Masonry & Brickwork 5 min read

Brick Arch Voussoir Spacing & Centering: Masonry Guide

Master guide on calculating brick arch voussoir counts, wedge mortar joint tapers, skewback angles, and building rigid timber centering formwork on site.

A Arch Calculator Editorial Team
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A structural masonry arch is one of humanity’s greatest architectural achievements: it spans wide horizontal openings entirely in compression without steel lintels or tensile reinforcement. The secret lies in wedge-to-wedge friction, radial thrust vectors, and precisely placed stone or brick voussoirs.

However, laying a brick arch requires strict mathematical layout and temporary timber support. A single miscalculation in mortar joint taper or an even brick count can destabilize the entire masonry ring. This guide breaks down the full engineering and practical craftsmanship workflow for calculating voussoir spacing, sizing timber centering, and safely striking formwork.

Need to calculate brick and mortar numbers immediately on site?
Use our interactive Brick Arch Calculator to compute odd voussoir counts, keystone sizing, radial mortar joint taper, and skewbacks instantly.

1. The Golden Rule of Masonry: The Keystone Must Be Centered

In structural brick and stone masonry, the total count of voussoirs must always equal an ODD integer (N = 2k + 1).

  • Odd Count: Ensures that exactly one single, symmetrical keystone sits plumb on the vertical centerline at the crown apex. Compressive vectors radiating down from the left and right halves lock against this central stone in pure compression.
  • Even Count: Forces a continuous vertical mortar joint directly down the center line of the crown. Because mortar possesses near-zero tensile strength and weak shear resistance under cyclic vibrations, a centerline mortar joint creates a structural hinge prone to sagging, water penetration, and collapse.
          [ KEYSTONE ]   ←  Plumb on Centerline (Odd Total)
         /            \
     [V4]              [V4]
     /                    \
   [V3]                  [V3]
   /                        \
 [V2]                      [V2]
 /                            \
[V1 (Springer)]           [V1 (Springer)]
==========================================
              SPRINGLINE

2. Calculating Voussoir Count & Intrados Geometry

To calculate the number of standard modular bricks needed across an arch curve, determine the Intrados Arc Length (L) and the target mortar joint thickness:

Step 1: Compute Intrados Arc Length

For circular and segmental arches:

R = (W^2 + 4H^2) / (8H)
θ = 2 × arcsin((W) / (2R))  (in radians)
L = R × θ

Where:

  • W = Clear opening span width between finished jambs
  • H = Vertical crown rise from springline to intrados apex
  • R = Intrados radius of curvature
  • L = Curved perimeter distance along the soffit

Step 2: Estimate Brick Count

Using standard modular brick face thickness (W_b = 2.25 in or 57 mm) and target intrados mortar joints (t_int = 0.375 in or 3/8 in):

N_raw = (L) / (W_b + t_int)

Round N_raw to the nearest integer. If the result is an even number, add 1 to ensure an odd count (N = 2k + 1).

Step 3: Back-Calculate Exact Intrados Joint Width

With an odd integer N fixed, back-calculate the exact average intrados mortar joint thickness to achieve a tight fit:

t_int = (L - (N × W_b)) / (N - 1)

Target an intrados mortar bed between 1/4 in (6 mm) and 3/8 in (10 mm). If the calculated joint is too thick or too thin, adjust the brick orientation (e.g., soldier course vs. header course).

3. Calculating Mortar Joint Taper (Intrados vs. Extrados)

Because the arch curve is concave, rectangular modular bricks will naturally produce wedge-shaped mortar joints. Mortar joints are tightest at the intrados (bottom face) and fan open wider at the extrados (top perimeter).

To calculate the extrados joint thickness (t_ext) for an arch ring of depth d (typically 3.625 in for header course or 8.0 in for full-wythe soldier course):

t_ext = t_int + [ d × ((W_b + t_int) / R) ]

Maximum Allowable Mortar Taper

  • In structural masonry, the extrados mortar joint should not exceed 3/4 in (19 mm).
  • If the calculated t_ext exceeds 3/4 in, standard rectangular bricks cannot be used safely. The mason must either:
    1. Cut custom wedge-shaped bricks (gauged brick arch), or
    2. Increase the arch radius (R) to reduce curvature sharpness, or
    3. Step the arch ring into two concentric concentric rings of lower wythe depth.

4. Worked Numerical Example: 48-Inch Segmental Fireplace Opening

Let’s calculate a real-world segmental brick arch over a fireplace lintel:

  • Span (W): 48.0 in
  • Rise (H): 12.0 in
  • Brick Type: Modular clay brick laid as headers (W_b = 2.25 in wide, depth d = 3.625 in)

Calculations:

  1. Radius (R):

R = (48^2 + 4(12^2)) / (8 × 12) = (2304 + 576) / (96) = 30.00 in

2. **Central Angle (`θ`):**

θ = 2 × arcsin((48) / (60)) = 2 × arcsin(0.80) = 2 × 0.9273 = 1.8546 rad ≈ 106.26°

3. **Intrados Arc Length (`L`):**

L = 30.00 × 1.8546 = 55.64 in

4. **Target Brick Count (`N`):**

N_raw = (55.64) / (2.25 + 0.375) = (55.64) / (2.625) ≈ 21.19

   Rounding to the nearest odd integer gives **`N = 21 bricks`** (1 keystone + 10 voussoirs on each side).
5. **Exact Intrados Mortar Bed:**

t_int = (55.64 - (21 × 2.25)) / (20) = (55.64 - 47.25) / (20) = (8.39) / (20) = 0.419 in ≈ (13) / (32) in

6. **Extrados Mortar Bed:**

t_ext = 0.419 + [ 3.625 × (2.25 + 0.419) / (30.0) ] = 0.419 + 0.322 = 0.741 in ≈ (3) / (4) in


The extrados joint measures exactly `3/4 in`, confirming modular bricks are structurally acceptable without individual diamond-wheel gauge cuts.

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## 5. Designing & Constructing Timber Centering (Falsework)

A brick arch cannot support its own weight until the final keystone is driven and the mortar has cured. Centering formwork must support the full dead load of wet masonry without deflection.

======================== [ 1x2 Timber Lagging Slats ] / (Plywood Master Rib)
| [2x4 Block Ribs] | | | ================================================ [ Tie Beam ] | | | [Vertical 4x4 Posts] | | | [W] [W] ← Hardwood Decentering Wedges


### Anatomy of a Sturdy Centering Rig:
1. **Dual Plywood Profile Ribs:** Scribe the calculated intrados radius on two sheets of 3/4" CDX plywood or OSB. Clamp them together and cut simultaneously with a jigsaw to ensure identical profiles.
2. **Spacing Infill Blocks:** Fasten 2x4 framing blocks between the dual plywood faces spaced every 8" to 12" on center. The overall depth of the wooden form should match the thickness of the brick wall minus 1/4" to allow mortar squeeze-out.
3. **Lagging Slats:** Nail 1x2 or 1x3 softwood laths across the top curved rim of the ribs. Leave 1/4" gaps between slats so masonry dust and wash water do not pool on the curve.
4. **Tie Beam:** Screw a horizontal 2x4 tie beam across the bottom of the dual ribs at the springline elevation to prevent the wooden form from spreading horizontally.

---

## 6. Shoring, Leveling, and Striking Wedges

Never support centering formwork directly on solid masonry jambs or non-adjustable posts. When wet mortar cures, the brick ring compresses slightly, and without mechanical release wedges, the timber centering will become wedged permanently into the opening.

### The Double-Wedge Decentering System:
- Support the centering formwork on vertical 4x4 timber shores resting on the floor or sill.
- Place **opposing pairs of hardwood wedges** (cut at a 1:5 taper) between the bottom of the centering ribs and the top of the 4x4 support posts.
- Screw the paired wedges with a temporary retaining strap so they do not vibrate loose during masonry tapping.

### Safe Striking Protocol:
1. **Minimum Cure Time:** In normal 65°F–75°F (18°C–24°C) weather with Type N mortar, allow a minimum of **7 full days** before easing centering formwork. In cold weather (under 50°F / 10°C) or for arches exceeding 6-foot spans, allow **14 to 28 days**.
2. **Gradual Decentering:** Back out the retaining screws on the hardwood wedges. Strike the thin end of the wedges gently with a hammer, easing the wedges downward symmetrically on both jambs by 1/4" increments.
3. **Load Transfer Inspection:** Observe the arch crown as the form drops. The arch will settle between 1/32" and 1/16" as voussoir compression engages. If mortar joint cracks appear, tap the wedges back in immediately and consult a structural engineer.

---

## 7. Professional Laying Sequence & Mortar Selection

Follow this jobsite protocol for flawless brick arches:

1. **Mortar Mix Specification:** Use **[ASTM C270 Type N mortar](https://www.astm.org/c0270-19ae01.html)** (1 part Portland cement, 1 part hydrated lime, 6 parts clean masonry sand) for residential and non-loadbearing arches. Type N offers high water retention, high elasticity, and accommodates thermal movement. For structural civil arches or exterior severe weathering, specify **Type S mortar**.
2. **Pre-Soaking Clay Bricks:** High-suction clay bricks rapidly draw water out of wet mortar beds, causing "dry-out" and weak bonding. Dip bricks in clean water for 1 to 2 minutes and allow surface sheen to dissipate before laying.
3. **Symmetrical Laying from Skewbacks Inward:** Never lay an arch continuously from left to right! Work symmetrically from both skewbacks (springlines) toward the crown. Lay 2 courses on the left, then 2 courses on the right. This maintains balanced lateral pressure on the centering formwork.
4. **Dry Fit the Keystone:** When 2 courses remain on either side of the apex, dry-fit the keystone brick. Check that the final joint thicknesses will be uniform.
5. **Driving the Keystone:** Butter both side faces of the keystone with mortar. Drive the stone firmly down into the apex slot using a wood block and rubber mallet. Mortar should extrude evenly from all four joint edges.
6. **Joint Tooling:** Once the mortar is thumbprint-hard, strike the joints using a convex or curved jointer tool. Tooling compacts the mortar surface against the brick edges, creating a weather-tight hydrostatic seal.

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## 8. Standards & Technical References
- **ASTM International:** [ASTM C270 - Standard Specification for Mortar for Unit Masonry](https://www.astm.org/c0270-19ae01.html)
- **Brick Industry Association (BIA):** [Technical Note 31 - Brick Masonry Arches](https://www.gobrick.com/resources/technical-notes)
- **International Code Council (ICC):** [International Residential Code (IRC) Chapter 6 - Wall Construction](https://codes.iccsafe.org/)

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