Per‑brick schedule
| # | Center angle (deg) | Cumulative arc (unit) | Template angle (deg) |
|---|
| Use case | Span | Rise | Ring | Brick | Joint | Tol | Units |
|---|---|---|---|---|---|---|---|
| Segmental doorway | 1200 | 300 | 100 | 215 | 10 | 2 | mm |
| Garden niche | 900 | 180 | 90 | 200 | 8 | 2 | mm |
| Masonry opening | 48 | 10 | 4 | 8 | 0.375 | 0.0625 | in |
For a circular segment arch with span s and rise h, the radius at the chosen reference face is:
R = s² / (8h) + h / 2
The central angle is θ = 2·arcsin(s / (2R)) (radians). The arc length is L = R·θ.
With brick length b and joint j, the voussoir length is v = b + j. A provisional count is n ≈ L / v then rounded per preference. The exact joint to fit n is j* = L / n − b. The skewback at springing equals the tangent angle there, θ/2.
If inputs are intrados or extrados, the centerline radius is offset by half the ring thickness before computing θ and L.
- Select the measurement face and units.
- Enter span and rise at that face.
- Enter ring thickness, brick length along the arc, and joint.
- Set tolerance and a rounding method; toggle keystone if required.
- Click Compute to see geometry, counts, and the schedule.
- Export CSV or PDF for records or shop drawings.
Always verify outputs against project standards and detailing requirements.
| Symbol | Name | Meaning |
|---|---|---|
s | Span | Clear chord between springings at selected reference face |
h | Rise | Vertical height from springline to crown at that face |
t | Ring thickness | Total thickness of the brick ring (intrados to extrados) |
R | Radius | Radius of arch circle at the reported face |
θ | Central angle | Subtended angle of the segment; θ = 2·asin(s/(2R)) |
L | Arc length | Length of the curved centerline; L = R·θ |
b | Brick length | Nominal brick length measured along the arc face |
j | Joint | Typical mortar thickness between bricks along the arc |
v | Voussoir length | v = b + j (brick plus joint) |
n | Brick count | Number of bricks along the arc (keystone optional) |
α | Per‑brick angle | α = θ / n (template/wedge angle) |
β | Skewback angle | β = θ / 2 at springing |
All geometry is evaluated at the selected reference face; centerline adjustments are handled internally for arc calculations.
Using Load example values (units: mm): s = 1200, h = 300, t = 100, b = 215, j = 10, reference: centerline.
- Radius
R = s²/(8h) + h/2 = 750.000mm - Central angle
θ = 2·asin(s/(2R)) = 1.85459rad (≈106.260°) - Arc length
L = R·θ = 1390.943mm - Voussoir
v = b + j = 225.000mm
| Rounding | n (count) | Angle per brick (deg) | Required joint to fit (mm) |
|---|---|---|---|
| Nearest | 6 | 17.710 | 16.824 |
| Floor | 6 | 17.710 | 16.824 |
| Ceil | 7 | 15.180 | -16.294 |
If a keystone is required (odd count), joint or brick length must be adjusted to avoid negative or excessive joints. Always verify against project tolerances.
Which inputs are required?
Provide span, rise, ring thickness, brick length along the arc, joint thickness, tolerance, units, and the reference face. Optionally select a rounding method and a centered keystone.
What does “reference face” mean?
Choose where measurements are taken: centerline, intrados, or extrados. The tool offsets to centerline for central angle and arc length, but reports radius at the selected face.
How is brick count calculated?
Count is estimated by L / (b + j), then rounded per your setting. If a keystone is reserved, we enforce an odd count. The exact joint to fit n is j* = L/n − b.
What is the skewback angle?
It’s the tangent angle at the springing, equal to half the central angle, β = θ/2. Use it to set abutment cuts or template guides.
Are results suitable for all arches?
The calculator assumes a circular segment arch. Complex profiles, tapered rings, or variable joints require engineering review. Always verify outputs against drawings, tolerances, and site conditions before fabrication or construction.
Can I mix millimeters and inches?
No. Select one unit system and enter all inputs in that unit. All results and exports use the same unit for consistency and clarity.
How do I ensure a keystone?
Enable “Reserve a centered keystone.” If the rounded count is even, we add one. Adjust joint or brick length to keep required joint within tolerance.