Masonry Arch Geometry

Odd numbers (3, 5, 7, 9...) produce a true center keystone.

Masonry Arch Calculator — Voussoir Angles & Template

Calculation Results & Voussoir Arch Layout Blueprints

Full-scale masonry arch blueprint, individual voussoir brick taper wedge detail, and angular set-out ordinates:

🏛️ Brick Arch — Voussoir Layout Blueprint
Brick Arch Voussoir Blueprint Scaled masonry arch blueprint showing radius of curvature, voussoir division joints, keystone, and springline datums.

Print 1:1 wedge template without page scaling to cut cardboard/plywood brick taper gauges or mark wooden centering formers.

📐 Single Voussoir Brick / Stone Taper Wedge Geometry Detail

Single Voussoir Wedge Detail Detail showing intrados arc width, extrados arc width, and wedge taper angle per individual voussoir.
Radius of Curvature (r)
30.00 in
Center Origin to Intrados
Voussoir Wedge Angle (θ)
11.81°
Per Brick / Voussoir
Total Arch Arc Angle
106.26°
Springline to Springline
Keystone Configuration
True Keystone
Odd Voussoir Count (9)

🔨 Voussoir Layout & Angular Matrix Table

Sequential voussoir angles and arc lengths from left springline:

Voussoir # Cumulative Angle Intrados Arc Width Extrados Arc Width

📦 Masonry Arch Materials & Centering Checklist

Select Item Description Est. Quantity Fabrication / Shoring Notes

Related Arc & Layout Calculators

⚠️ Structural Engineering & Arch Safety Disclaimer: This masonry arch calculator provides geometric voussoir layout, radius of curvature, and wedge taper angles for layout purposes. Structural masonry arches over clear wall openings require structural engineering calculation for thrust, abutment stability, and load capacity. Always build rigid temporary wooden centering formers to support bricks until mortar fully cures.

Worked Example & Mathematical Proof

Consider a segmental brick arch designed for a clear span S = 48.0 inches and a rise R = 12.0 inches, using 2.25-inch thick voussoir bricks and 0.375-inch mortar joints:

Verification Note: 22 voussoirs × 4.83° taper angle = 106.26° total sweep closure. Radius of 30.0" reproduces exact span of 48.0" and rise of 12.0".

Required Tools, PPE & Trade Pitfalls

Essential Masonry Tools

  • 14" Diamond Blade Wet Masonry Saw: Precision cutting of radial voussoir brick tapers.
  • Plywood Centering Form & Screw Jacks: Rigid support during voussoir laying.
  • Mason Trowel & Concave Jointer: Type N mortar placement and weather-struck joints.
  • Trammel String & Center Pin: Verification of radial voussoir alignment to center point.
  • ANSI Z87.1 Face Shield & N95 Silica Respirator: Mandatory dust and eye protection PPE.

Trade Pitfalls & Quality Mistakes

  • Premature Centering Removal: Striking wooden forms before 7 days causes arch sagging.
  • Unbalanced Keystone Fitting: Forcing a mis-sized keystone creates point-load stress cracks.
  • Weak Springline Abutment: Inadequate pier thickness fails under horizontal thrust forces.
  • Inconsistent Mortar Thickness: Thicker joints at crown reduce compressive arch strength.

Related Masonry & Structural Calculators

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Frequently Asked Questions (FAQ)

What is the formula for calculating voussoir brick counts in a segmental brick arch?

Voussoir brick count n = ceil(Arc Length L / (Brick Thickness T + Mortar Joint M)), where Arc Length L = Radius r * Sweep Angle θ (in radians).

How do you calculate the radius of a segmental arch from span and rise?

Arch Radius r = (S² + 4 * R²) / (8 * R), where S is clear arch span and R is arch rise at the crown.

What is the wedge taper angle for voussoir bricks in a circular arch?

Wedge Taper Angle α = Total Sweep Angle θ / Voussoir Count n. Each voussoir brick is tapered by α / 2 on left and right cuts.

What is the difference between a segmental arch, semicircular arch, and jack arch?

A segmental arch is a partial circular arc (rise < span/2); a semicircular arch has rise = span/2 (180° sweep); a jack arch is flat horizontal with tapered radial voussoirs.

What is the minimum recommended mortar joint thickness for structural brick arches?

Standard mortar joints for voussoir brick arches range from 1/4 inch (6 mm) to 3/8 inch (9.5 mm) using ASTM C270 Type N or Type S mortar.

How does a wooden centering form support a brick arch during construction?

A wooden centering form cut to exact intrados radius supports voussoir bricks and mortar until the central keystone is laid and mortar cures.

What is a keystone and why is it critical in brick arch geometry?

The keystone is the central top voussoir brick laid at the arch crown; it locks all radial voussoirs into compressive equilibrium against springline skewbacks.

What is skewback angle in a segmental brick arch?

Skewback angle is the inclination angle of the arch abutment at the springline, calculated as α_skew = 90° - (Sweep Angle θ / 2).

How do you calculate intrados versus extrados arc lengths for brick arch voussoirs?

Intrados arc length L_in = r * θ_rad; Extrados arc length L_out = (r + Arch Depth D) * θ_rad.

What brick type is specified for structural masonry arches under BIA Technical Notes?

Use solid severe weathering (SW) grade face brick conforming to ASTM C216 or ASTM C652 to prevent freeze-thaw spalling.

How long must wooden centering stay in place under a newly mortared brick arch?

Wooden arch centering should remain fully clamped for at least 7 days until mortar reaches at least 70% of structural compressive strength.

What is the maximum span recommended for unreinforced brick arches?

Unreinforced brick segmental arches are typically limited to 6 to 8 feet clear span unless supported by structural steel lintels.

How does wall abutment lateral thrust affect brick arch stability?

Arches convert vertical loads into lateral outward thrust at skewbacks; adjacent masonry piers or tie-rods must resist this horizontal thrust force.

Can standard rectangular bricks be used for arches without tapering?

Yes, for wide radius segmental arches, standard rectangular bricks can be laid with wedge-shaped mortar joints (thicker at extrados, thinner at intrados).

What is rise-to-span ratio for optimal structural strength in brick arches?

An optimal rise-to-span ratio for segmental brick arches is between 1:6 and 1:4 (rise equal to 1/6th to 1/4th of clear span).

How do freeze-thaw cycles affect brick arch mortar joints?

Water penetration into joint hairline cracks can freeze and pop mortar; concave or V-groove struck joints shed water effectively.

What tool is best for precision cutting tapered voussoir bricks?

Use a continuous-rim diamond blade masonry wet saw with a miter guide fence to cut exact radial wedge angles into face bricks.

How do you estimate brick and mortar quantities for a multi-centered arch?

Calculate total arch volume V = (Extrados Arc Length * Arch Depth * Wall Thickness) and multiply by 1.10 for waste factor.

Sources & Governing Codes

  1. Wikipedia — Arch Structural Geometry: Arch masonry mechanics, voussoir compression, and crown keystone principles View Standard
  2. Wikipedia — Brickwork & Masonry Bonding: Structural brickwork, voussoir mortar jointing, and arch bonding patterns View Reference