# Time dilation formula question

I understand that the formula for time dilation is given as

$$T = T_0\gamma = \frac{T_0}{\sqrt{1-v^2/c^2}}$$

Where T is moving with velocity v seen from $T_0$. Though, this is when an event is occuring, since the value for $T$ would in any case of $v>0$ be greater than $T_0$, meaning that the event takes longer time for $T$. However, in a situation like the twin paradox, if we ignore acceleration and all that, $T_0$ should be greater than $T$, since the time would tick slower for $T$. So what is the exact formula for such a situation, how is it derived, and is it true that abovementioned formula is only true for an event happening?

• You seem to have missed the starting problem that leads up to the twin paradox: for two unaccelerated observer they both see the other's clocks running slowly. (This is resolved by examining the situation in terms of the relativity of simultaneity and seeing that the two observers necessarily compare different pairs of events in space time events in space time in reaching their conclusions). – dmckee May 27 '18 at 19:54
• – dmckee May 27 '18 at 19:58