Time interval (Δt)
sec
Observer velocity (v)
mi/s
Relative time (Δt')
sec

Time Dilation Calculator

By Bogna Haponiuk

You've probably heard about the concept of time relativity. Whether you are already familiar with the idea of time dilation or just taking your first steps in the field of special relativity, this time dilation calculator is for you. It will help you to get a better understanding of relativistic effects and of the time dilation equation.

Time is relative: twin astronauts

The time dilation principle states that time isn't perceived in the same way by everyone. If you move at a very high speed, time begins to slow down. Obviously, you don't get to move in slow motion - from your perspective, it passes as usual. Instead, you can observe that time passes much slower for all objects you move relative to.

A famous thought experiment of twin astronauts is a good example that makes time dilation easier to understand. Imagine that one of the twins stays at home on Earth, and the other one gets on a high-speed rocket. He spends some time traveling through space and returns home after what he thought was a few years. To his surprise, he finds that his twin has aged much more and is now an older man.

Time dilation equation

How much faster did the 'stationary' twin age? It is possible to calculate the exact value with the time dilation equation:

Δt' = γΔt = Δt / √(1 - v²/c²)

where:

  • Δt' is the time that has passed as measured by the traveling observer (relative time);
  • Δt is the time that has passed as measured by a stationary observer;
  • v is the speed of the traveling observer;
  • c is the speed of light (299,792,458 m/s); and
  • γ is called the Lorentz factor.

You can probably see (or have already discovered it while playing with our time dilation calculator) that for the difference in the two time intervals to be noticeable, the observer speed must be extremely high - of the same order of magnitude as the speed of light. That's why relativistic effects are so counterintuitive: we are unable to experience them in everyday life.

Of course, these effects are real and measurable. Clocks on satellites run slightly slower than the ones on the surface of Earth due to their speed (see the escape velocity calculator for more information on their speed) - though they might run faster overall, once general relativity is taken into account.

Once we can travel at a speed close to the speed of light - for example, at 0.8c - we will also observe a more dramatic relativistic effect.

Bogna Haponiuk