GEOMETRY AND CAD / FIELD NOTE 08
Measuring a Circular Radius From Chord and Rise
For a circular arc with chord c and rise s, the radius is c² divided by 8s plus s divided by 2. A chord of 1,200 mm and a rise of 100 mm give a radius of 1,850 mm.
What to check on your project
Use values from the same section and the same endpoints. This estimate applies to a circular profile. A changing-curvature section needs multiple measurements or its CAD curve, and one section cannot establish the second curvature.
Worked example
If the same chord has a measured rise of 95 mm instead of 100 mm, the computed radius rises to about 1,942 mm. A small rise measurement difference can therefore create a much larger radius difference. On shallow curves it is especially important to use reliable section endpoints and a clear definition of the visible face.