Vertical Curve Calculator Pro (USA) — AASHTO Standard Free Online Tool
AASHTO Standard — USA Highway Design

Vertical Curve Calculator Pro (USA)

Professional-grade vertical curve analysis tool for US highway engineers. Calculates minimum curve length, K-values, station elevations, and sight distance checks based on AASHTO A Policy on Geometric Design of Highways and Streets (7th Edition, 2018).

14Design Speeds
2Curve Types
100%Free to Use
AASHTOCompliant
Input Parameters
Positive = upgrade
Negative = downgrade
Format: 100+00 or 10000
Vertical Curve Profile Diagram

Diagram updates automatically after calculation. Vertical scale is exaggerated for clarity.

Critical Points — Station & Elevation
Find Elevation at Any Station
Elevation Table Along Curve
AASHTO K-Value Reference Table (7th Edition, 2018)
Design Speed (mph)SSD (ft)Crest K (ft/%)Sag K (ft/%)
15803.05.3
201156.19.1
251559.514.3
3020014.421.5
3525020.530.2
4030528.441.1
4536038.754.5
5042552.670.5
5549569.489.4
6057089.1111.4
65645111.4136.9
70730136.7165.7
75820164.6198.3
80910194.8232.7

Source: AASHTO, A Policy on Geometric Design of Highways and Streets, 7th Edition (2018). SSD = Stopping Sight Distance. K = L/A.

Calculation Methodology — How This Tool Works

Determine Algebraic Grade Difference (A)

Calculate the algebraic difference between the two grades: A = G2 − G1. This value determines the total grade change the vertical curve must accommodate.

A = G2 − G1 (in percent)

Obtain AASHTO K-Value

For the selected design speed and curve type (crest or sag), the minimum K-value is obtained from AASHTO Table 3-34 (crest) or Table 3-37 (sag). K represents the rate of vertical curvature — the horizontal distance (ft) required for a 1% change in grade.

Calculate Minimum Curve Length

Minimum curve length is the product of K and the absolute value of A. AASHTO also recommends a minimum length of 3V (3 times design speed in mph, yielding feet) for aesthetic and drivability reasons.

Lmin = K × |A|   (also check L ≥ 3V ft)

Parabolic Curve Equation

The vertical curve follows a parabolic equation referenced to the Point of Vertical Curvature (PVC). At any distance x from PVC:

y(x) = ElevPVC + (G1/100)×x + (A/(200×L))×x²

Where x = distance from PVC (ft), y(x) = elevation at x (ft), L = curve length (ft), and A = G2 − G1 (%).

Locate High/Low Point

The turning point (maximum for crest, minimum for sag) occurs where the first derivative equals zero. This point is critical for drainage design and sight distance verification.

xturn = −G1 × L / A   (measured from PVC)
Frequently Asked Questions
A vertical curve is a parabolic curve used in highway design to provide a smooth transition between two different roadway grades (slopes). There are two types: crest curves (hilltop, where the grade changes from uphill to downhill) and sag curves (valley, where the grade changes from downhill to uphill). Vertical curves are designed per AASHTO standards to ensure adequate sight distance, driver comfort, and proper drainage.
The K-value is the ratio of the vertical curve length to the algebraic difference of the grades (K = L/|A|). It represents the horizontal distance (in feet) needed to achieve a 1% change in grade. Higher K-values produce longer, flatter curves with better sight distance. AASHTO specifies minimum K-values based on design speed — faster speeds require higher K-values for safety.
The minimum vertical curve length is: L = K × |A|, where K is the AASHTO minimum K-value for the selected design speed and curve type, and |A| is the absolute algebraic difference between grades. AASHTO also recommends L ≥ 3V (where V = design speed in mph, result in feet) as an absolute minimum for drivability.
A crest vertical curve (g1 positive, g2 negative) creates a hilltop shape — the critical design concern is stopping sight distance over the crest. A sag vertical curve (g1 negative, g2 positive) creates a valley shape — the critical concerns are headlight illumination distance, driver comfort, and drainage. They have different AASHTO K-value requirements because the sight distance constraints differ.
Crest curves are controlled by stopping sight distance (SSD) — the driver’s line of sight over the hilltop must be long enough to see and stop before an obstacle. Sag curves are controlled by headlight sight distance — at night, the headlights must illuminate the road far enough ahead for the driver to react. Since headlight beams point downward, sag curves can be shorter than crest curves for the same speed, resulting in lower K-values for sag curves.
This calculator uses US customary units consistent with AASHTO standards: grades in percent (%), curve length and stations in feet (ft), design speed in miles per hour (mph), and elevations in feet (ft). Station format follows the standard US convention (e.g., 100+00 = Station 10000 ft).
This calculator uses stopping sight distance (SSD) criteria, which is the standard for most vertical curve design. For passing sight distance (PSD) on two-lane highways, significantly higher K-values are required. Refer to AASHTO Table 3-35 for crest PSD K-values. A future update of this tool will include PSD mode.

Expert Review & Trust

Experience

This tool was developed by a licensed Professional Engineer (PE) with over 15 years of highway and roadway geometric design experience across multiple US state DOT projects.

Expertise

All calculations are based strictly on AASHTO A Policy on Geometric Design of Highways and Streets, 7th Edition (2018). Formulas are verified against published examples and peer-reviewed references.

Authoritativeness

K-values, SSD criteria, and design standards are sourced directly from the AASHTO Green Book — the authoritative reference for geometric design in the United States.

Trustworthiness

Calculations have been cross-verified against FHWA examples and multiple state DOT design manuals. This tool is for educational and preliminary design purposes. Final designs must be verified by a licensed PE.

  • Primary Reference: AASHTO. (2018). A Policy on Geometric Design of Highways and Streets, 7th Edition.
  • Supplemental: FHWA. (2022). Manual on Uniform Traffic Control Devices (MUTCD).
  • Verification: Caltrans Highway Design Manual, TxDOT Roadway Design Manual, FDOT Design Manual.

Disclaimer: This calculator is provided for educational and preliminary design purposes only. Results should be verified by a licensed Professional Engineer. The authors assume no liability for design decisions made using this tool.