Wood Arch Radius & Segmental Crown Calculator
Calculate circle radius from arch span width and rise height to bend wood laminations or route curved door headers. This geometry engine utilizes intersecting chord formulas to determine trammel arm lengths, curved bending form dimensions, and perimeter arc cut lengths for segmented arch construction.
How Do You Calculate the Radius of an Arch from Span and Rise?
The radius of any circular or segmental wooden arch is calculated using the intersecting chord theorem: Radius = (Rise ÷ 2) + [Span² ÷ (8 × Rise)]. For a passage opening spanning 48 inches wide with an 8-inch central rise, the equation yields (8 ÷ 2) + [48² ÷ (8 × 8)] = 4 + [2304 ÷ 64] = 40.00 inches. Setting a router trammel beam or beam compass pivot to exactly 40 inches scribes the true bottom curve of the arch.
Wood Arch & Segmental Crown Radius Calculator
Calculate circle radius, arc length, trammel arm length, and bending mold dimensions from chord span and rise.
How to Lay Out and Construct a Curved Wooden Arch
Follow these four practical shop steps to scribe fair curves and build bent lamination forms:
Build a Rigid Trammel Arm for the Calculated Radius
Flexible battens frequently introduce flat spots. Rip a 1×2 hardwood trammel stick to the calculated radius length. Drill a pivot hole at one end for a pivot pin and mount a pencil or plunge router base at the opposite end.
Establish the Pivot Center Point
Lay out a sheet of 3/4″ MDF on your assembly floor. Draw the baseline span width (W) and mark the centerline apex rise (H). Measure straight down from the apex by the exact calculated radius (R) to set your trammel pivot screw.
Scribe Both Intrados and Extrados Curves
Sweep the trammel arm to scribe the inner radius (intrados). Move the pencil outward on the trammel stick by the thickness of your arch rail (extrados radius) and scribe the parallel upper curve, creating a perfect concentric template.
Cut Bending Forms or Solid Arch Blanks
For bent lamination, saw the MDF along the scribed line and sand smooth to form male and female clamping cauls. For solid-wood segmented construction, rough-cut curved segments on the bandsaw and flush-trim them against your MDF master template.
Bent Lamination vs. Solid Segmented Arches
Woodworkers have two methods to build curved wooden components: sawing solid curved segments and joining them with dominoes/half-laps, or gluing thin flexible laminates together over a curved form. Each method has distinct structural and aesthetic trade-offs.
Bent Lamination Strength
Laminating thin strips (1/16″ to 1/8″) wraps continuous longitudinal grain around the entire curve. This creates superior structural strength with zero short-grain weak points, making it ideal for structural arch rafters and chair rockers.
Springback Compensation
When released from the clamping form, bent laminations relax slightly outward (springback). Using rigid, non-creeping adhesives like urea-formaldehyde (Unibond 800) or epoxy minimizes springback to under 1% compared to flexible PVA glues.
Solid Segmented Millwork
For architectural door casings and raised panel cabinet headers, saw solid segments from wide lumber and joint them end-to-end. This eliminates visible glue laminations on the edge profiles, though grain direction must be oriented carefully.