling twin undergoes acceleration and deceleration, breaking the symmetry of the reference frames. The traveling twin experiences less proper time due to their high-speed journey.
Is time dilation real or just theoretical?
Time dilation is a real, experimentally verified phenomenon. The Hafele-Keating experiment in 1971 flew atomic clocks around the world on commercial airliners and confirmed the predicted time differences. Particle accelerators regularly observe that unstable particles moving at near-light speed decay much slower than stationary particles. Muons created by cosmic rays in the upper atmosphere reach Earth's surface only because time dilation extends their otherwise brief lifespan.
Does light experience time dilation?
No. For an observer traveling at the speed of light, the Lorentz factor γ becomes infinite (1/0), so time dilation is undefined. Photons do not experience time — from a photon's perspective, its journey across the universe is instantaneous. This is consistent with the fact that the speed of light is the same in all reference frames and represents the ultimate cosmic speed limit.