Free Surveying Tool
Vertical Curve Calculator
Enter two grades and a curve length. Get PVC, PVI, PVT elevations, K-value, high/low point, and a full station elevation table — instantly.
Curve Parameters
Required
Positive = uphill, negative = downhill
Horizontal distance PVC to PVT
Optional — for elevations & stations
Enter as decimal feet (e.g. 1000.00)
Vertical Curve Reference
PVC
Point of Vertical Curvature — where the parabolic curve begins. The incoming tangent grade g₁ ends here.
PVI
Point of Vertical Intersection — where the two tangent grades would meet if extended. Located at the midpoint of the curve horizontally.
PVT
Point of Vertical Tangency — where the curve ends and the outgoing tangent grade g₂ begins.
A (Grade Difference)
A = g₂ − g₁. Positive A means a sag curve (valley). Negative A means a crest curve (hill).
K-value
K = L ÷ |A|. The horizontal distance required to achieve a 1% change in grade. Used to evaluate sight distance adequacy.
High / Low Point
The point where the grade is zero — the peak of a crest curve or bottom of a sag curve. Located at x = −g₁ × L ÷ A from the PVC.
Key Formulas
E(x) = EPVC + (g₁/100)·x + (A/200L)·x²
PVI station = PVC station + L/2
PVT station = PVC station + L
High/Low point: x = −g₁·L / A (from PVC)
K = L / |A|
Where x = distance from PVC (ft), A = g₂ − g₁ (%)
AASHTO K-Value Minimums (Stopping Sight Distance)
Not sure which curve type your job calls for? See Horizontal, Vertical, and Spiral Curves Explained. Vertical curves are usually staked alongside a horizontal alignment at the same stations — the horizontal curve calculator solves that side, including PC and PT stationing.
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