Horizontal curves are essential in highway and railroad design, ensuring smooth and safe transitions between straight path segments, or tangents. These curves allow vehicles to maintain speed without abrupt changes, minimizing accidents and improving travel efficiency.

A horizontal curve is typically defined by its geometric relationship to two tangents that meet at an intersection point (P.I.), where a simple curve is introduced to connect them. The back tangent refers to the initial tangent leading to the P.I., while the forward tangent represents the straight segment connecting the P.I. and the end of the curve. The angle between these tangents, known as the intersection angle (I), influences the curve's design and smoothness.

Key components of a horizontal curve include the radius (R), which determines its size and sharpness, and the tangent distance (T), which measures the length from the P.I. to the beginning or end of the curve. The external distance (E) is the perpendicular measure from the P.I. to the curve's midpoint, while the curve length (L) represents the entire curved segment.

Beyond simple curves, advanced designs include compound curves, featuring multiple arcs with varying radii for flexibility, and reverse curves, where consecutive arcs bend in opposite directions. Spiral or transition curves gradually change curvature, enhancing comfort and stability during entry and exit, making them crucial in modern road and rail engineering.