Vertical Curve Calculator
Easily calculate vertical curves in road design with our efficient calculator. Get precise results for parabolic curves, including high/low points, elevations & stations.
Designing a sag curve with G₁ = -2% and G₂ = +3%, the algebraic difference would be 5%.
Using a 200-meter curve length, we can calculate precise elevations at any point along the curve profile.
Vertical Curve Calculation Table
| Station | Distance from PVC (x) | Elevation at PVC (E₀) | Grade Adjustment (G1 * x) | Curve Adjustment (-Ax²) | Final Elevation (E) |
|---|---|---|---|---|---|
| PVC (0+00) | 0 | E₀ | 0.00 | 0.00 | E₀ |
| 0+50 | 50 | E₀ | G1 * 50 | -A * 50² | Computed |
| 1+00 | 100 | E₀ | G1 * 100 | -A * 100² | Computed |
| 1+50 | 150 | E₀ | G1 * 150 | -A * 150² | Computed |
| PVT (2+00) | L | E₀ | G1 * L | -A * L² | Computed |
Formulas To Calculate Vertical Curve:
Length of Vertical Curve (L):
L = G × A where:
- G = Rate of grade change per station (100 ft)
- A = Algebraic difference in grades (G2 – G1)
Station of Vertical Point of Intersection (VPI):
VPI Station = Beginning Station + Distance to VPIHigh/Low Point Station:
x = -g1 × L / (g2 - g1) where:
- x = Distance from BVC to high/low point
- g1 = Initial grade (%)
- g2 = Final grade (%)
- L = Length of curve
Elevation at any point (y):
y = y₁ + g₁x + (g₂-g₁)x²/2L where:
- y₁ = Elevation at beginning of curve
- x = Distance from beginning of curve
- L = Length of curve
External Distance (E):
E = (A × L) / 800 where:
- A = Algebraic difference in grades
- L = Length of curve
Middle Ordinate (M):
M = (A × L) / 8
where:
- A = Algebraic difference in grades
- L = Length of curve
Tangent Length (T):
T = L/2Parabolic K Value:
K = L/A where:
- L = Length of curve
- A = Algebraic difference in grades
Stopping Sight Distance (SSD) Check:
L = (A × S²) / 2158 where:
- S = Stopping sight distance
- A = Algebraic difference in grades
- 2158 = Constant for headlight height of 2 feet and object height of 6 inches
Grade at any Point (Gx):
Gx = G1 + (x/L)(G2 - G1) where:
- G1 = Initial grade
- G2 = Final grade
- x = Distance from BVC
- L = Length of curve
How to Accurately Calculate Vertical Curve
- Determine the point of vertical intersection (PVI) where grade lines intersect
- Establish design parameters (sight distance, drainage requirements)
- Calculate required curve length using stopping sight distance criteria
- Compute high/low points using derivative equations
- Generate station elevations at regular intervals
Crest Curve Analysis:
- Initial grade: +4%
- Final grade: -2%
- Length: 300m
- PVC elevation: 100m Result: Peak elevation occurs at x = 180m, reaching 103.6m
Sag Curve Design:
- Initial grade: -3%
- Final grade: +2%
- Length: 250m
- Starting elevation: 95m Result: Minimum elevation at x = 125m, reaching 91.8m
Equal Tangent Profile:
- Initial grade: +2.5%
- Final grade: -2.5%
- Length: 400m Result: Symmetrical curve with peak at midpoint
Unequal Tangent Solution:
- Initial grade: +1%
- Final grade: -4%
- Length: 350m Result: High point occurs at x = 87.5m
Compound Curve Design:
- Initial grade: -1%
- Middle grade: +3%
- Final grade: 0%
- Total length: 500m Result: Complex profile with two transition points