Radius
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Shop estimate. Measure your stock and cut a test on scrap.
How to use it
- Choose chord and rise if you have measured the span and the bulge. Choose radius and chord if you already know the form.
- Enter the two lengths in the same unit.
- Read the radius or the rise, the central angle, and the length along the curve.
- A rise taller than half the chord is more than a semicircle. The page still returns it.
The formula
Radius = chord² ÷ (8 × sagitta) + sagitta ÷ 2.
- Chord. The straight line between the two ends of the arc.
- Sagitta. The rise, measured at the middle of the chord, out to the curve.
- Arc length. Distance along the curve. It is longer than the chord.
Worked example
A 48 inch chord with a 3 inch rise has a radius of 97.5 inches. The curve itself is 48.498 inches, longer than the straight span, and the central angle is 28.5°.
The same radius and the same chord return the 3 inch rise. A rise of half the chord is a semicircle: the radius equals the rise.
What it will not decide
- One circular radius. An ellipse or a freehand curve is not this number.
- It does not say whether a sawn lamination or a kerf bend can make it. Those are the other pages, and they still need a test.
- The radius-and-chord mode returns the minor arc, the one that bulges less than a semicircle.
Questions
What is a sagitta?
The height of the arc above the middle of its chord. On a table apron it is how far the curve kicks out from the straight line between the legs.
Why is the radius so much larger than the rise?
A shallow bulge on a long span is a large circle. A 3 inch rise on a 48 inch chord is a 97.5 inch radius. That is the worked example.
Can I use this for a kerf-bent panel?
Yes, for the radius. Take that radius to the kerf-bending page. This page does not space the saw cuts.