Brick Voussoir & Keystone Calculator
Calculate odd brick counts with keystone centering, radial mortar joint taper at intrados vs. extrados, skewback rake angles, and centering formwork templates.
Quick Reference: Standard Brick Arch Voussoir Counts (Odd Total for Centered Keystone)
| Opening Span | Arch Type | Crown Rise | Standard Bricks | Keystone Sizing |
|---|---|---|---|---|
| 36 inches | Semicircular | 18.0 in | 19 bricks | Centered (Odd count) |
| 36 inches | Segmental | 8.0 in | 15 bricks | Centered (Odd count) |
| 48 inches | Semicircular | 24.0 in | 25 bricks | Centered (Odd count) |
| 48 inches | Segmental | 10.0 in | 19 bricks | Centered (Odd count) |
Interactive Radial Mortar Joint Simulator
Inspect the wedge taper expansion of individual mortar joints between intrados and extrados to ensure compliance with BIA (Brick Industry Association) mortar bed standards.
Offset-Coordinate "Mark-Out" Table & Interactive Plotter
For large arches where the swing radius exceeds your compass or room length. Simply draw your baseline, measure out horizontal intervals from center (X), and mark vertical height (Y) to plot perfect curves directly on wood or wall.
| Pt # | Dist from Center (X) | Height (Y) | Fraction | Drop |
|---|
Live Plywood Scribing Simulator
🔨 Carpentry Technique: Tap finish brads at coordinate marks. Bend a flexible batten against the pins to scribe a smooth curve.
Voussoir Math, Keystone Centering & Skewbacks
In unreinforced masonry arches, compression forces follow the radial geometry of each tapered voussoir block, transferring loads safely to side abutments.
Ensures an equal number of identical voussoir stones flank the left and right sides of the central keystone.
Skewback cuts on abutment bricks must match angle α to prevent shear slippage at the springlines.
Step-by-Step Worked Numeric Example
Suppose you are laying a brick fireplace arch with a span of W = 48.0 inches, rise of H = 12.0 inches, using 3-5/8" standard modular bricks with 3/8" (0.375") intrados mortar joints.
Standard Brick Arch & Voussoir Opening Sizes
Opening spans, radius curves, odd brick voussoir counts (including keystone), and extrados mortar joint tapers.
| Opening Purpose | Span (W) | Crown Rise | Radius (R) | Arc Length | Voussoir Count | Extrados Joint | Recommended Substrate |
|---|---|---|---|---|---|---|---|
| Fireplace Opening (3-Foot) | 36.0" | 9.0" | R = 22.50" | L = 41.74" | 11 Bricks | 0.45" Extrados | Firebrick + Refractory Mortar |
| Fireplace Opening (4-Foot) | 48.0" | 12.0" | R = 30.00" | L = 55.85" | 15 Bricks | 0.48" Extrados | Standard Modular Clay Brick |
| Garden Gate Masonry Arch | 42.0" | 14.0" | R = 22.75" | L = 53.64" | 15 Bricks | 0.52" Extrados | Severe Weathering (SW) Brick |
| Wine Cellar Barrel Portal | 60.0" | 30.0" | R = 30.00" | L = 94.25" | 25 Bricks | 0.49" Extrados | Reclaimed Solid Clay Common |
How to Lay Out & Build a Brick Arch: 5-Stage Masonry Guide
Step-by-step master mason guide for constructing rigid timber centering, cutting radial skewbacks, spacing voussoirs, and striking falsework.
Erect & Wedge Timber Centering Formwork
Set the curved timber centering securely between supporting piers. Support centering legs on dual opposing hardwood wedges or sand jacks. Verify the timber crown matches finished springline elevation plus rise minus brick depth.
Layout & Chisel Skewback Abutment Beds
Cut skewbacks directly on supporting piers angled along the true radial sightline toward the curve pivot. Voussoirs must transfer compressive thrust perpendicular to skewback faces, never onto a flat horizontal shelf.
Dry-Fit Voussoirs & Verify Odd Unit Count
Dry-fit all voussoirs along the timber lagging using wood spacer shims. Confirm an ODD total count so a single symmetrical keystone locks the apex. Verify intrados joint width ($t_{int} approx 3/8"$) and extrados taper ($t_{ext} < 1/2"$).
Bed Voussoirs Symmetrically from Springline to Crown
Lay voussoirs in pairs from left and right springlines upward toward the apex. Never lay one side completely first, which distorts centering falsework under uneven thrust. Check every radial joint angle with your pivoted radial story line.
Drive Keystone & Execute Controlled Decentering
Butter both sides of the central keystone with mortar and firmly tap it into the apex gap until flush with adjacent voussoirs. Allow mortar to cure (minimum 48-72 hours). Gently ease opposing falsework wedges symmetrically from center outward to transfer full compressive dead load into abutment piers.
Structural Thrust Dynamics & Lateral Force Engineering
Understand how gravitational loads resolve into outward lateral forces, and how to size king studs, headers, and abutments to prevent framing deflection.
The Fundamental Law of Arch Thrust
The horizontal outward thrust (H_thrust) generated at each springline abutment is inversely proportional to the rise height (H):
Key Rule: Halving the rise height doubles the outward lateral force pushing against your king studs or masonry abutment piers!
General residential partition guidelines. For load-bearing walls, second-story floor loads, or heavy masonry, consult a structural engineer and local building codes (IRC R602).
Semicircular (Roman) Arch
Because the curve meets the springline at a true vertical 90° tangent, the majority of dead load is directed vertically down into the supporting jambs.
Gothic (Pointed) Arch
The pointed apex divides the curve into steeper arcs, reducing horizontal outward vector forces compared to flatter round arches.
Segmental (Shallow) Arch
As the rise decreases relative to the span, the thrust vector angles sharply outward, exerting immense lateral force on the supporting side walls.
Jack (Flat) Lintel Arch
Flat arches rely solely on wedge friction and severe horizontal thrust to hold the voussoirs aloft. Requires massive abutments or structural tie rods.
Common Masonry Voussoir & Centering Mistakes
Prevent apex joint weakness, mortar crushing, and centering collapse during brick arch construction.
Using an Even Number of Voussoirs
Laying an even number of brick wedges in a masonry arch ring, resulting in a weak vertical mortar joint directly at the crown apex.
Always specify an ODD total count of voussoirs so that a solid, symmetrical keystone locks the apex in pure compression.
Using Uniform Thickness Mortar Joints on Curved Rings
Attempting to maintain equal mortar thickness from intrados to extrados without tapering, creating uneven bearing pressure and crushed brick edges.
Calculate wedge taper so intrados joints measure 1/4" to 3/8" while extrados joints widen proportionally based on ring depth, or use gauged wedge-cut bricks.
Improper Skewback Angle on Springline Abutments
Pouring or laying springline skewback skew blocks horizontally rather than perpendicular to the arch radius thrust line, risking horizontal slip.
Cut skewbacks precisely along the radial center line so voussoirs transfer load in 90-degree square compression against the abutment.
Field Master Pro-Tips for Clean Execution
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Frequently Asked Questions
Common carpentry, masonry, and geometric questions regarding arch calculations and construction layout.
Q1 Why must a brick or stone masonry arch have an odd number of voussoirs?
An odd number of voussoirs ensures there is a single central keystone positioned exactly at the highest crown apex of the arch ring. This places a solid stone/brick unit at the point of maximum compressive stress. If an even number were used, a weak vertical mortar joint would sit at the apex.
Q2 How do you calculate the taper of radial mortar joints in a brick arch?
Because the extrados perimeter is longer than the intrados perimeter, mortar joints naturally widen toward the outside. The extrados joint thickness is t_ext = t_int + (Ring Depth × (Brick Width + t_int)) / R_intrados. In standard brickwork, the extrados joint should not exceed 1/2" to 5/8" (12-16mm) to prevent mortar slippage.
Q3 What is a skewback in a masonry arch?
A skewback is the angled, sloping bearing surface on the supporting abutment pier that receives the lowest springer voussoir. The skewback angle is cut perpendicular to the arch radius line at the springline.
Q4 What is the formula to calculate voussoir count for a segmental brick arch?
Calculate the intrados arc length L = R × θ. Divide L by the effective unit width (Brick Width + Mortar Joint). Round to the nearest whole integer, and if the result is even, add 1 to guarantee an odd count with a centered keystone.