Brick Arch Calculator

This calculator sizes a brick masonry arch -- either a shallow segmental arch or a full semicircular arch -- from its span, rise, and brick geometry. Arch Type is a mode selection (Segmental or Semicircular arch), not a continuous dimension. For a segmental arch (the default), Arch Radius is derived from the span and rise using the standard chord-and-rise formula, and Arc Length follows from that radius. For a semicircular arch, the geometry simplifies: radius is fixed at exactly half the span, Skewback Angle is always 90 degrees, and Spring Point Offset is always zero. Switching Arch Type from 1 to 2 at the default 36-inch span, 8-inch rise changes Arch Radius from 24.25 in to 18 in, Voussoir Count from 11 to 15, and Skewback Angle from 47.9 degrees to a flat 90 degrees.

Near these default proportions (rise well under half the span), Span Width has the largest effect on Arch Radius and Arc Length in the segmental mode -- widening the span from 36 to 40 inches (about 11%) raises Arch Radius from 24.25 to 29 inches and Arc Length from 40.57 to 44.14 inches, larger swings than an equivalent change to Rise Height produces. That flips once Rise Height passes half the Span Width (a reachable combination, e.g. a 36-inch span with a 20-inch-plus rise): the arch curls in past a semicircle into a "horseshoe" shape, and Rise Height -- not Span Width -- becomes the larger driver of Arch Radius, Arc Length, and Spring Point Offset in that regime -- at a 36-inch span with a 24-inch rise, Rise Height moves Arc Length roughly 4x further than Span Width does, and the gap widens to roughly 45x at a 40-inch rise. Voussoir Count (the number of wedge-shaped arch bricks) divides Arc Length by Brick Width plus Mortar Thickness at the Intrados, then is forced to the next odd number so the arch closes on a center keystone rather than a joint. This is a geometry and brick-count tool, not a structural design -- arch thrust and abutment sizing require a mason or engineer's review.