From this site

One project, every trade

Each calculator adds its lines to a single estimate — consolidated BOM, schedule and cash-flow included.

Open My Project →

Radial Arch Brick Wedge Taper Calculator

Compute the wedge taper cut and brick count needed for a segmental or semicircular masonry arch.

Computed in your browser — nothing you enter is uploaded. Figures are presented for United States against IRC 2024, and every formula is cited under regulatory standards below.

Last verified 2026-08-26 · v1.0.0

Market
Imperial · sales tax
13.12 ft
Schematic, drawn to the proportions you entered — not to scale on screen.

Bricks needed for the arch

32 bricks (per ring)

Check your inputs

Assumes a constant mortar joint width along the inner face and a wedge-cut (or tapered joint) to close the gap at the outer face — for a very tight radius, verify the taper doesn't exceed what a simple tapered mortar joint can accommodate without actually cutting wedge-shaped bricks.

Angle per brick
5.73 °
Wedge taper per brick
0.39 in

With the figures above, the bricks needed for the arch comes to 32 bricks (per ring). Note that total arch span angle sits at the high end of the range this calculator was checked against, so treat the output as indicative rather than settled. The method behind this is well established, though site conditions and material batches will move it somewhat. This is calculated for United States and cites IRC 2024. Building in another market? Change the selector above so the units and code reference follow.

Estimated cost — your price

This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — confirmed fixes become pinned regression tests.

[Schema Verified] Computed in alignment with American Concrete Institute (ACI 318-19) formulas and International Residential Code (IRC 2024) spatial boundaries.

Regulatory standards & verification citations

  • Arc geometry: angle subtended per brick = arc length (brick length) / radius; the outer (extrados) face width = outer radius x that angle, and the taper is the difference between the outer and inner face widths

Your workspace

Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.

Frequently asked questions

Why do arch bricks need a taper at all?
A curved arch ring has a larger circumference at its outer (extrados) face than its inner (intrados) face — using rectangular bricks with a uniform mortar joint width on the inside means the joint must widen toward the outside to close the gap created by the curve.
When do I need actual wedge-cut bricks instead of just a tapered mortar joint?
For tight radius arches, the required taper can exceed what a mortar joint can reasonably accommodate (commonly cited as roughly 3/4 in max at the wide end) — beyond that, purpose-cut wedge (voussoir) bricks or a gauged arch technique becomes necessary.
Does this account for multiple rings (arch thickness) at once?
No — this calculates one ring of bricks. A multi-ring arch (common for wider spans) needs this calculation repeated for each ring at its own radius.