How to calculate the last third of the night for performing tahajjud

When is the correct time to pray tahajjud? Where I live fajr is at 6 so I pray it an hour before. How exactly do we work out last 3rd of the night?

From what I understand, the last third of the night is calculated this way: If the time between the isha prayer and the fajr prayer is nine hours, the last three hours of these nine hours would be the last third of the night.

Note that if it is more convenient, you can perform tahajjud (more commonly called qiyam) before going to bed. You can even perform the same kind of worship during the daytime, though it would not exactly be tahajjud, but inshaAllah God will still reward you amply for it. See my essay: Mysticism without Sufism: A Guide to Tahajjud, Islam’s Meditation Practice