How long does it take NTP to "sync up"

Assuming "sync up" means achieving similar (~1ms) times, how long does it take to:

  1. "Sync up" my local computer to an NTP server?
  2. "Sync up" my alternate local (networked) computers to one central computer set up as an NTP server?

There is no simple answer.

The time that it takes for your local clock to become highly accurate is heavily dependent on your ntp configuration and the state of your system clock when ntp starts. That latency between you and your peer NTP servers and the accuracy of their clocks will also factors into how long it takes.

By default the ntp daemon will gradually correct (slew) the clock when it starts. How long this takes obviously is directly related to current offset between your clock and the correct time.

If the clock has too high of an offset when the NTP daemon starts using a default config, the daemon will immediately quit, log an error and expect you to correct manually.

There are options to control the frequency you pool your peers, you can set options to send a burst of sync packets when the daemon starts so you daemon can get the determine the correct time quickly (but this doesn't mean your system clock will be immediately corrected).

If you need highly accurate time then you probably should spend time reviewing the official documentation on ntp.org.