What is the evidence for making up missed prayers (qada salah)?

Although there is no explicit statement in the Qur’an regarding making up missed prayers (qada salah), the Prophet Muhammad (peace be upon him) himself made up prayers he was unable to perform on time and advised his companions to do the same. The Messenger of Allah (peace be upon him) said, “If anyone forgets a prayer or sleeps through it, let him perform it when he remembers. There is no expiation for it except this.” (Muslim, Masajid, 315 [684]; see also Bukhari, Mawaqit al-Salat, 37 [597]). During the Battle of the Trench, the Prophet (peace be upon him) was unable to perform the Asr prayer due to the intensity of the battle; he then said, “They have kept us from the Asr prayer. May Allah fill their houses and graves with fire.” and made up the Asr prayer at the time of Maghrib. (Muslim, Masajid, 205 [627]; see also Bukhari, Da‘awat, 58 [6396]). Additionally, while returning from the conquest of Khaybar, they stopped to rest and overslept, missing the Fajr prayer, which they then made up after sunrise. (Muslim, Masajid, 309 [680])

The obligatory five daily prayers and the Witr prayer are to be made up if missed. If the Fajr prayer is to be made up before the time for Dhuhr on the same day, its sunnah is also made up. Also, the four rak‘ahs of the initial sunnah of Dhuhr can be performed after the obligatory Dhuhr prayer as long as the time has not expired. Furthermore, missed prayers are performed in the same manner as they were missed; if missed while traveling, they are made up as a traveler, and if missed while resident, they are made up as a resident. (Mawsili, al-Ikhtiyar, 1/63)

There is no hadith regarding making up prayers that were deliberately missed without a valid excuse such as forgetfulness or sleep. However, this does not mean that making up such deliberately missed prayers is not required. For example, the Prophet (peace be upon him) commanded both expiation and making up the fast for someone who deliberately broke their fast in Ramadan by engaging in sexual intercourse (Ahmad b. Hanbal, al-Musnad, 2/208 [6944-6945]; Bayhaqi, al-Sunan al-Kubra, 4/382 [8059-8060]), which is evidence that making up a missed obligatory act of worship is required even if it was deliberately omitted. Moreover, considering that the Prophet (peace be upon him) made up prayers he missed due to an excuse and commanded his companions to do likewise, it follows that making up prayers missed without an excuse is even more necessary. (Nawawi, al-Majmu‘, 3/68)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu