# Time Dilation Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

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.

Are you looking for the effect of massive objects on spacetime (the one very well represented in Interstellar?) visit our gravitational time dilation calculator!

## 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:

$\small \Delta t' = \gamma\Delta t = \frac{\Delta t}{\sqrt{1 - v^2 / c^2}}$

where:

• $\Delta t'$ – Time that has passed as measured by a stationary observer (relative time);
• $\gamma$ – Lorentz factor;
• $\Delta t$ – Time that has passed as measured by the traveling observer;
• $v$ – Speed of the traveling observer; and
• $c$ – Speed of light (299,792,458 m/s).

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.

You can meet another fundament of special relativity at our E=mc2 calculator, or a similar effect to time dilation originating in the same framework at the length contraction calculator.

## FAQ

### What is time dilation?

Time dilation is the difference in a time interval measured by two observers who move relative to each other. In particular, the higher your velocity is, the slower you move through time. However, this phenomenon is only truly noticeable at speeds close to that of light.

### How to calculate time dilation?

To calculate the time dilation for an observer moving with some relative velocity to a stationary observer:

1. Determine the time interval measured by the stationary observer.
2. Substitute the traveling viewer's velocity for v in the Lorentz factor formula, γ = √(1 - v²/c²).
3. Multiply the change in time by the Lorentz factor.
4. The result is the time as measured by the moving observer.

### How do I calculate proper time?

To calculate proper time, you need to divide both sides of the time dilation formula by the Lorentz factor, γ.

Remember that this quantity applies only to events that occurred at the same stationary position for the measuring observer.

### Does light experience time dilation?

No. Notice that for an observer traveling at the speed of light, the time dilation is undefined (1/0) due to the Lorentz factor. In fact, the velocity of light is the same in all reference frames (Lorentz invariant), so in the case of photons, it's difficult to talk about any time passage at all.

Bogna Szyk Time interval (Δt)
sec
Observer velocity (v)
km/s
Relative time (Δt')
sec
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