# Calculate time dilation with Lorentz transformation [duplicate]

It is possible to calculate the time dilation with Lorentz transformation? So with the equation $$t'=\gamma(t-\frac{x v}{c^2}) \tag{1}$$ in which $\gamma$ is the Lorentz-Factor?

In an exercise I have succeeded.

So why can be calculated with the equation $(1)$ the time dilation? What is the reason?

• The first step is to be comfortable with the interpretation of each of the symbols, as well with the concept of proper time. After you are comfortable with that, one can turn your question into mathematics by realizing the quantity $t_2'-t_1'$ (for spacetime events 1 and 2) is what you're after. Also, this is a fairly standard derivation that you should be able to find in any special relativity book.
– BMS
Feb 12 '14 at 6:41
• My answer to the question I've linked shows how to calculate time dilation using the Lorentz transformations. See also this question. Feb 12 '14 at 6:50