Horizontal Curve Calculator

Find the principal dimensions of a simple circular horizontal curve from its radius and full central angle. A working PI station provides PC and PT chainages, and a table divides the arc into ten equal intervals for a basic geometry check.

How to use this tool

1. Enter the positive radius and a central angle strictly between 0° and 180°.
2. Use metres or international feet consistently for radius and stationing.
3. Enter the PI station as one decimal distance, without plus notation.
4. Read the tangent, chord, arc and offsets, then check the resulting PC and PT stations.

Formula

T = R tan(Δ/2); L = RΔ in radians; C = 2R sin(Δ/2)

Middle ordinate is R[1 − cos(Δ/2)] and external distance is R[sec(Δ/2) − 1]. PC station = PI station − T. PT station follows the curve, so it is PC station + L. The table’s deflection angle from the tangent is half the central angle subtended by the traveled arc.

Example

With R = 100 m, Δ = 90° and PI station = 1,000 m, the tangent is 100 m and the arc is 157.079633 m. PC is 900 m and PT is 1,057.079633 m. The long chord is about 141.421356 m.