Hagia Sophia is covered by a central dome which has a diameter of 31.87 meters and a height from floor level of 55.60 meters, slightly smaller than the dome of the Pantheon. The dome seems rendered weightless by the unbroken arcade of arched windows under it, which help flood the colourful interior with light.
The dome is carried on pendentives — four concave triangular sections of masonry which solve the problem of setting the circular base of a dome on a rectangular base. At Hagia Sophia the weight of the dome passes through the pendentives to four massive piers at the corners. Between them the dome seems to float upon four great arches.
At the western (entrance) and eastern (liturgical) ends, the arched openings are extended by half domes carried on smaller semidomed exedras. Thus a hierarchy of dome-headed elements builds up to create a vast oblong interior crowned by the main dome, a sequence unexampled in antiquity. All interior surfaces are sheathed with polychrome marbles, green and white with purple porphyry and gold mosaics, encrusted upon the brick. On the exterior, simple stuccoed walls reveal the clarity of massed vaults and domes.


A cross section through the building.

*Text and cross section from http://en.wikipedia.org/wiki/Hagia_Sophia