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Vertical Curve Calculator
Calculate elevations and gradients for road design vertical curves
Road Design
Smooth transitions between grade changes
Safety
Optimize sight distance and vehicle dynamics
Precision
Accurate parabolic curve calculations
Vertical Curve Parameters
%
%
meters
Must be between 0 and 200 meters
⚠️
Safety Critical
Vertical curve design affects vehicle safety, sight distance, and comfort. Always verify calculations and comply with design standards.
Curve Analysis Results
ELEVATION AT QUERY POINT
101.750 meters
at 100 meters from BVC
PVI Elevation
103.000 meters
Point of Vertical Intersection
EVC Elevation
101.000 meters
End of Vertical Curve
Gradient at Query Point
0.50%
Upward slope
Curve Statistics
Curve Type: Crest Curve
Algebraic Difference: 5.0%
Midpoint Distance: 100.0 meters
Curve Length: 200 meters
Input Summary
BVC Elevation: 100 meters
Initial Gradient (g₁): 3%
Final Gradient (g₂): -2%
Query Distance: 100 meters
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Vertical Curve Formula
Elevation Formula
Ex = EBVC + g₁ × x + (g₂ - g₁) × x² / (2 × L)
Where:
- • Ex = Elevation at distance x
- • EBVC = Beginning of Vertical Curve elevation
- • g₁ = Initial gradient (decimal)
- • g₂ = Final gradient (decimal)
- • x = Horizontal distance from BVC
- • L = Length of vertical curve
Key Points
PVI Elevation
EPVI = EBVC + g₁ × (L/2)
EVC Elevation
EEVC = EBVC + g₁ × L + (g₂ - g₁) × L/2
Gradient at Point
g(x) = g₁ + (g₂ - g₁) × x/L
Design Applications & Standards
Crest Curves (Convex)
Used when transitioning from an upward to downward grade. Critical for stopping sight distance and headlight sight distance at night.
Design Criteria:
- • Stopping sight distance requirements
- • Headlight illumination distance
- • Driver comfort (vertical acceleration)
- • Appearance and aesthetic considerations
- • Drainage and cross-slope maintenance
Sag Curves (Concave)
Used when transitioning from a downward to upward grade. Critical for headlight sight distance and underpass clearance.
Design Criteria:
- • Headlight beam distance at night
- • Comfort criteria for vertical forces
- • Drainage considerations
- • Clearance over structures
- • General appearance requirements
Design Standards
AASHTO Guidelines
- • Minimum curve length: K × A (K factor × algebraic difference)
- • Crest curves: K = 10-200 depending on design speed
- • Sag curves: K = 17-136 depending on design speed
- • Maximum gradient change without curve: 0.4-1.0%
Safety Considerations
- • Sight distance must exceed stopping requirements
- • Gradual transitions reduce driver discomfort
- • Adequate drainage prevents water accumulation
- • Consider snow removal and maintenance access
Related Construction Calculators
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