Time Dilation Calculator
Calculate time dilation effects in special relativity using the Lorentz factor
Calculate Time Dilation
Time interval as measured in the moving reference frame
Velocity must be less than the speed of light (c)
Time Dilation Results
Dilated Time (Δt')
Time Difference
Formula used: Δt' = γ × Δt = Δt / √(1 - v²/c²)
Where: Δt' = dilated time, γ = Lorentz factor, Δt = proper time, v = velocity, c = speed of light
Twin Paradox Example
Space Travel Scenario
Traveling twin: Takes a 10-year journey at 0.8c
Earth-bound twin: Stays on Earth
Velocity: v = 0.8c (80% speed of light)
Proper time: Δt = 10 years (traveling twin's clock)
Calculation
γ = 1 / √(1 - v²/c²) = 1 / √(1 - 0.8²) = 1 / √(1 - 0.64)
γ = 1 / √(0.36) = 1 / 0.6 = 1.667
Δt' = γ × Δt = 1.667 × 10 years
Result: 16.67 years pass on Earth
Age difference: 6.67 years
Velocity References
Everyday Speeds
Car highway: ~0.00000003c
Jet aircraft: ~0.0000003c
Earth orbit: ~0.0001c
Space Technology
Parker Solar Probe: ~0.0006c
Voyager spacecraft: ~0.00006c
Ion drive: ~0.00002c
Theoretical Speeds
0.1c: Noticeable effects
0.5c: Significant dilation
0.9c: Extreme effects
0.99c: Time nearly stops
Physics Constants
Note: Time dilation becomes significant only at very high speeds (>10% of c)
Understanding Time Dilation
What is Time Dilation?
Time dilation is a phenomenon predicted by Einstein's special theory of relativity where time passes differently for observers moving at different velocities relative to each other. As an object approaches the speed of light, time slows down relative to a stationary observer.
The Twin Paradox
The famous thought experiment involves identical twins where one travels to space at high speed while the other remains on Earth. When the traveling twin returns, they will have aged less than their Earth-bound sibling due to time dilation.
Real-World Applications
- •GPS satellites must account for time dilation
- •Particle accelerator experiments observe time dilation
- •Cosmic ray muons reach Earth due to time dilation
The Mathematics
Δt' = γ × Δt
γ = 1 / √(1 - v²/c²)
- Δt': Time measured by stationary observer (dilated time)
- Δt: Time measured by moving observer (proper time)
- γ (gamma): Lorentz factor
- v: Velocity of moving observer
- c: Speed of light in vacuum
Important: Time dilation only becomes significant at speeds approaching the speed of light. At everyday speeds, the effect is negligible.
Key Principle
Time is not absolute but depends on the observer's reference frame and relative motion.
Speed Limit
Nothing with mass can reach or exceed the speed of light. As v approaches c, γ approaches infinity.
Experimental Proof
Time dilation has been confirmed countless times in particle physics experiments and GPS technology.