Transportation
Horizontal Curve Design
Horizontal curve calculator — tangent length, arc length, external distance, middle ordinate, and long chord from radius or degree of curve.
Horizontal Curve Design
Horizontal curves connect two tangent sections of roadway along a circular arc. The curve is defined by either the radius (R) or degree of curve (D), along with the central (intersection) angle delta (Δ).
Degree of curve (arc definition) is the central angle subtended by a 100-foot arc: D = 5729.578 / R. Larger D means a tighter curve. The five key elements — T, L, E, M, C — are used for field layout, stationing, and sight line clearance checks.
T = R·tan(Δ/2) L = π·R·Δ / 180
E = R·(1/cos(Δ/2) − 1) M = R·(1 − cos(Δ/2))
C = 2R·sin(Δ/2) D = 5729.578 / R
For a 45° intersection angle and a 2,000-ft radius, the curve carries a 2.865° degree of curve, an 828-ft tangent length, and a 1,571-ft arc length. The external distance (E = 165 ft) and middle ordinate (M = 152 ft) tell the designer how far the curve pulls away from the tangent lines — critical for right-of-way and sight-line checks at the PI.
Horizontal Curve Calculator
Imperial units — degrees, feet