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Circular Curves Calculator
Calculate simple circular curve elements, stationing, setting-out values and chord/offset information for route and alignment surveying.
Simple Circular Curve
Enter the radius and intersection/deflection angle. Station values may be entered to determine the PI, PC and PT stations.
Curve Geometry
Stationing & Chords
Enter R and Δ to calculate the circular curve elements.
Curve Setting Out
Generate points along the curve at a chosen chord/arc interval. Coordinates are given in a local system with the PC at (0, 0) and the tangent along the positive X-axis.
Curve Definition
Setting-Out Interval
Enter the curve radius, angle and interval to generate setting-out points.
Circular Curve Formula Reference
Standard simple circular curve relationships used by the calculator.
Tangent lengthT = R tan(Δ/2)
Long chordLC = 2R sin(Δ/2)
Curve lengthL = πRΔ / 180
External distanceE = R[sec(Δ/2) − 1]
Middle ordinateM = R[1 − cos(Δ/2)]
Degree of curveUsing arc definition: D = 180 × C/(πR)
Stationing: PC = PI − T and PT = PC + L. For a simple curve, the tangent points are symmetric about the PI along the tangents.
Setting-out coordinates: for a right-hand curve with the PC at the origin and tangent on +X, a point subtending central angle θ has x = R sin θ and y = R(1 − cos θ). A left-hand curve uses the negative y sign.