Transportation
Vertical Curve Design
Vertical curve calculator for crest and sag geometry — K-value, PVC/PVT station and elevation, and high/low point.
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.
A = |g₂ − g₁| K = L / A
PVC = PVI − L/2 PVT = PVI + L/2
xₕₚ = −g₁ · L / (g₂ − g₁)
A +3.0% grade meeting a −2.0% grade over a 500-ft curve length produces a crest curve with K = 100 ft per 1% of grade change. With the PVI at station 50+00, elevation 100.00 ft, the curve begins at station 47+50 (elev. 92.50 ft) and ends at 52+50 (elev. 95.00 ft), with the high point at station 50+50, elevation 97.00 ft — the location to check for sight distance or drainage inlet placement.
Vertical Curve Calculator
Imperial units — feet, percent