Vertical Curve — Highway Surveying & Road Design
Compute vertical curve parameters for crest and sag curves. K-value, high/low point, station elevations. AASHTO Green Book standards.
Why This Construction Metric Matters
Why: Vertical curves provide smooth transitions for driver comfort and sight distance.
How: A = g₂ − g₁. K = L/|A|. High/low: x = −g₁×L/A. E = E_PVC + g₁×x/100 + (A×x²)/(200×L).
- ●Crest: sight distance critical
- ●Sag: drainage at low point
- ●K_min from AASHTO by speed
📋 Quick Examples — Click to Load
Planning estimates only. Verify with a licensed engineer or contractor before construction.
📐 Construction Industry Facts
K = L/|A|; rate of vertical curvature
— AASHTO
Crest: high point; Sag: low point
— Road design
Vertical curves provide smooth parabolic transitions between roadway grades. K = L/|A|; A = g2 − g1. Crest curves have a high point; sag curves have a low point. AASHTO specifies minimum K-values by design speed for stopping sight distance.
Sources: AASHTO Green Book, ASCE, State DOT Manuals.
Key Takeaways
- • K = L/|A|; A = g2 − g1; x = −g1×L/A for high/low point
- • Crest: high point; Sag: low point; PVC/PVI/PVT
- • E = E_PVC + g1×x/100 + (A×x²)/(200×L)
- • AASHTO K-min by design speed; crest > sag
Did You Know?
How Does It Work?
Algebraic Difference
A = g2 − g1. Positive for crest (up then down); negative for sag.
K-Value
K = L/|A|. Larger K = gentler curve. Minimum K from AASHTO by speed.
Elevation
Parabolic: E = E_PVC + g1×x/100 + (A×x²)/(200×L).
Expert Tips
AASHTO K-Values by Speed
| Speed (mph) | SSD (ft) | K Crest | K Sag |
|---|---|---|---|
| 20 | 115 | 7 | 4 |
| 25 | 155 | 12 | 6 |
| 30 | 200 | 19 | 9 |
| 35 | 250 | 29 | 13 |
| 40 | 305 | 44 | 18 |
| 45 | 360 | 61 | 23 |
Frequently Asked Questions
What is a vertical curve in road design?
A vertical curve provides a smooth parabolic transition between two roadway grades. Crest curves connect downgrade to upgrade; sag curves connect upgrade to downgrade. Essential for driver comfort and sight distance.
What is the K-value for vertical curves?
K = L / |A|, where L is curve length and A is algebraic difference (g2 − g1). K represents the rate of vertical curvature. Higher design speeds require larger minimum K-values per AASHTO.
Where is the high or low point on a vertical curve?
Distance from PVC to high/low point: x = −g1 × L / A. Crest curves have a high point; sag curves have a low point. Elevation: E = E_PVC + g1×x/100 + (A×x²)/(200×L).
What are PVC, PVI, and PVT?
PVC = Point of Vertical Curvature (curve start). PVI = Point of Vertical Intersection (curve midpoint). PVT = Point of Vertical Tangency (curve end).
How does design speed affect minimum curve length?
AASHTO specifies minimum K-values by design speed. L_min = K_min × |A|. At 60 mph, K_min crest ≈ 151, K_min sag ≈ 45. Higher speeds need longer curves for sight distance.
When is sight distance critical on vertical curves?
Crest curves limit stopping sight distance (SSD). Sag curves need drainage at the low point. Both must meet AASHTO minimum curve length for the design speed.
Key Statistics
Official Data Sources
⚠️ Disclaimer: This calculator is for educational purposes only. Verify with AASHTO and local design standards. Not for final design.
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