Work out curve radius from deflection instantly with clear inputs, formula shown and shareable results.
Degree of curve is the central angle subtended by a standard length, usually 100 feet. On the arc definition the radius is 180 x basis / (pi x D), which gives the familiar 5729.58 divided by D for a 100 foot arc. The chord definition, used in railway practice, gives a slightly larger radius for the same degree.
Arc definition
R = 180 x basis / (pi x D), giving R = 5729.58 / D for a 100 ft arc
Chord definition
R = (basis / 2) / sin(D / 2)
R = 180 x basis / (pi x D), giving R = 5729.58 / D for a 100 ft arc. Degree of curve is the central angle subtended by a standard length, usually 100 feet.
It made curve setting out possible with a chain and a transit: a one degree deflection per station meant the field party could lay out the curve without computing a radius.
This calculator takes 3 inputs: Degree of curve, Arc or chord basis length, Definition used. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.