Horizontal Curve Layout

Tangent, length, external, middle ordinate, chord, and PC/PT stations for a circular curve.

Run the calculator

Example

You enter

You get

Details, formula, and sources

T = R*tan(delta/2); L = R*delta_rad (arc definition); E = R*(sec(delta/2)-1); M = R*(1-cos(delta/2)); LC = 2*R*sin(delta/2); arc-definition D = 5729.58/R; PC = PI - T, PT = PC + L.

Simple circular-curve geometry per the AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) and FM 5-233 Construction Surveying, by name; first-principles trig.

FM 5-233 is public-domain US Government work, free at US Army publication archives. The design of record and the engineer of record govern the alignment.

Estimate. Engineer of record governs the design and acceptance. Verify against the project structural drawings and the manufacturer's published capacity / chart.

Field names used by the API: mode, radius_ft, delta_deg, pi_station_ft, tangent_ft, curve_length_ft, long_chord_ft

Related tools