Brick Arch Calculator — Geometry, Voussoirs & Skewback

The number of voussoirs = Soffit (arc) Length / (Brick Length + Joint Width). For a segmental arch over a 1.8m opening with 300mm rise: radius ≈ 1.5m, soffit (arc) length ≈ 1.93m. With 215mm bricks and 3mm joints that is about 9 voussoirs. Brick arches are conventionally built with an ODD number of voussoirs so a single key brick sits centrally at the crown (BIA Technical Notes 31), so this calculator rounds the count up to the next odd number.

The skewback is the inclined bearing bed at each end of the arch (the springing) where the arch loads onto the wall. The skewback angle is the inclination of that bearing face from the horizontal — it is what a bricklayer actually cuts. Because the voussoir bed joints are radial, the skewback bed for a circular arch sits at (180 − θ)/2 from horizontal, where θ is the included central angle (this matches the standard convention where a 160° arch gives 10° skewbacks). For a 1.8m segmental arch with a 300mm rise (θ ≈ 73.7°) the skewback bed is ≈53° from horizontal. A true semicircular arch (θ = 180°) gives a 0° skewback — the springing bed is horizontal, sitting on the spring line, and the springing voussoir's joint face is vertical. (The complementary θ/2 figure the calculator also shows is the tangent to the arch at the springing — 90° for a semicircle, ≈37° for that segmental arch — used as a setting-out reference, not the bed cut.) A FLAT (jack/gauged) arch is set out differently: its skewbacks are cut at 60° from the horizontal by the inverted equilateral-triangle method (60–70° in practice), radiating to a single strike point on the opening centreline.

A temporary centre (or former) is a shaped timber support built to the exact profile of the arch underside. Bricks are laid on top of the centre, which maintains the arch shape during construction. The centre must stay in place until the mortar has cured (typically 7-14 days). It is then carefully removed ('struck'), allowing the arch to become self-supporting.

Use a strong mortar for arches — typically 1:4 cement:sand (class M6 ≈ 6 N/mm²) or 1:1:6 cement:lime:sand (class M4 ≈ 4 N/mm², designation (iii)) per BS EN 998-2. A 1:3 cement:sand mix is much stronger (≈ M12) and is normally reserved for engineering brickwork; remember the mortar should not be stronger than the brick. The joints between voussoirs should be very thin (2–5mm) for gauged arches using rubbed/cut bricks, or up to 10mm for rough arches. Lime mortar is traditional and allows slight movement, but cement mortar provides faster strength gain. See our Mortar Calculator for material quantities.

A semicircular arch has a rise equal to half the span (a perfect half-circle). A segmental arch has a rise less than half the span (a shallow arc) and is the most common domestic arch as it needs less headroom. A flat (jack/gauged) arch has a STRAIGHT, flat soffit — there is no structural rise; only a small camber of about 10–15mm per metre of span (≈1/8 inch per foot) is added to the extrados to counter the optical illusion that the soffit sags. Its skewbacks are cut at 60° from the horizontal (equilateral-triangle method) and the voussoirs radiate to a single strike point, so it is set out completely differently from a circular arch.