Calculate circular arch radius of curvature, central angle, arc length, sagitta rise, chord span, segmental area, and woodworking framing jig coordinate offsets.
| Station (x) | Distance from Center | Offset Height y(x) |
|---|
Trammel Arm: 5.00 ft
Order Trim: 85.0 in (7.1 ft)
When retrofitting an archway or building a curved doorway header, you only know the rough opening width and desired ceiling clearance rise. You cannot physically measure the arc's center point, which often sits 5 to 10 feet below the floor. Our calculator applies the chord-sagitta Pythagorean theorem to immediately solve the radius of curvature.
Carpenters cannot swing an 8-foot trammel arm in tight residential hallways with finished floors. By providing coordinate offset heights $y(x) = \sqrt{R^2 - x^2} - (R - H)$ at measured intervals across the opening, builders can easily mark grid points onto plywood or 2x4 blocking to cut flawless matching arch templates.
Measuring curved arc length along the crown is prone to tape measure slippage and expensive ordering errors. Calculating precise arc length via central subtended angle $L = R \theta$ guarantees you purchase the correct linear footage of flexible polyurethane moulding, arched drywall bead, or wood veneer laminates.
Masonry window arches and framed transom headers require knowing the exact two-dimensional surface area enclosed between the curved arc and the horizontal springline chord. This calculator provides instantaneous segmental area in square inches, square feet, or square meters for brickwork and drywall infill.
| Arch Application | Span Width (W) | Rise Sagitta (H) | Curvature Radius (R) | Arc Length (L) | Central Angle (θ) | Trammel Pivot Below |
|---|---|---|---|---|---|---|
| Roman Arch (Semicircular) | 36.0 in | 18.0 in | 18.00 in | 56.55 in | 180.0° | 0.0 in (On Springline) |
| Standard Interior Doorway | 36.0 in | 6.0 in | 30.00 in | 38.54 in | 73.74° | 24.0 in |
| Pass-Through Hallway | 48.0 in | 8.0 in | 40.00 in | 51.39 in | 73.74° | 32.0 in |
| Wide Double-Door Cased Opening | 72.0 in | 12.0 in | 60.00 in | 77.08 in | 73.74° | 48.0 in |
Measure the horizontal chord width between support jambs or rough framing opening (W).
Input the desired vertical rise from the horizontal springline to the highest crown point (H).
Compute radius using $R = (H / 2) + (W^2 / (8 \times H))$ to determine trammel compass arm length.
Determine the total linear length of the curve (L) for flexible casing moulding and drywall trim.
Inspect the calculated coordinate offset table plotting vertical heights across the span to cut smooth templates.
Computes true mathematical radius $R = \frac{H}{2} + \frac{W^2}{8H}$ with sub-millimeter precision.
Generates equidistant station coordinates $y(x)$ for cutting rough opening carpentry blocks.
Seamless conversion between Inches, Decimal Feet, Centimeters, and Millimeters.
Real-time SVG schematic accurately plots chord, crown rise, radius center, and subtended arc.
