Vertical Curve Calculator

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Construction

Calculate parabolic vertical curve elevations for road design: y = PVC_elev + g₁x + (g₂−g₁)/(2L) × x².

Formula

y = PVC_elev + g₁x + (g₂−g₁)/(2L) × x²; High/Low point: x = −g₁L/(g₂−g₁)
  • PVC = Point of Vertical Curvature (start of curve). PVI = Point of Vertical Intersection.
  • g₁ and g₂ are grades in decimal (e.g. −2% = −0.02).
  • High/low point only exists within the curve when g₁ and g₂ have opposite signs.

PVC=100 ft, g₁=−2%, g₂=+3%, L=500 ft, x=250 ft

Inputs
  • PVC Elevation: 100 ft
  • Initial Grade (g₁): -2 %
  • Final Grade (g₂): 3 %
  • Curve Length: 500 ft
  • Station Distance from PVC: 250 ft

y = 100 + (−0.02)(250) + (0.05/1000)(62500) = 100 − 5 + 3.125 = 98.125 ft

Frequently asked questions

What is PVC?
PVC (Point of Vertical Curvature) is where the straight grade transitions into the curved section. Station and elevation are your starting reference.