Calculate special relativistic time dilation from velocity. Find the Lorentz factor, dilated time, and compare effects at various speeds from walking to near-light.
Time dilation is one of the most remarkable predictions of Einstein's special relativity: a moving clock ticks slower than a stationary one. The faster you travel, the more pronounced the effect becomes, governed by the Lorentz factor γ = 1/√(1 − v²/c²). At everyday speeds the effect is negligibly small, but as you approach the speed of light, time slows dramatically.
This effect is not theoretical speculation — it has been confirmed countless times. GPS satellites must correct for time dilation to maintain accuracy, cosmic ray muons survive to reach Earth's surface because their internal clocks run slow, and precision atomic clocks flown on aircraft have measured exactly the predicted difference.
This calculator computes the Lorentz factor and time dilation for any velocity from walking speed to 99.999% of light speed. Enter a proper time experienced by a moving traveler and see how much time passes for a stationary observer, or explore the comprehensive comparison table spanning 14 orders of magnitude in speed.
Time dilation connects fundamental physics to practical technology (GPS) and science fiction scenarios (interstellar travel). This calculator makes the math accessible and provides the comprehensive speed-comparison table that textbooks rarely include, from everyday speeds to near-light velocities. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Lorentz factor: γ = 1/√(1 − β²), where β = v/c. Time dilation: t = γ × t₀, where t₀ is proper time (moving frame) and t is coordinate time (stationary frame). The time difference is Δt = (γ − 1) × t₀.
Result: γ = 2.00, Observer time = 2.00 years
At 86.6% the speed of light, the Lorentz factor is exactly 2. A traveler experiencing 1 year would find that 2 years have passed on Earth — the twin paradox in action.
Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.
Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes
Use this for repeatability, keep assumptions explicit. ## Practical Notes
Track units and conversion paths before applying the result. ## Practical Notes
Use this note as a quick practical validation checkpoint. ## Practical Notes
Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes
Use as a sanity check against edge-case outputs. ## Practical Notes
Capture likely mistakes before publishing this value. ## Practical Notes
Document expected ranges when sharing results.
A consequence of special relativity where a moving clock runs slower than a stationary clock. The effect increases with speed and is described by the Lorentz factor γ.
Yes. It has been experimentally confirmed many times, including with atomic clocks on aircraft, GPS satellite corrections, and the extended lifetime of cosmic ray muons.
If one twin travels at high speed and returns, they will have aged less than the twin who stayed home. This is not a paradox but a real prediction confirmed by experiment.
Special relativistic time dilation is caused by velocity (moving clocks run slow). Gravitational time dilation is caused by gravity (clocks in stronger gravity run slow). Both effects are real and additive.
Yes. GPS satellites orbit at ~3.87 km/s, causing their clocks to tick about 7 microseconds/day slower due to velocity. This is partially offset by gravitational effects (45 μs/day faster). Without corrections, GPS would drift by ~10 km/day.
No. As v approaches c, γ approaches infinity, meaning infinite energy would be needed. Only massless particles (like photons) travel at c.