Five times a day Muslims turn towards the Kaaba in Makkah. The direction is called the qibla. Lay a ruler on an ordinary world map from Reykjavík to Makkah and the line points southeast. But that is not the right direction. From Iceland, Makkah is almost due east.
“Wherever you are”
The Qur’an says to turn towards the Sacred Mosque, wherever you are.
قَدۡ نَرَىٰ تَقَلُّبَ وَجۡهِكَ فِي ٱلسَّمَآءِۖ فَلَنُوَلِّيَنَّكَ قِبۡلَةٗ تَرۡضَىٰهَاۚ فَوَلِّ وَجۡهَكَ شَطۡرَ ٱلۡمَسۡجِدِ ٱلۡحَرَامِۚ وَحَيۡثُ مَا كُنتُمۡ فَوَلُّواْ وُجُوهَكُمۡ شَطۡرَهُۥۗ وَإِنَّ ٱلَّذِينَ أُوتُواْ ٱلۡكِتَٰبَ لَيَعۡلَمُونَ أَنَّهُ ٱلۡحَقُّ مِن رَّبِّهِمۡۗ وَمَا ٱللَّهُ بِغَٰفِلٍ عَمَّا يَعۡمَلُونَ
We have certainly seen the turning of your face, [O Muhammad], toward the heaven, and We will surely turn you to a qiblah with which you will be pleased. So turn your face toward al-Masjid al-Haram. And wherever you [believers] are, turn your faces toward it [in prayer]. Indeed, those who have been given the Scripture well know that it is the truth from their Lord. And Allah is not unaware of what they do
In the first years in Madinah, Muslims prayed towards Jerusalem:
كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلم صَلَّى نَحْوَ بَيْتِ الْمَقْدِسِ سِتَّةَ عَشَرَ أَوْ سَبْعَةَ عَشَرَ شَهْرًا
“The Messenger of God ﷺ prayed towards Jerusalem for sixteen or seventeen months.”
When the verse came, the direction changed. The news reached people at Qubāʾ, just outside Madinah, in the middle of the dawn prayer, and they turned around where they stood (Sahih al-Bukhari 403). There is more on these verses in The middle of the middle.
106 degrees
From Reykjavík, Makkah lies at 106°, only 16° south of east.
The earth is a sphere, and the shortest route between two places on a sphere is part of a great circle, a circle around its middle. On a flat map that route looks curved. The shortest route from Reykjavík to Makkah, about 6,500 km, first crosses the Faroe Islands and the North Sea, then Denmark, Poland, Romania and Turkey, and down over Sinai. It sets off at a bearing of 106°, just 16° south of east.
A straight line on an ordinary map points at 135° instead, southeast. Someone going by the map would face almost 30° too far south. And the further east in Iceland you are, the further south the qibla turns: 111° in Akureyri and 114° in Egilsstaðir.
How precise?
“To God belong the east and the west.”
وَلِلَّهِ ٱلۡمَشۡرِقُ وَٱلۡمَغۡرِبُۚ فَأَيۡنَمَا تُوَلُّواْ فَثَمَّ وَجۡهُ ٱللَّهِۚ إِنَّ ٱللَّهَ وَٰسِعٌ عَلِيمٞ
And to Allah belongs the east and the west. So wherever you [might] turn, there is the Face of Allah. Indeed, Allah is all-Encompassing and Knowing
Scholars agree that someone far from Makkah should do their best to find the direction, and that the prayer is valid if they did. The schools differ on how precise this must be: most hold that the general direction is enough when the Kaaba cannot be seen, while the Shafiʿi school asks you to aim at the Kaaba itself as closely as you can. No one demands a protractor, but the difference between 106° and 135° is too large to ignore.
In Iceland today
Most prayer apps and websites calculate the great circle, and in the mosques the direction is already set. One thing to keep in mind in Iceland: magnetic north is not true north. A compass here points several degrees west of true north, so a traditional compass needs correcting. Phones usually do this themselves, but it is good to check against a landmark, such as the sunrise, which is in the southeast in winter and the northeast in summer.