I want to know when does the fajr waqt end.
Say if sunrise is at 7.30 AM. Then how do we calculate the last minute?
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The fajr time will last long till the sun-rises.
It was narrated from Abdullah bin Amr (RA) that the Prophet (PBUH) said, “The time for Zuhr is so long as Asr has not come. The time for Asr is so long as the sun has not turned yellow. The time for Maghrib is so long as the twilight has not disappeared. The time for Isha is so long as half of the night has not passed. The time for Fajr is so long as the sun has not risen.”- Muslim, Vol.2, 1386.
If you have time to pray atleast one rakat of fajr prayer before sun-rise, then pray Fajr,
It is narrated By Abu Huraira : Allah's Apostle said, "If anyone of you can get one Rak'a of the 'Asr prayer before sunset, he should complete his prayer. If any of you can get one Rak'a of the Fajr prayer before sunrise, he should complete his prayer."- Bukhari Volume 001, Book 010, Hadith 531.
It is also Narrated By Abu Huraira : Allah's Apostle said, "Whoever could get one Rak'a of a prayer, (in its proper time) he has got the prayer."- Bukhari Volume 001, Book 010, Hadith 554.
The salat of Fajr starts when (True) Fajr comes in, up until the sun starts rises. Once the sun has risen, the time of the salat ends, and so from that time you would have to make it up. So qaza (قضاء) time would be, if sun rise is at 7:30, after the sun has fully risen.
For further information see this (Arabic)