⏱️ Time Dilation Calculator
Calculate relativistic time dilation using Einstein's special theory of relativity. Solve for dilated time, proper time, or velocity using the Lorentz factor γ = 1/√(1 − v²/c²). Includes step-by-step solutions and reference tables.
What Is Time Dilation?
Time dilation is a relativistic effect predicted by Albert Einstein's special theory of relativity (1905). It states that time passes more slowly for an object in motion relative to a stationary observer. The faster an object moves, the greater the time dilation effect.
This effect is not a mechanical defect of clocks — it is a fundamental property of spacetime itself. Time and space are not absolute; they are relative to the observer's frame of reference.
Key concepts of time dilation:
- Proper time (Δt₀): The time measured in the moving object's own frame of reference.
- Dilated time (Δt): The time measured by a stationary observer watching the moving object.
- Lorentz factor (γ): The factor by which time is dilated, always ≥ 1.
- Symmetry: Each observer sees the other's clock running slow — the effect is reciprocal.
The Time Dilation Formula
The formula for velocity-based time dilation is:
Δt = γ · Δt₀
where the Lorentz factor is: γ = 1 / √(1 − v²/c²)
Δt = dilated time (stationary frame), Δt₀ = proper time (moving frame), v = relative velocity, c = 299,792,458 m/s
At low velocities (v ≪ c), γ ≈ 1 and time dilation is negligible. As v approaches c, γ increases without bound, meaning time effectively slows to a stop as v → c.
Key Lorentz Factor Values
The following table shows how the Lorentz factor γ changes with velocity:
- 0.1c → γ = 1.005 (0.5% dilation)
- 0.5c → γ = 1.155 (15.5% dilation)
- 0.9c → γ = 2.294 (129% dilation)
- 0.99c → γ = 7.089 (609% dilation)
- 0.999c → γ = 22.37 (2,137% dilation)
At 0.5c, 1 second of proper time corresponds to 1.155 seconds of dilated time. At 0.99c, 1 second of proper time stretches to 7.089 seconds in the stationary frame.
Real-World Applications
Time dilation is not just a theoretical concept — it has been measured and verified in numerous experiments:
- GPS satellites: Clocks on GPS satellites run about 38 microseconds per day faster than clocks on Earth (combining special and general relativistic effects). Without correction, GPS accuracy would drift by ~10 km per day.
- Hafele-Keating experiment (1971): Atomic clocks flown around the world on commercial jets showed measurable time differences compared to clocks on the ground.
- Muon lifetime: Muons created in the upper atmosphere have a lifetime of only 2.2 μs at rest, but they reach the ground because their lifetime is dilated by γ ~ 7 at near-light speeds.
- Particle accelerators: At CERN, particles moving at 0.999999c experience time dilation factors exceeding 1,000 — their lifetimes are extended accordingly.
Why Use This Calculator?
- Solve for any variable: Calculate Δt, Δt₀, or v depending on what's unknown.
- Multiple velocity units: Enter velocity as a fraction of c, or in m/s or km/s.
- Step-by-step solution: See exactly how the calculation is performed.
- Gamma curve visualization: See how γ changes with velocity.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Time Dilation Calculator FAQ
What is time dilation?
Time dilation is the relativistic effect where time passes more slowly for an object in motion relative to a stationary observer. The effect becomes significant only at velocities approaching the speed of light.
What is the time dilation formula?
The formula is Δt = γ · Δt₀, where γ = 1/√(1 − v²/c²). Δt is the dilated time (stationary frame), Δt₀ is the proper time (moving frame), v is velocity, and c is the speed of light.
What is the Lorentz factor?
The Lorentz factor (γ) is the factor by which time dilates. It equals 1 at rest and increases without bound as velocity approaches the speed of light. At 0.5c, γ = 1.155; at 0.9c, γ = 2.294; at 0.99c, γ = 7.089.
Why can't we reach the speed of light?
As an object with mass approaches the speed of light, its relativistic mass increases without bound, requiring infinite energy to accelerate further. The Lorentz factor γ goes to infinity as v → c, making it physically impossible for massive objects to reach c.
Is time dilation symmetric?
Yes. In special relativity, each observer sees the other's clock running slow. This apparent paradox is resolved when one observer accelerates and turns around (the twin paradox), which breaks the symmetry.
What is the twin paradox?
The twin paradox is a thought experiment where one twin travels at high speed into space and returns, while the other stays on Earth. When they reunite, the travelling twin has aged less. This is resolved by the fact that the travelling twin undergoes acceleration, breaking the symmetry of special relativity.
Does time dilation affect GPS?
Yes. GPS satellite clocks run about 38 microseconds per day faster than clocks on Earth. This is a combination of special relativistic time dilation (satellites move fast, slowing their clocks) and general relativistic gravitational time dilation (satellites are farther from Earth's gravity, speeding their clocks). GPS systems correct for this to maintain accuracy.
What is gravitational time dilation?
Gravitational time dilation is a separate effect predicted by general relativity. Clocks closer to a massive object run slower than clocks farther away. This effect is not included in this calculator, which covers only velocity-based (special relativistic) time dilation.
How accurate is this calculator?
This calculator uses the exact special relativistic time dilation formula. Results are accurate to the precision you select. For velocities very close to c, extremely high precision is needed to see the effect.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.