Spákonufellshöfði in Höfðahreppur was protected as a country park in 1980. The country park is bounded by sea to the north, west and south. To the east, a line is drawn from the beach between the so-called “Salthús” and “Lifrarbræðsluhús” to the east along the roots of the rock wall to the north-west corner of the building, at Bankastæti 14. From there, as rule, the plot boundaries of houses by Bankastræti define the area, but after that, the roots of the cliff wall east and north of the house Laufás and onwards alongside the roots of the cliff wall all the way to the sea. Skerries off shore from the cape also belong to the country park.

The country park covers an area of 22.5 ha.