Vertical Curve K Values — AASHTO Crest & Sag Reference
K is the rate of vertical curvature — the horizontal distance in feet required to produce a 1 percent change in grade. Curve length follows directly: L = K · A, where A is the algebraic difference in grades in percent. Design K is controlled by sight distance: headlight throw on sag curves, and the driver's line of sight over the crest on crest curves.
Crest Vertical Curves — Stopping Sight Distance
| Design speed (mph) | SSD (ft) | K (design) | Notes |
|---|---|---|---|
| 15 | 80 | 3 | local / parking |
| 20 | 115 | 7 | |
| 25 | 155 | 12 | residential collector |
| 30 | 200 | 19 | |
| 35 | 250 | 29 | |
| 40 | 305 | 44 | urban arterial |
| 45 | 360 | 61 | |
| 50 | 425 | 84 | |
| 55 | 495 | 114 | rural two-lane |
| 60 | 570 | 151 | |
| 65 | 645 | 193 | |
| 70 | 730 | 247 | freeway |
| 75 | 820 | 312 | |
| 80 | 910 | 384 |
Crest SSD basis: driver eye height h₁ = 3.50 ft, object height h₂ = 2.00 ft.
Sag Vertical Curves — Headlight Sight Distance
| Design speed (mph) | SSD (ft) | K (design) | Notes |
|---|---|---|---|
| 15 | 80 | 10 | |
| 20 | 115 | 17 | |
| 25 | 155 | 26 | |
| 30 | 200 | 37 | |
| 35 | 250 | 49 | |
| 40 | 305 | 64 | |
| 45 | 360 | 79 | |
| 50 | 425 | 96 | |
| 55 | 495 | 115 | |
| 60 | 570 | 136 | |
| 65 | 645 | 157 | |
| 70 | 730 | 181 | |
| 75 | 820 | 206 | |
| 80 | 910 | 231 |
Sag basis: headlight height 2.00 ft, upward divergence of the light beam 1°.
Governing Sight Distance Equations
| Case | Equation (US units, L and S in ft, A in percent) |
|---|---|
| Crest, S < L | L = A·S² / 2158 |
| Crest, S > L | L = 2S − 2158 / A |
| Sag (headlight), S < L | L = A·S² / (400 + 3.5·S) |
| Sag (headlight), S > L | L = 2S − (400 + 3.5·S) / A |
The 2158 constant is 100(√(2h₁) + √(2h₂))² evaluated at h₁ = 3.50 ft and h₂ = 2.00 ft. The S > L cases rarely govern on design-speed curves but do control short curves at small A.
Other Length Criteria to Check
| Criterion | Requirement | When it governs |
|---|---|---|
| Drainage (curbed sections) | K ≤ 167 | Flat sag or crest on curb-and-gutter — caps K so a 0.3% grade is reached within 50 ft of the apex and water keeps moving |
| Rider comfort (sag) | L = A·V² / 46.5 | Sag curves with overhead lighting where headlight criterion is relaxed; V in mph |
| General appearance | L ≥ 100 ft | Very small A, low speed |
| Minimum length | Lmin = 3V | AASHTO minimum; V in mph, L in ft |
High and Low Point Location
Elevation at any station x from the BVC: y = yBVC + g₁x/100 + A·x² / (200·L), with grades in percent and x, L in feet. The turning point exists on the curve only when g₁ and g₂ have opposite signs; otherwise the high or low point is at one of the tangent ends.
Sources: AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book), 7th ed., 2018 — crest and sag rate-of-vertical-curvature exhibits and the stopping sight distance table. Values are the rounded design K values; confirm against the edition your agency has adopted, and against any state DOT supplement, before use on a project.
Related cheat sheets and tools
Designing the profile is half the job — for the horizontal side see horizontal curve and superelevation. Once grades are set, the curb-and-gutter flow that the K ≤ 167 drainage cap protects is sized from Manning's n and rational method C values. For the full roadway drainage network — inlets, laterals, and outfall tied back to the watershed — see HydroComplete, the SaaS sister product to PE-Calc.