Question Summary:
What is the prayer to supplicate when one is distressed and a huge calamity has befallen him? Is there anything advised from hadith by the prophet

Question Detail:

What is the prayer to supplicate when one is distressed and a huge calamity has befallen him? Is there anything advised from hadith by the prophet

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
When Nabi Salalahu Alayhi Wasallam would be faced with a calamity he would recite the following dua: [1]
"أَعُوذُ بِكَلِماتِ اللَّهِ التَّامَّةِ مِنْ غضبه ومن شره عِبادِهِ، وَمِنْ هَمَزاتِ الشَّياطِينِ وأنْ يَحْضرُونِ "
Transliteration: Authu bii kalimatillahi taamati min gadabihi wa min shari ibadihi wa min shari hamazati shaytan wa anyhduroon.
 
Nabi Salalahu Alayhi Wasallam would recite the following dua when He would be distressed: [2]
اللَّهُمَّ أَنَا عَبْدُكَ، وَابْنُ عَبدِكَ، وابْنُ أَمَتِكَ، فِي قَبْضَتِكَ، ناصِيَتِي بِيَدِكَ، ماضٍ فِيَّ حُكْمُكَ، عدلٌ فِيَّ قَضَاؤُكَ، أسألُكَ بِكُلّ اسْمٍ هُوَ لَكَ سَمَّيْتَ بِهِ نَفْسَكَ، أوْ أنْزَلْتَهُ فِي كِتابِكَ، أوْ عَلَّمْتَه أحَداً مِنْ خَلْقِكَ، أوِ اسْتَأثَرْتَ بِهِ فِي عِلْمِ الغَيْبِ عِنْدَكَ، أنْ تجعل القرآن العظيم نُورَ صَدْرِي، وَرَبِيعَ قَلْبِي، وَجلاءَ حُزْنِي، وَذَهَابَ هَمّي" 
Allahuma ana abduk wabnu abdik wabnu amatik fi qabthatik nasiyati biyadik mathin fi hukmuk adlun fi qadauk asaluka bikuli ismin huwa laka sammayta bihi nafsak aw anzultahu fi kitabik aw ullamtahu ahadan min khalqik aw istatharta bihi fi ilmil ghaibi indak an tjalal Quraan al-atheem nura sadri wa rabeea qalbi wa jalaa a huzni wa thahaba hummi.
حدثنا محمد بن علي بن عبد الله بن عباس، عن أبيه، أنه حدثه، عن ابن عباس، أنه حدثه، قال: قال رسول الله صلى الله عليه وسلم: «من لزم الاستغفار، جعل الله له من كل ضيق مخرجا، ومن كل هم فرجا، ورزقه من حيث لا يحتسب» 
It is also mentioned in a hadith that person who continuously reads istigfar Allah Taala will create a path for him from every difficulty and from every grief relief, and Allah Taala will give him rizq from where he wouldn’t fathom. [3]
And Allah Ta’āla Knows Best
Ismail Dawoodjee
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net
الاذكار لنووى ص196-316 دار ابن كثير[1]
الاذكار لنووى ص196-317 دار ابن كثير[2]
ابو داود-1513 دار اليسر [3]