Relativistic Time Dilation Calculator
Calculate how moving clocks run slow by finding the Lorentz factor and the dilated time for a given velocity.
Velocity unit
s
Dilated time = γ × proper time
- 1
1 − β²
1 − 0.9² = 0.19 - 2
√(1 − β²)
√0.19 = 0.43588989 - 3
Lorentz factor γ = 1 ÷ √(1 − β²)
1 ÷ 0.43588989 = 2.294157
How does this calculator work?
Relativistic time dilation makes moving clocks run slow. The Lorentz factor γ = 1/√(1 − v²/c²) multiplies the proper time Δt₀ to give the observed time Δt = γ·Δt₀. Enter a velocity (in m/s or as a fraction of light speed) below c to get γ, the dilated time, and the extra time gained.
Formula
How this is calculated
Enter the velocity v of the moving object and the proper time Δt₀ (the time interval measured by a clock at rest in the moving frame). The velocity can be given directly in meters per second or as a fraction of the speed of light c = 2.99792458×10⁸ m/s using the unit selector; in the latter case v = β·c where β is the chosen fraction.
The Lorentz factor is γ = 1/√(1 − v²/c²). Because Δt = γ·Δt₀ and γ ≥ 1, the elapsed time observed in a frame relative to which the clock moves is always longer than the proper time — moving clocks tick slow. The time gained is simply Δt − Δt₀, which grows without bound as v approaches c.
The calculator requires v < c (|β| < 1); at or above light speed the square root becomes zero or imaginary and γ diverges, so no finite result is returned. At everyday speeds β is tiny and γ ≈ 1, making dilation negligible, while near β = 0.999 the factor blows up dramatically, as shown in the γ-versus-v/c curve.
Frequently asked questions
The Lorentz factor γ = 1/√(1 − v²/c²) quantifies relativistic effects. It equals 1 at rest and increases toward infinity as the speed approaches that of light, scaling time, length, and relativistic mass.
For v ≥ c the term 1 − v²/c² becomes zero or negative, so √(1 − v²/c²) is zero or imaginary and γ is undefined. Massive objects cannot reach c, so the model only applies for v < c.
Longer. Since γ ≥ 1, the dilated time Δt = γ·Δt₀ is always at least the proper time, meaning a moving clock appears to run slow compared with a stationary observer.
Also known as
TG we-Calculate Editorial Team. (2026). Relativistic Time Dilation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/time-dilation-calculator
TG we-Calculate Editorial Team. "Relativistic Time Dilation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/time-dilation-calculator.
TG we-Calculate Editorial Team, "Relativistic Time Dilation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/time-dilation-calculator
@misc{wecalculate_time_dilation_calculator, title = {Relativistic Time Dilation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/time-dilation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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