Transportation
Horizontal Curve Design
Horizontal curve calculator — tangent length, arc length, external distance, middle ordinate, and long chord from radius or degree of curve.
Transportation · AASHTO
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.
Horizontal Curve Elements
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
Reference: AASHTO Green Book 2018, Chapter 3. Input Δ in decimal degrees, R in feet.
Horizontal Curve Calculator
Imperial units — degrees, feet
Curve Elements
Radius (R)—
Degree of Curve (D)—
Tangent Length (T)—
Arc Length (L)—
External Distance (E)—
Middle Ordinate (M)—
Long Chord (C)—
Reference only. Requires PE review before use in any design document.