Road Vertical Curve Design Calculator
What is Road Vertical Curve Design Calculator?
A vertical curve is a parabolic transition curve used in highway geometric design to connect two tangent grades smoothly, ensuring driver comfort, adequate stopping sight distance (SSD), headlight sight distance (HSD), and aesthetic appearance. The Road Vertical Curve Calculator (parabolic), for highway/civil engineers, instantly computes all geometric elements of crest and sag vertical curves, including stationing, elevations, high/low points, required curve length for sight distance, and compliance checks.
This vertical curve calculator online, parabolic vertical curve design tool, crest vertical curve calculator, sag vertical curve SSD calculator, highway vertical alignment calculator, stopping sight distance vertical curve, and AASHTO vertical curve length calculator provides relevant visualizations (profile view with curve, tangent lines, high/low point markers, sight distance lines), a dedicated section for comments, analysis and recommendations, full step-by-step calculation with every station and elevation shown, CSV export/download of results (station-elevation table, sight distance report), and a Colorblind view for effective accessibility.
How to use Vertical Curve Design Calculator
Purpose: Design or verify any crest or sag vertical curve according to AASHTO/IHDM standards and check whether the chosen length provides adequate stopping sight distance (SSD), headlight sight distance (HSD), and comfort.
Inputs you will enter:
- Initial grade g₁ (%)
- Final grade g₂ (%)
- Curve length L (m/ft)
- PVI station and elevation
- Design speed V (km/h or mph)
- Driver reaction time t (default 2.5 s)
- Friction coefficient f (default 0.35–0.40)
- Eye height h₁ (1.08 m / 3.5 ft)
- Object height h₂ (0.60 m / 2.0 ft) for SSD
- Headlight height h₃ and beam angle β for sag curves
Road Vertical Curve Formula
Algebraic equation of the curve (x from PVC) \(EL(x) = EL_{PVC} + \frac{g_1 x}{100} + \frac{A x^2}{200 L}\)
Grade difference \(A = g_2 – g_1\)
Stopping Sight Distance (SSD) – SI units \(SSD = 0.278 V t + \frac{V^2}{254 f}\)
Crest curve minimum length (S ≤ L) \(L = \frac{A S^2}{200 (\sqrt{h_1} + \sqrt{h_2})^2}\)
Sag curve minimum length (headlight control, S ≤ L) \(L = \frac{A S^2}{200 (h_3 + S \tan \beta)}\)
Where:
- A = algebraic difference in grades (%)
- L = curve length (m)
- S = sight distance (m)
- h₁, h₂ = eye and object heights (m)
How to Calculate Road Vertical Curve (Step-by-Step)
- Enter incoming grade g₁, outgoing grade g₂, and desired curve length L.
- Input PVI station and elevation.
- Calculator finds PVC and PVT stations/elevations.
- Computes high point (crest) or low point (sag) location and elevation.
- Enters design speed and sight distance parameters.
- Computes required SSD/HSD.
- Checks whether provided L satisfies crest or sag sight distance criteria (Case 1 & Case 2).
- Generates full station-elevation table, profile diagram, and PASS/FAIL verdict with recommendations.
Examples
Example 1 – Crest Vertical Curve g₁ = +3.2 %, g₂ = –2.8 %, L = 180 m, V = 100 km/h A = –6.0 % Required SSD ≈ 185 m Minimum L for crest (S ≤ L) ≈ 162 m → Provided L = 180 m → PASS High point at x = 96 m from PVC, elevation = PVI elev – 1.44 m
Example 2 – Sag Vertical Curve (Headlight Control) g₁ = –1.5 %, g₂ = +4.0 %, L = 140 m, V = 80 km/h A = +5.5 % Required HSD ≈ 130 m Minimum L (headlight) ≈ 148 m → Provided L = 140 m → FAIL (recommend increase to 150 m)
Vertical Curve Categories / Normal Range (AASHTO Typical K-Values & L_min)
| Design Speed (km/h) | Crest K (SSD) | Sag K (SSD) | Sag K (Headlight) | Typical L for A=4% (m) |
|---|---|---|---|---|
| 50 | 19 | 26 | 37 | 76–148 |
| 80 | 61 | 79 | 75 | 244–316 |
| 100 | 105 | 136 | 115 | 420–544 |
| 120 | 170 | 220 | 170 | 680–880 |
Limitations
- Parabolic curves only (no spiral or cubic parabolas).
- Sight distance uses simplified AASHTO assumptions (no passing sight distance for crest, no comfort for sag).
- No vertical curve through fixed points or offset calculations.
- Speed consistency check is advisory only.
- Does not replace full highway design software (e.g., Civil 3D, Bentley OpenRoads).
Disclaimer
This calculator is provided for educational purposes, learning, and preliminary highway geometric design checks only. All final vertical curve designs must be reviewed and certified by a qualified professional highway/traffic engineer as per the governing design code (AASHTO, IRC, Austroads, etc.). The developer and platform are not liable for any errors, misinterpretations, or consequences arising from the use of these results in actual road construction projects.