This Demonstration gives a visual illustration of relativistic time dilation according to the Lorentz transformation. When the velocity of a rocketship is zero, all clocks display the current time. The faster the rocket's velocity, as represented by the slider, the greater the time dilation factor gets. You can then see the resulting discrepancies in time measurement from the perspectives both of travellers located inside the moving rocketship and that of a stationary observer.
The left column shows two clocks from the perspective of the moving observer, an inside clock and an outside clock. The inside clock displays time as it passes for the moving observer, while the outside clock is not moving. The faster he is travelling, the faster the outside clock seems to be ticking relative to his own clock.
The time dilation is given by the formula .
The right column shows both clocks from the perspective of a stationary observer. The top clock displays the rate of the passage of time within the rocketship and will therefore appear to be ticking at a slower rate relative to his own clock displayed underneath.