Arch Trim & Moulding Calculator
Calculate flexible moulding order lengths, extrados stretch vs. intrados compression ($\Delta L$), reveal offsets, and multi-piece solid hardwood segmented miter joints.
Interactive Casing Width & Stretch Simulator
Adjust the casing width slider to see how wider mouldings exponentially increase the outer perimeter stretch elongation ($\Delta L$), dictating flexible polyurethane vs. segmented hardwood construction.
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.
Curved Casing Geometry & Plumb Cut Math
Properly calculate the transition point where curved arch casing meets straight vertical side casing trim.
For a 180 degree semicircle (angle = pi), Delta L = pi * w_casing regardless of the opening span.
Glue and biscuit-join straight segment blanks on a plywood template before routing the final smooth curve.
Step-by-Step Worked Numeric Example
Suppose you are casing a 3-foot wide semicircular passage arch (W = 36.0", H = 18.0") with 3-1/2" flat casing moulding and a 3/16" (0.1875") reveal margin.
Standard Arch Opening Sizes: Quick Reference Table
Pre-calculated dimensions, radius curves, arc lengths, and material recommendations for standard residential and commercial architectural openings.
| Opening Purpose | Span (W) | Rise (H) | Radius (R) | Arc Length (L) | Center Drop | Min Casing Trim | Recommended Substrate |
|---|---|---|---|---|---|---|---|
| Interior Single Door | 30.0" | 6.0" | 21.75" | 33.25" | 15.75" | 3 ft 6 in | 1/4" High-Flex Drywall or Flex Poly |
| Bedroom / Bath Door | 32.0" | 8.0" | 20.00" | 37.10" | 12.00" | 3 ft 10 in | 1/4" High-Flex Drywall / Polyurethane |
| Main Entry / Passage | 36.0" | 9.0" | 22.50" | 41.74" | 13.50" | 4 ft 3 in | 1/4" High-Flex / Kerfed MDF Jamb |
| Hallway / Corridor | 42.0" | 10.5" | 26.25" | 48.70" | 15.75" | 4 ft 10 in | Double 1/4" High-Flex Gypsum |
| Double Doorway / Pass-Through | 48.0" | 12.0" | 30.00" | 55.65" | 18.00" | 5 ft 6 in | Double 1/4" High-Flex or 3/8" Gypsum |
| French Door Opening | 60.0" | 15.0" | 37.50" | 69.56" | 22.50" | 6 ft 8 in | 1/4" Bendable Plywood / Wiggle Board |
| Living Room Cased Archway | 72.0" | 18.0" | 45.00" | 83.47" | 27.00" | 8 ft 0 in | Standard 1/2" Drywall (Wetted) or Plywood |
| Grand Room Divider / Great Hall | 96.0" | 24.0" | 60.00" | 111.30" | 36.00" | 10 ft 6 in | Standard 1/2" Drywall (Dry Bend OK) |
How to Lay Out & Build an Arch: Complete Field Guide
Follow this proven 5-stage jobsite workflow to translate calculated geometry into accurate physical templates, framing, and finish trim.
Establish the Springline Datum & Rough Opening
Snap a perfectly level chalk line at the springline elevation across both jambs. Measure the total rough opening width ($W$) and verify both king studs are plumb. Mark the exact center point on the horizontal springline.
Plot the Curve onto 3/4" Plywood Template
For circular arcs with center points within reach, swing a trammel bar from the pivot point. For large-radius or elliptical arches, mark our calculated Offset Coordinates ($X, Y$) at 2"–3" intervals, tap finish brads at each point, and bend a flexible batten across the pins to scribe the smooth line.
Cut & Duplicate Arch Rib Gussets
Cut the primary arch rib out of 3/4" CDX plywood or OSB using a jigsaw. Sand the curved edge smooth to eliminate high spots. Use this master rib with a flush-trim bearing router bit to produce identical duplicate ribs for the front and back wall faces.
Install 2x4 Infill Blocking & Mount Rib Assembly
Fasten 2x4 blocking (cut to wall depth minus two plywood thicknesses, typically 2.0" for 2x4 walls or 5.0" for 2x6 walls) between the dual plywood ribs at 6" to 8" on center. Anchor the completed arch assembly securely into the rough opening header and king studs.
Apply Finish Substrate (Drywall, Flex Trim, or Casing)
For drywall, fasten two layers of 1/4" High-Flex drywall to the curved soffit (dampening the backing paper with a spray bottle for tight radii). Apply flexible archway corner bead and finish mud. For trim, install pre-curved polyurethane moulding matching the calculated intrados arc length.
Material Bending Limits & Substrate Specifications
Understand the physical minimum bend radii and structural limitations of gypsum boards, bendable plywood, kerfed jambs, and flexible trim.
1/4" High-Flex Gypsum Board
Specially engineered core with high tensile facing paper. Apply in two laminated 1/4" layers for 1/2" total thickness.
3/8" Standard Drywall
Moderate flexibility. Suitable for wide residential pass-throughs and hallway arches with radius over 5 feet.
1/2" Standard Drywall
Rigid board. Must not be bent dry under 10 ft radius. For wet bending, spray both sides with water and allow to soak for 15 minutes.
1/4" Bendable Plywood (Wiggle Wood)
Multi-ply rotary cut veneer with cross-grain plies omitted. Available in Column Bend (8-ft axis) and Barrel Bend (4-ft axis).
Kerfed 3/4" MDF or Clear Pine
Saw kerfs cut to 5/8" depth (leaving 1/8" face veneer) spaced 1/2" to 3/4" apart. Fill kerfs with PVA glue during mounting for rigidity.
Flexible Polyurethane Moulding
Seamless imitation of wood grain that flexes effortlessly along the intrados. Order based on calculated Arc Length + 10%.
Common Arch Doorway Framing & Casing Mistakes
Prevent unlevel springlines, irregular cripple stud lengths, and misaligned trim casing.
Exceeding Drywall Minimum Bending Radius
Attempting to force standard 1/2" drywall around tight curves (under 10 ft radius) dry, causing catastrophic gypsum core fracture and unsightly faceted creases.
Use two layers of 1/4" High-Flex gypsum (bends dry to 24" radius, wet to 12" radius). For ultra-tight arches, use kerfed 3/4" MDF or 1/4" bendable plywood (wiggle board).
Underestimating Lateral Horizontal Thrust
Treating shallow segmental or flat jack arches like standard post-and-beam lintels without reinforcing the side supporting piers or king studs.
Install double or triple king studs tightly fastened with structural framing screws. For masonry arches, ensure skewbacks are angled toward the radius center with stout abutments.
Ordering Casing by Span Width Instead of Arc Length
Ordering flexible polyurethane or wood moulding based on the horizontal rough opening width ($W$), leaving the installer short by 15% to 57%.
Always order moulding based on the true calculated Intrados Arc Length (L_intrados) plus a minimum 10% allowance for trimming springline plumb cuts.
Uneven Springline Heights Across Jambs
Measuring the arch rise from the finished floor without verifying that the left and right springline points are level, resulting in a tilted, lopsided arch crown.
Shoot a laser level line across the opening to establish an absolute level springline datum before tracing or mounting curved plywood ribs.
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 is the outside edge (extrados) of curved trim moulding longer than the inside edge?
Because the outside edge of the casing travels along a larger radius (R_ext = R_int + Casing Width). For a standard 3-1/2" wide casing wrapped around a 180° Roman arch, the outer edge is exactly π × 3.5" ≈ 11.0 inches longer than the inside edge. Flexible polyurethane trim easily absorbs this elongation, whereas rigid solid wood requires multi-piece segmented mitering or steam-bending.
Q2 What length of flexible moulding should I order for an arched doorway?
Order flexible moulding based on the centerline arc length plus 12 inches of extra margin for trimming the springline plumb cuts. Total Cut Length = L_centerline + 12". For a 36" wide opening with an 18" rise and 3.5" casing: Intrados = 56.55", Centerline = 62.05", so order at least 74" (or one standard 8-foot flexible moulding stick).
Q3 What is a standard casing reveal margin on an arched opening?
A standard architectural casing reveal margin is 3/16" (0.1875") or 1/4" (0.250") stepped back from the inside face of the curved drywall corner bead or wood jamb.
Q4 How do you calculate segmented solid wood miter cuts for curved arches?
When fabricating arched casing out of solid hardwood without flexible polyurethane, carpenters cut 5 to 7 straight segment blocks. For N segments spanning sweep angle θ, each segment subtends angle δ = θ / N. The miter saw bevel cut angle at each segment joint is Miter Angle = δ / 2.