I would recommend not using the time dilation formula. It is too easy to misuse. Instead, you should always use the Lorentz transform.
While it's safer to use the full Lorentz transform, IMO the time dilation formula can give better physical intuition if you're trying to picture how things are behaving in a given frame. It's always true that a clock which is moving in a given inertial frame is running slower in that frame, so for example if gamma=1.25, that means in the frame of the observer who sees the clock in motion, it takes 1.25 seconds for the clock to tick forward by 1 second. So the larger the value of gamma, the slower the clock is ticking in the observer's frame. If gamma=1, then that means the clock is at rest relative to the observer, and it's ticking at 1 second per second of time in the observer's frame (no relativistic time dilation).I do not fully understand the time dialation formula, if the answer is nearer to 1 does that mean time itself under perspection has slowed or increased?
