Free Web Tool

Highway Curve Calculator

Horizontal circular curves and vertical parabolic curves — get T, L, M, E, K, BVC/EVC elevations, sight distance, and full station report.

Inputs

m
decimal degrees
measured along tangent
Formulas
  • Horizontal: T = R·tan(Δ/2), L = R·Δ (rad) = π·R·Δ°/180, LC = 2R·sin(Δ/2), M = R(1−cos(Δ/2)), E = R(sec(Δ/2)−1).
  • PC = PI − T, PT = PC + L. Stations may carry through at PT.
  • Vertical: A = G₂ − G₁; K = L/|A|. Curve is sag if A>0, crest if A<0.
  • Crest SSD (AASHTO): L = A·S²/[100(√(2h₁)+√(2h₂))²]; h₁=1.08 m, h₂=0.6 m (metric). Imperial: L = A·S²/[200(√h₁+√h₂)²]; h₁=3.5 ft, h₂=2.0 ft (SSD).
  • Sag SSD (headlight): L = A·S² / (200·(h+S·tan(α))) with α=1°, h=0.6 m.

Results

Tangent T
Curve Length L
Long Chord LC
Middle Ordinate M
External E
PC station
PT station
Degree of Curve (arc, 100)