SettingsSettings for this calculationUS
The radius to the inner (intrados) face of the arch.
For a semicircular arch, this equals half the span.
The brick's length as measured along the curve.
Typically the brick's standard length or width, depending on orientation in the arch.
The brick's depth in the radial direction (arch thickness per ring).
The depth measured along the RADIUS — how far one ring of the arch reaches from intrados to extrados. It is the dimension that sets the taper: the deeper the ring, the more the outer face of each brick has to exceed the inner one, and a deep ring turned with parallel bricks opens joints at the extrados that the mortar cannot fill honestly. Turning an arch as several shallow rings instead of one deep one exists for exactly this reason.
The total angle the arch spans, in degrees.
180° for a full semicircular arch; less for a segmental arch.
Bricks needed for the arch
32 bricks (per ring)
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
- 5.69 °
- Wedge taper per brick
- 0.4 in
They open the calculator with your figures already in it
Radial Arch Brick Wedge Taper Calculator: 32 bricks (per ring) — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- 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
Inputs used
- Arch Radius (Intrados)
- 6.5 ft
- Brick Length (Along the Arc)
- 7.75 in
- Brick Radial Depth
- 4 in
- Total Arch Span Angle
- 180
Intermediate steps
- Angle per brick
- 5.69 °
- Wedge taper per brick
- 0.4 in
Confidence note: 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.
What this calculation does not cover
- The calculation carries no mortar joint. The brick length you enter is taken as the whole spacing along the inner face, so enter brick plus bed joint if you want the count and taper to describe a jointed arch - enter the bare brick and you get the figures for bricks laid touching.
- This is setting-out geometry, not a structural check. It says nothing about whether the ring depth is adequate, how much horizontal thrust the arch drives into the abutments, or what the centering has to carry until the mortar has gained strength.
- The answer is one ring of bricks at the radius you enter, one brick deep through the wall. A second or third ring sits at its own larger radius and needs its own run, and an arch through a wall thicker than one brick needs the count multiplied for that extra depth.
- Bricks are rounded up to the next whole one and nothing is added for cutting waste or breakage. The leftover fraction is not set out for you: no keystone is allowed for, the count is not forced odd, and on site the odd part-brick is normally absorbed by adjusting joint widths around the arch.
- It covers segmental and semicircular arches - span angles from 30 to 180 degrees and radii up to 10 m (33 ft). Flat and jack arches fall outside that, and a figure typed beyond a bound is pulled back to the bound before the answer is worked out. Each brick is also treated as an arc rather than the straight chord it really is, which puts the count slightly high on tight radii.
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.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-02 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- 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
Cite this page
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.
Tools and safety for this job
To lay brick and mix mortar. Generic types, no brands, no prices.
Protection this work requires
- Cutting or grinding concrete, masonry, screed, tile or fibre-cement board releases respirable silica: cut wet or extract at the tool, and wear a P2/N95 respirator at minimum — a nuisance dust mask does not filter it.
- Wet cement and lime burn skin and eyes painlessly until the damage is done: waterproof gloves to EN 374, safety glasses whenever the mix can splash, and never kneel in wet mix in permeable trousers.
- Saws, grinders and breakers run above 85 dB, where hearing damage accumulates and does not recover: defenders or plugs for every cut, not just the long ones.
- Breakers and grinders cause permanent nerve damage: limit continuous trigger time, keep hands warm, and stop if fingers tingle or blanch.
- Boards, blocks and bagged material cause most lasting back injuries on small sites: two people or a lifter for full sheets, and never a bag on one shoulder up a ladder.
Show the 9 tools this job needsHide tools
Essential
Brick trowel and jointer
Mixing bucket or tub
Shovel and spade
Spirit level
String line and pins
Tape measure
Wheelbarrow
Recommended
Angle grinder
Cement mixer
Also needed as materials: cutting and diamond discs.
what each masonry tool is for, and the spec that decides which to buy where one does.