From ahadith, we know the Holy Prophet^(sa) generally offered eleven rak’aat during Tahajjud prayer (eight nawafil and Witr prayer) however at times he also offered two nafl after Witr prayers too, totalling 13 rak’aat.

The Holy Prophet^(sa) offered Tahajjud prayers in various ways – sometimes he would offer it in sets of two rak’aat and at other times he would offer four rak’aat at a time. Sometimes he would offer some rak’aat briefly, with short recitations and at other times he would prolong them. At times the prophet would offer some Tahajjud, go to sleep, then awaken and after performing ablution again, he would resume Tahajjud prayer.

حَدَّثَنَا يَحْيَى بْنُ يَحْيَى، قَالَ قَرَأْتُ عَلَى مَالِكٍ عَنْ سَعِيدِ بْنِ أَبِي سَعِيدٍ الْمَقْبُرِيِّ، عَنْ أَبِي سَلَمَةَ بْنِ عَبْدِ الرَّحْمَنِ، أَنَّهُ سَأَلَ عَائِشَةَ كَيْفَ كَانَتْ صَلاَةُ رَسُولِ اللَّهِ صلى الله عليه وسلم فِي رَمَضَانَ قَالَتْ مَا كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلم يَزِيدُ فِي رَمَضَانَ وَلاَ فِي غَيْرِهِ عَلَى إِحْدَى عَشْرَةَ رَكْعَةً يُصَلِّي أَرْبَعًا فَلاَ تَسْأَلْ عَنْ حُسْنِهِنَّ وَطُولِهِنَّ ثُمَّ يُصَلِّي أَرْبَعًا فَلاَ تَسْأَلْ عَنْ حُسْنِهِنَّ وَطُولِهِنَّ ثُمَّ يُصَلِّي ثَلاَثًا فَقَالَتْ عَائِشَةُ فَقُلْتُ يَا رَسُولَ اللَّهِ أَتَنَامُ قَبْلَ أَنْ تُوتِرَ فَقَالَ ‏ “‏يَا عَائِشَةُ إِنَّ عَيْنَىَّ تَنَامَانِ وَلاَ يَنَامُ قَلْبِي ‏”‏

Hazrat Abu Salama bin Abdur Rahman asked Hazrat Aisha^(ra) about the Tahajjud prayer of the Holy Prophet^(sa) during the month of Ramadan. She said:

“The Messenger^(sa) of Allah did not observe either in Ramadan or in other months more than eleven rak’aat [of the Tahajjud prayer]. He [in the first instance] observed four rak’aat. Ask not about their excellence and their length [these were matchless in perfection and length]. He again observed four rak’aat, and ask not about their excellence and their length. He would then observe three rak’aat [of the Witr prayer]. Aisha again said: I said: ‘Messenger of Allah, do you sleep before observing the Witr prayer?’ He said: ‘O Aisha, my eyes sleep but my heart does not sleep.’” (Sahih Muslim, The Book of Prayers – Travellers)

In another Hadith it is narrated:

كَانَ صَلاَةُ النَّبِيِّ صلى الله عليه وسلم ثَلاَثَ عَشْرَةَ رَكْعَةً‏.‏ يَعْنِي بِاللَّيْلِ‏.‏

“The [Tahajjud] prayer of the Holy Prophet^(sa) used to be of thirteen rak’aat.”