Why do Muslims turn their heads at the end of prayer?

Mostly it's a greeting of peace. Turning the head right and then left is part of the taslim, where the worshipper says "Assalamu alaikum wa rahmatullah" ("Peace be upon you and Allah's mercy"). It is the Muslim way of ending the prayer, and it greets the people beside you and the angels with you.
The taslim ends the prayer
Every Muslim prayer closes with the same words. Ali reported that the Prophet ﷺ said: "The key to prayer is purification; its beginning is takbir and its end is taslim" (Sunan Abi Dawud 61). The takbir ("Allahu akbar") opens the prayer, and the taslim closes it.
The Companions described how the Prophet ﷺ did it: he said the salam to his right and to his left until the whiteness of his cheek could be seen (Sahih Muslim 582). That is why the head turns, one side after the other.
Who are you greeting?
The salam is a real greeting, not just a signal that the prayer is over. Many scholars say that when you turn right and left, you greet the worshippers beside you and the two angels who accompany you. The Prophet ﷺ taught his Companions to love one another and to greet one another (Sunan Abi Dawud 1001). Islam puts great value on a greeting of peace:
If you pray in a mosque, the person next to you may turn and greet you. You can smile and say it back. If you're not Muslim and you're just curious, see Can I say "Assalamu alaikum" if I'm not Muslim?
Do it with a calm turn
Jabir ibn Samurah reported that the Companions once waved their hands as they said the salam, and the Prophet ﷺ asked why they waved "like the tails of headstrong horses". He told them it is enough to turn the face toward the person beside you (Sahih Muslim 431). So keep it simple: turn your head, say the words, and keep your hands still on your knees.
- First turn: right, saying "Assalamu alaikum wa rahmatullah".
- Second turn: left, saying the same words.
- Praying alone: do exactly the same. The angels are still with you.
The schools differ on whether the second salam is required or recommended, so everyone does both. For the words that come before it, see What is the tashahhud? What follows the salam is the remembrance said after prayer. See What should I say after every prayer?
What it means for you
You enter the prayer shutting out the world, and you leave it with peace on your lips for everyone around you. The final salam is a small reminder to carry that peace into your day. For the full prayer, see How do I pray as a Muslim?
- The head turns during the taslim, which ends the prayer.
- You say "Assalamu alaikum wa rahmatullah" to the right, then to the left.
- It greets the worshippers beside you and the angels.
- Keep the turn calm, without waving the hands.
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