Question Summary:
Lunar Calendar in Islam

Question Detail:

Why do muslims use moon calendar?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
There are many divine laws based on the lunar calendar. For example, Ramadan is in the ninth month of the lunar calendar and Dhul Hijjah is in the twelfth month of the lunar calendar. Allah Ta'ala also indicates towards the Islamic Calendar in the Quran:
إِنَّ عِدَّةَ الشُّهُورِ عِنْدَ اللَّهِ اثْنَا عَشَرَ شَهْرًا فِي كِتَابِ اللَّهِ يَوْمَ خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ مِنْهَا أَرْبَعَةٌ حُرُمٌ(التوبة:٣٦)
"Indeed the number of months according to Allah is twelve months (as specified) in the Book of Allah since the day of the creation of the skies and earth. Of these, four are sacred." (Al Tawbah: 36)
(The four sacred months are Dhu Al Qa'dah, Dhu Al Hijjah, Muharram, and Rajab[1]; this clearly specifies the Islamic calendar).
Acts of 'Ibadat are by divine decree and are deemed acceptable only when performed in the allocated time. As such, we simply submit to the decree of Allah and worship Allah in the times He has ordered us to do so.
There may be other underlying wisdoms of following the lunar calendar. As Muslims we simply submit to the orders of Allah and believe Allah is Al-Hakeem (The All Wise); every order of Allah is full of wisdom.   
And Allah Ta’āla Knows Best
Hisham Dawood
Student Darul Iftaa
Chicago, U.S.A.
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net