Why do buildings have arches?
One-line takeaway
BLUF: An arch converts the downward load above an opening into compression running along its curve to the supports. Stone, brick and concrete are strong in compression and weak in tension, so an arch lets them span far wider gaps than a flat beam could.
It is the clearest case of geometry substituting for material strength.
Squeeze good, stretch bad
Put a stone slab across two supports and the underside stretches while the top squeezes. Stone resists squeezing well and pulls apart easily, so the slab cracks from below and the span is limited to a metre or two. Curve the opening instead, build it from wedge-shaped blocks called voussoirs, and every block is pressed against its neighbours. The load travels around the curve as compression until it reaches the ground. The price is that the arch pushes outward as well as downward at its base, so it needs mass, a buttress, or an opposing arch to absorb that thrust. Roman arches typically used semicircles; the pointed Gothic arch steepens the curve and directs more of the force downward.
Follow the thrust line
The principle generalises to a rule about matching form to material. Every structure has a shape at which it carries a given load in pure compression, called the thrust line, and an arch works as long as that line stays inside the masonry. Robert Hooke expressed this in 1675 as a hanging chain: the shape a chain takes under its own weight, inverted, is the ideal arch. Extend an arch along a line and you get a vault; rotate it about a vertical axis and you get a dome. The Pantheon in Rome, completed under Hadrian around 126 CE, still holds the record for the largest unreinforced concrete dome, at about 43 metres across.
Steel made arches optional
Structural steel and reinforced concrete carry tension well, so modern buildings no longer need arches to span openings; a steel lintel or reinforced beam does the job in less depth. Arches survive today where their economics still hold: long-span bridges, tunnel linings, culverts, dams, and any structure in masonry or plain concrete. They also survive as pure ornament, since a brick arch over a window in a steel-framed building carries nothing. Engineers assessing historic masonry bridges still use thrust-line analysis to decide whether a Victorian railway arch can take a modern lorry, so the medieval idea remains a live working tool.
Where the arch myths fall down
Common misconceptions are widespread. The myth is that Romans invented the arch. The reality is that Mesopotamian, Egyptian and Etruscan builders used arches earlier; Rome industrialised them at scale, especially in aqueducts and bridges. The myth is that the keystone holds an arch up and removing it collapses everything. The reality is that every voussoir carries load and the keystone is simply the last placed; arches fail when the supports spread or the thrust line leaves the stonework. The myth is that pointed Gothic arches were a purely aesthetic choice. The reality is that they allowed vaults of different spans to reach the same height.