Transportation

Vertical Curve Design

Vertical curve calculator for crest and sag geometry — K-value, PVC/PVT station and elevation, and high/low point.

Transportation · AASHTO

Vertical Curve Design

Vertical curves provide smooth parabolic transitions between two tangent grades at a PVI (Point of Vertical Intersection). AASHTO uses symmetrical parabolic curves, which provide constant rate-of-grade change and simplify earthwork and stationing calculations.

The K-value is the length of curve (ft) required per 1% change in grade. Higher K = flatter, longer curve. AASHTO specifies minimum K by design speed for crest curves (sight distance) and sag curves (headlight distance and rider comfort). This calculator locates the high or low point, critical for drainage on sag curves and sight lines on crest curves.

Vertical Curve Equations
A = |g₂ − g₁|   K = L / A PVC = PVI − L/2   PVT = PVI + L/2 xₕₚ = −g₁ · L / (g₂ − g₁)
Reference: AASHTO Green Book 2018, Chapter 3. Grades in %, stations and elevations in feet.

Vertical Curve Calculator

Imperial units — feet, percent

Vertical Curve Results
Curve Type
K-Value
A (Algebraic Difference)
PVC Station
PVC Elevation
PVT Station
PVT Elevation
High/Low Point Station
High/Low Point Elevation
Reference only. Requires PE review before use in any design document.

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