Android - How to get exact call time?

For Android 5.0.x Lollipop:

  1. Either on "Recents" or "Call History", tap the entry you want to see. It will open a mini-menu under the entry with options "Call back" and "Details".
  2. Select "Details" to see the call details.
  3. From here, you can see the time when you receive/miss a call, and also the duration of the call.

Call Details on Phone app

Click the image for larger variant

In addition to Andrew's answer, you need to click the entry and not the picture of the contact for the mini-menu to appear. I was clicking the picture of the contact, and it pulls up the contact info - not the call detail.