What Is the Arch Calculator?
An arch looks effortless once it is standing, but its curve is pure geometry, and getting the curve right on paper is what separates a graceful arch from a lopsided one. This arch calculator works out the key dimensions from two measurements you can take on site: the span, the clear width between the legs, and the rise, the height of the curve from the springline (where the curve begins) to the crown (the top). From those it computes the radius, the arc length, the included angle, and the segment area. The radius is what you need to lay out the curve, with a trammel, a string and pencil, or a CNC-cut plywood template. The arc length, which is always longer than the straight span beneath it, is what you need to order bendable trim, flexible molding, laminated wood, or metal conduit. The calculator handles the two common arch families: the semicircular arch, where the radius is simply half the span, and the segmental arch, a flatter curve whose radius comes from R = (span squared divided by 8 times rise) plus (rise divided by 2). Arches appear in stair halls, entryways, and over landings, and the same math sizes garden arches and arbors.
How to Use This Calculator
- Measure the span, the clear horizontal distance between the two legs or jambs of the opening.
- Measure the rise, the vertical distance from the springline, where the curve starts, to the crown at the top of the curve.
- Enter both numbers and read the radius of the arc, the number you will use to draw the curve.
- Check the arc length, which is the true curved distance, and use it, not the span, when ordering bendable material.
- Compare against a semicircular arch: if the rise equals half the span, the radius equals half the span and the math simplifies.
- Note the included angle and segment area if you are cutting a template or estimating infill material.
- Check the clearance under the arch against the 6 feet 8 inches headroom minimum wherever people walk through it.
- Use the radius to lay out the curve full-size on plywood or with a string compass, then cut or bend to the template.
