Time Dilation Calculator
Calculate how time runs slower for objects moving at relativistic speeds
Velocity of the moving object relative to the observer (must be less than 299,792,458 m/s)
Proper time - time measured in the moving object's reference frame
How to Use This Calculator
Enter the Velocity
Input the velocity of the moving object relative to the observer in meters per second. Must be less than the speed of light (299,792,458 m/s).
Enter the Time Interval
Input the time interval as measured in the moving object's reference frame (proper time) in seconds.
Calculate
Click "Calculate Time Dilation" to get the dilated time, time difference, and Lorentz factor.
Interpret Results
The dilated time shows how much time passes in the stationary frame. Higher velocities result in greater time dilation.
Formula
Time Dilation: t = γt₀
Lorentz Factor: γ = 1 / √(1 - v²/c²)
where t is dilated time (stationary frame), t₀ is proper time (moving frame), v is velocity, c is speed of light
Example 1: Moderate Speed
Given: Velocity = 200,000,000 m/s (66.7% c), Time interval = 1 s
γ = 1 / √(1 - 0.667²) = 1.342
t = 1.342 × 1 = 1.342 s
Time runs 34.2% slower for the moving object.
Example 2: High Speed
Given: Velocity = 260,000,000 m/s (86.7% c), Time interval = 1 s
γ = 1 / √(1 - 0.867²) = 2.028
t = 2.028 × 1 = 2.028 s
Time runs 2.03× slower (more than double!).
Example 3: Very High Speed
Given: Velocity = 298,000,000 m/s (99.4% c), Time interval = 1 year
γ = 1 / √(1 - 0.994²) = 9.19
t = 9.19 × 1 = 9.19 years
One year for the traveler equals 9.19 years on Earth!
About Time Dilation
Time dilation is one of the most famous and counterintuitive effects of special relativity. It states that time runs slower for objects moving relative to an observer. This effect has been confirmed by numerous experiments and is essential for GPS satellites, which must account for time dilation to maintain accuracy.
Understanding Time Dilation
According to special relativity, there's no absolute time. Time measurements depend on the observer's reference frame. An observer moving relative to you will measure time differently than you do. The faster they move, the more pronounced the difference becomes.
When to Use This Calculator
- Physics Education: Teaching students about special relativity and time dilation
- GPS Systems: Understanding why GPS satellites need time corrections
- Particle Physics: Calculating time dilation for particles in accelerators
- Astrophysics: Understanding relativistic effects in cosmic rays
- Science Communication: Explaining relativity to general audiences
Why Use Our Calculator?
- ✅ Instant Results: Calculate time dilation immediately
- ✅ Accurate: Uses precise relativistic formulas
- ✅ Educational: Clear explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Comprehensive: Shows time differences for various intervals
- ✅ Easy to Use: Simple interface for quick calculations
Experimental Confirmation
Atomic Clocks: In 1971, scientists flew atomic clocks around the world on commercial jets. The clocks that traveled showed a measurable time difference compared to stationary clocks, confirming time dilation.
Particle Accelerators: Particles like muons created in the upper atmosphere should decay before reaching Earth's surface. However, due to time dilation at their high speeds, they survive long enough to reach the surface.
GPS Satellites: GPS satellites move at high speeds and experience time dilation. If not corrected, GPS would be inaccurate by about 7 microseconds per day, leading to positioning errors of several kilometers.
The Twin Paradox
The famous "Twin Paradox" illustrates time dilation: if one twin travels at high speed to a distant star and back while the other stays on Earth, the traveling twin will age less. When they reunite, the traveling twin will be younger. This is a real effect, though the acceleration required makes it more complex than simple time dilation.
Tips for Best Results
- Time dilation becomes significant above about 50% of the speed of light
- At 86.6% of c, time runs at half speed (γ = 2)
- At 99% of c, time runs about 7× slower (γ ≈ 7)
- At everyday speeds, the effect is negligible (less than one part in a trillion)
- Remember that velocity must always be less than the speed of light
Frequently Asked Questions
What is time dilation?
Time dilation is a relativistic effect where time runs slower for objects moving relative to an observer. It's one of the key predictions of special relativity and has been confirmed by numerous experiments.
Why does time slow down for moving objects?
According to special relativity, the speed of light is constant for all observers. This requires that space and time be relative. To maintain the constancy of the speed of light, time must slow down for moving objects. This is a fundamental feature of spacetime, not just an optical effect.
Is time dilation real or just theoretical?
Time dilation is a real, measurable effect. It has been confirmed by experiments with atomic clocks on aircraft, GPS satellites, and particle accelerators. The effect is small at everyday speeds but becomes significant at speeds approaching the speed of light.
Do we experience time dilation in everyday life?
At everyday speeds, time dilation is so small it's completely undetectable. For example, even at airplane speeds (about 300 m/s), the time dilation is only about one part in 10¹² - completely negligible. However, GPS satellites must account for it for accurate positioning.
What is the Lorentz factor?
The Lorentz factor (γ) quantifies how much time dilation and length contraction occur at a given velocity. It's calculated as γ = 1/√(1 - v²/c²) and approaches infinity as velocity approaches the speed of light. At low speeds, γ ≈ 1, meaning no significant relativistic effects.
Can time stop completely?
From a distant observer's perspective, time appears to stop at the event horizon of a black hole. However, for objects with mass, you can never reach the speed of light (where γ would be infinite), so time never stops completely for moving objects. As velocity approaches c, time dilation becomes extreme but never reaches infinity.