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The Last Third of the Night
Sayyidina Abu Huraira radhiyallahu anhu relates Allah's Messenger ﷺ saying, "Our Lord, the Blessed, the Superior, comes every night down on the nearest Heaven to us when the last third of the night remains, saying: "Is there anyone to invoke Me, so that I may respond to invocation? Is there anyone to ask Me, so that I may grant him his request? Is there anyone seeking My forgiveness, so that I may forgive him?"
Sahih al-Bukhari, 1145
In another narration the Prophet ﷺ says, "The most excellent prayer after that which is obligatory is the (voluntary) late-night prayer." - Muslim, 1163. The time above is the start of the last third portion of the night and is the optimum and most rewarding time for Tahajjud salah, though the prayer is still valid during the time of Isha.
Ibn Rajab rahimahullah says, “The time for Tahajjud during the night is the best time to perform sunnah prayer. At the time, a slave is close to His Lord. The time is when the doors of the heavens are opened and supplications are granted. This is also the time to ask the various matters we want from Allah Subhanahu Wa Ta'ala."
Midnight and Isha
The Islamic "midnight" is different to the conventional midnight which is 12am. The Islamic night actually starts from maghrib and lasts until Fajr. Hence, the Islamic midnight is the halfway point between Maghrib and Fajr and is known as Nisf al-Layl. As for the ʿIshaʾ prayer, it is permitted after midnight and ʿIshaʾ time lasts until the Adhan of Fajr. The misconception that it is not, may stem from the ruling that refers to the congregational prayer: the scholars in the Hanafi madh'hab consider the Isha prayer in congregation past midnight to be makruh - either tahrimi (Ibn Nujaym, Shurunbulali, and Zahidi) or tanzihi (Ibn Amir Haj, Ibn Abideen, Tahawi). Therefore, when praying alone, there is no karahah (dislike) at all.
Despite this, it would still be superior for the one praying alone to do so before half of the night passes as there are other wisdoms in this, namely ensuring that one actually prays the obligatory prayer in its respective time, and fulfilling the sunna of avoiding unnecessary worldly activity at night.
The Isha Angle
The angle chosen by this website is the primary Hanafi opinion of 18 degrees correlating with shafaq al-abyad. However, during daylight saving time (BST), shafaq al-ahmar (the secondary Hanafi opinion), which correlates to 15°, is adopted due to difficulties with the late Isha in the UK and higher latitude nations. One still has the option to pray at the later time that will be available to view here but generally across the UK, most masajid will adopt the earlier time.
During persisting twilight in the summer months where the Maghrib twilight lasts until Isha, 11:15pm will be the fixed time as per aqrabul ayyam until the twilight no longer persists. The table below shows the three angular perspectives of the start of Isha':
12°- The onset of shafaq al-ahmar via some observational data in higher latitude countries.
15°- The onset of shafaq al-abyad via observational data and the onset of shafaq al-ahmar via historic angular calculation.
18°- The onset of shafaq al-abyad via historic angular calculation.
The times of Isha fall into the early shafaq al-ahmar - the Red Twilight - and the later shafaq al-abyad - the White Twilight. The majority of classical scholars consider the early time as the commencement of Isha while others hold the later opinion. In times where daylight adjustment as well as persisting twilight causes Isha to become quite late, this poses a haraj on the masses hence the 15 degree option is better suited for BST.