Time Dilation Calculator (Special Relativity)

Compute the observer elapsed time and Lorentz factor from speed and proper time.

Input

Enter the proper time of a moving clock and its speed to compute the elapsed time measured by a stationary observer and the Lorentz factor.

Proper time delta-t0

Time ticked by the moving clock itself, in seconds

Speed input method

Specify either as a fraction of light speed beta or in meters per second

Speed v

× c

Enter a value of 0 or more and less than 1 (for example 0.9 is 90 percent of light speed)

Result

Elapsed time measured by the observer delta-t

2.294157s

This is 1.294157 seconds longer than the proper time.

Lorentz factor gamma

2.294157

Dilation factor

about 2.294157 times

Fraction of light speed beta

0.9

Speed v

269,813,212.2 m/s

In the twin paradox the proper time delta-t0 belongs to the traveling twin, while delta-t is the elapsed time for the twin who stayed on the ground.

beta equals v over c, gamma equals 1 over the square root of 1 minus beta squared, and delta-t equals gamma times delta-t0. The speed of light c is 299792458 meters per second.

How it works

The speed ratio beta is defined as beta equals v divided by c, where c is the speed of light 299792458 meters per second.
The Lorentz factor is gamma equals 1 divided by the square root of 1 minus beta squared.
The elapsed time measured by the observer is delta-t equals gamma times delta-t0, where delta-t0 is the proper time of the moving clock.
Speeds that give beta of 1 or more (at or above light speed) cannot be computed. An object speed must stay below light speed.
In the twin paradox, the proper time delta-t0 belongs to the traveling twin, while delta-t is the elapsed time for the twin who stayed on the ground.

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