Physics & Mechanics

Time Dilation Calculator

Calculate the dilated time interval for an object moving at relativistic speeds relative to a stationary observer.

s
m/s
Dilated Time (Δt)
1.155

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Time is Relative

Before Einstein, everyone believed that time was an absolute, ticking cosmic clock that moved at the same rate for everyone in the universe. Special Relativity shattered this idea, proving that time is a local experience.

Time Dilation is the phenomenon where a clock moving at high speeds ticks slower relative to a clock that is at rest. The faster you move through space, the slower you move through time.

The Twin Paradox

If you leave Earth on a spaceship traveling at 99% the speed of light, time for you slows down dramatically. You might travel for 1 year (according to your ship's clock), but when you return to Earth, you will find that 7 years have passed for everyone else. You have effectively time-traveled into the future.

The Formula

Δt=Δt01v2c2\begin{aligned} \Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}} \end{aligned}

Where:
Δt\Delta t=
Dilated Time (Time passed for stationary observer)
Δt0\Delta t_0=
Proper Time (Time passed for moving object)
v=
Velocity of the object
c=
Speed of Light

Example Calculation

An astronaut travels at 86.6% the speed of light ($v = 259,620,311 , \text{m/s}$) for exactly $10 , \text{years}$ of proper time ($\Delta t_0$).

  1. Calculate v/c: $0.866$.
  2. Square it: $0.866^2 \approx 0.75$.
  3. Subtract from 1: $1 - 0.75 = 0.25$.
  4. Square Root: $\sqrt{0.25} = 0.5$.
  5. Divide Proper Time: $10 / 0.5 = 20 , \text{years}$.

While the astronaut aged 10 years, $20 , \text{years}$ passed on Earth.

Frequently Asked Questions

Time literally slows down. Biological aging, radioactive decay, and mechanical ticking all slow down perfectly. To the moving astronaut, time feels completely normal; they only notice the dilation when they compare clocks with Earth.

Yes, GPS satellites orbit Earth at roughly $14,000 , \text{km/h}$. At this speed, time dilation causes their onboard atomic clocks to tick $7$ microseconds slower every day. If engineers didn't program your phone's GPS to correct for Einstein's equations, Google Maps would drift off by $10 , \text{kilometers}$ every day!

If you plug $v=c$ into the equation, the denominator becomes zero, resulting in infinity. For a photon of light traveling at $c$, time stops completely. From a photon's perspective, it crosses the universe in an instant of zero time.