Calculate PVC and PVT elevations and stations, high or low point location and elevation, and K-value for any parabolic vertical curve. Enter PVI elevation, station, incoming grade g1, outgoing grade g2, and curve length L. Includes AASHTO minimum K-value table by design speed for crest and sag curves.
A parabolic vertical curve connects two grade lines at a Point of Vertical Intersection (PVI). The curve begins at the PVC (Point of Vertical Curvature) and ends at the PVT (Point of Vertical Tangency), each located L/2 horizontally from the PVI. Elevations along the curve follow the parabolic equation: y = elevPVC + g1·x + (g2−g1)/(2L)·x².
The K-value (K = L / A, where A = |g2 − g1| in percent) measures the length of curve needed per 1% grade change. AASHTO minimum K-values range from 6 (crest, 25 mph) to 181 (crest, 70 mph) for stopping sight distance. Sag curves have lower K minimums because headlight sight distance is less critical than crest stopping distances.
A vertical curve is a parabolic transition between two grade lines at a PVI. It smooths the grade change for driver comfort and adequate sight distance. Crest curves are concave downward; sag curves are concave upward.
K-value = L / |g2 − g1| — curve length per 1% grade change. AASHTO sets minimum K-values by design speed. Higher speeds require longer curves (higher K) for safe stopping sight distance.
Distance from PVC = −g1 × L / (g2 − g1). A high point (crest curve) occurs when g1 > 0 and g2 < 0. A low point (sag curve) occurs when g1 < 0 and g2 > 0. If this distance is outside 0–L, the high/low point is outside the curve.
PVC = start of vertical curve. PVI = intersection of incoming and outgoing grade tangents (design reference point). PVT = end of vertical curve. PVI is horizontally midway between PVC and PVT for a symmetric parabola.
PVC/PVT elevations, high/low point, and K-value for parabolic vertical curves in road design.
Total stations and GPS rovers for precise vertical curve layout in the field.
Shop Express Tools →A vertical curve is a parabolic transition between two grade lines at a PVI. It smooths the grade change for driver comfort and adequate sight distance. Crest curves are concave downward; sag curves are concave upward.
K-value = L / |g2 − g1| — curve length per 1% grade change. AASHTO sets minimum K-values by design speed. Higher speeds require longer curves (higher K) for safe stopping sight distance.
Distance from PVC = −g1 × L / (g2 − g1). A high point (crest curve) occurs when g1 > 0 and g2 < 0. A low point (sag curve) occurs when g1 < 0 and g2 > 0. If this distance is outside 0–L, the high/low point is outside the curve.
PVC = start of vertical curve. PVI = intersection of incoming and outgoing grade tangents (design reference point). PVT = end of vertical curve. PVI is horizontally midway between PVC and PVT for a symmetric parabola.
Full curve length (PVC to PVT). Use positive grades for uphill, negative for downhill.
| Design Speed (mph) | Crest K (SSD) | Sag K (SSD) |
|---|---|---|
| 25 | 6 | 7 |
| 30 | 11 | 10 |
| 35 | 18 | 14 |
| 40 | 26 | 18 |
| 45 | 37 | 23 |
| 50 | 52 | 30 |
| 55 | 73 | 38 |
| 60 | 100 | 47 |
| 65 | 136 | 57 |
| 70 | 181 | 70 |
Source: AASHTO Green Book (A Policy on Geometric Design of Highways and Streets). SSD = stopping sight distance.