Vertical Curve Calculator - AASHTO Crest and Sag Curve Design
Calculate vertical curve length, K-value, PVC/PVT stations, and stopping sight distance for crest and sag curves using AASHTO Green Book design controls. Built for road, driveway, and site grading design alongside our elevation grade calculator.
📏 Vertical Curve Calculator
Crest & Sag Curves | K-Value Lookup | Stopping Sight Distance | Elevation Profile
💰 Estimate Your Project Cost
Get accurate cost estimates before calling a contractor — compare prices and plan your budget.
Rebar Weight Chart
US Standard Rebar Sizes (#2–#18) with weight per foot, diameter, and cross-sectional area.
View Chart →How This Vertical Curve Calculator Works
Pick a Design Speed
Select a design speed to auto-fill the AASHTO K-value, or type in your own K-value from a project design manual.
Enter Both Grades
Type approach grade G1 and departure grade G2 in percent. The tool detects crest or sag automatically from the sign change.
Set the PVI
Enter the station and elevation where the two grade lines intersect (PVI), the reference point for the whole curve.
Get Full Curve Data
Receive curve length, PVC/PVT stations and elevations, high/low point, sight distance check, and an elevation profile chart.
AASHTO K-Value Lookup by Design Speed
These rounded K-values come from AASHTO's A Policy on Geometric Design of Highways and Streets, based on stopping sight distance for each design speed [1]. Find your design speed, then read the crest and sag K-value directly.
| Design Speed (mph) | Stopping Sight Distance (ft) | Crest K | Sag K |
|---|---|---|---|
| 20 | 115 | 7 | 17 |
| 25 | 155 | 12 | 26 |
| 30 | 200 | 19 | 37 |
| 35 | 250 | 29 | 49 |
| 40 | 305 | 44 | 64 |
| 45 | 360 | 61 | 79 |
| 50 | 425 | 84 | 96 |
| 55 | 495 | 114 | 115 |
| 60 | 570 | 151 | 136 |
| 65 | 645 | 193 | 157 |
| 70 | 730 | 247 | 181 |
| 75 | 820 | 312 | 206 |
| 80 | 910 | 384 | 231 |
Drainage threshold for curbed sections: K ≤ 167 [1]. Values above this threshold need extra drainage design attention near the level point.
What a Vertical Curve Does in Roadway Design
A vertical curve smooths the transition between two roadway grades so vehicles do not experience an abrupt change in slope. AASHTO uses a simple parabolic curve for this transition, defined by the equation L = KA, where L is curve length in feet, K is the rate of vertical curvature, and A is the algebraic difference between grade G1 and grade G2 in percent [1].
The two curve types behave differently. A crest curve bends downward, so sight distance is limited by the road surface blocking the view ahead. A sag curve bends upward, so sight distance is limited by headlight beam divergence at night rather than the road surface itself [2]. This is why crest and sag curves use different K-value tables even at the same design speed.
Why K-Value Controls Curve Length
K represents the horizontal distance, in feet, needed for a 1 percent change in grade while still meeting the minimum stopping sight distance for a design speed. Multiplying K by A in percent gives curve length directly, which is why designers reference K instead of recalculating sight distance for every curve [1]. Our elevation grade calculator is useful for checking the resulting grades once a curve is set.
Minimum Curve Length Rule
Even when a sight-distance-based calculation returns a very short length, AASHTO recommends a preferable minimum curve length of three times the design speed in mph: Lmin = 3 x design speed [1]. This prevents curves so short they read as a visual kink rather than a smooth transition.
Example Scenarios from Site and Road Design
📏 Crest Curve on a Collector Road
G1 = +3.0%, G2 = -2.0%, design speed = 45 mph
A = 5.0%, K = 61 (crest, AASHTO)
This length satisfies AASHTO stopping sight distance for 45 mph and clears the minimum length check of 3 x 45 = 135 ft with margin [1].
📍 Sag Curve at a Low-Speed Driveway Entrance
G1 = -1.5%, G2 = +2.5%, design speed = 30 mph
A = 4.0%, K = 37 (sag, AASHTO)
Because this is a curbed section, the resulting K of 37 falls well below the 167 drainage threshold, so pooling at the low point is not a design concern [1].
⚠ Common Error: Wrong Sign Convention
Entered G1 = -2.0%, G2 = +2.0% intending a crest curve
Always confirm grade sign against direction of travel before locking in curve type, since sag and crest use different K-value tables [1].
Common Mistakes in Vertical Curve Design
💡 Mixing Up Crest and Sag K-Tables
Crest and sag curves use separate K-value tables at the same design speed because sight distance is governed by different factors. Using a crest K-value on a sag curve under-designs the curve for nighttime headlight sight distance [1][2].
⚠ Forgetting the 3x Design Speed Minimum
For small values of A, the SSD-based formula can return a curve length near zero. AASHTO requires a minimum length of three times the design speed regardless of how small A is [1].
💡 Ignoring the Drainage K = 167 Threshold on Curbed Roads
On curbed sections, a K-value above 167 means the road may stay too flat too close to the level point, risking standing water. This does not apply to open, uncurbed roadside ditches [1].
⚠ Confusing PVI Station with PVC Station
The PVI is the intersection of the two straight grade lines, not the start of the curve. The curve actually begins at the PVC, located L/2 before the PVI station.
💡 Overlooking Overhead Clearance on Sag Curves
Structures crossing over a sag curve, such as bridges or sign bridges, can cut off headlight sight distance even when the ground-level SSD calculation checks out. Verify overhead clearance separately per AASHTO guidance [1].
Where Vertical Curve Calculations Apply
Vertical curves appear on public roads, private driveways, parking lot access points, and site grading plans wherever two grades meet. Municipal and DOT projects generally require design compliance with AASHTO Green Book or an adopted local supplement, while private site work often follows the same K-value tables as informal best practice [1].
For construction sequencing after the curve geometry is set, pair this tool with our excavation calculator for cut/fill volumes and the construction schedule calculator for grading timeline planning. Driveway aprons and approach curves often connect directly into a driveway base design.
Frequently Asked Questions
L = K x A, where L is curve length in feet, K is the design control value tied to stopping sight distance, and A is the algebraic difference in grades G1 minus G2, in percent, per AASHTO Green Book [1].
K is the horizontal distance in feet required to produce a 1 percent change in grade while meeting minimum stopping sight distance for a given design speed. It differs for crest and sag curves at the same speed [1].
A crest curve transitions from a positive to a negative grade, forming a hill shape where the pavement itself blocks sight distance. A sag curve transitions from negative to positive, forming a valley shape where headlight beam divergence governs sight distance at night [2].
AASHTO recommends K at or below 167 on curbed sections so the road reaches at least a 0.30 percent grade within roughly 50 feet of the level point, reducing the risk of standing water [1].
AASHTO's preferable minimum vertical curve length is three times the design speed in mph (Lmin = 3 x design speed), applied even when the sight-distance formula alone returns a shorter value [1].
Use y = elevation at PVC + G1(x) + [(G2 - G1) / (2L)] (x squared), where x is distance from the PVC, G1 and G2 are grades as decimals, and L is curve length in the same units as x.
The high point on a crest curve or low point on a sag curve marks the location of maximum or minimum elevation. It is used to place drainage inlets on sag curves and to check clearance under overhead structures on crest curves.
Sources and Methodology
Last reviewed: July 2026.
- [1] AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book), K-value tables and L = KA formula, as summarized in TxDOT Roadway Design Manual, Section 4.8.2.
- [2] Engineering LibreTexts, Fundamentals of Transportation, Section 7.5, Vertical Curves, crest versus sag sight distance discussion.
- Elevation formula y = PVC elevation + G1(x) + [(G2-G1)/(2L)]x^2 is the standard parabolic vertical curve equation used across US DOT design manuals.
Unlock Your Complete Results
Your calculation is ready. Enter your email to unlock:
- ✔ Download a printable PDF estimate
- ✔ Get 2026 US concrete material prices
- ✔ Save your project calculations instantly
- ✔ Access contractor cost-saving tips