Calculating...
Enter grades and a length, K-value, or design speed to calculate the vertical curve K-value.
K-Value Visual Guide
K-value is the curve length divided by the absolute percent grade change. Higher K means a flatter, more gradual vertical curve.
What Is K-Value in a Vertical Curve?
The K-value of a vertical curve is the horizontal curve length required for each 1 percent change in grade. It is written as K = L / |A|, where L is curve length and A is the algebraic difference between the departure grade and approach grade. A higher K-value produces a more gradual curve, which usually improves driver comfort, sight distance, and visual smoothness.
This calculator focuses on K-value rather than full vertical alignment design. It is useful when a plan sheet gives a curve length and grades, when a reviewer needs to check a minimum K requirement, or when a designer wants a quick AASHTO-style reference length for a sag or crest curve.
Sag vs Crest Vertical Curve K-Values
A crest curve occurs when the grade decreases through the curve, such as a road rising and then falling. A sag curve occurs when the grade increases, such as a road descending into a low point and climbing out. The calculator classifies the curve from A = G2 - G1: negative values are crest curves, positive values are sag curves, and near-zero values are treated as tangent grade with no meaningful K-value.
Crest and sag curves use different design controls. Crest curves are commonly controlled by stopping sight distance over the top of the curve. Sag curves are commonly controlled by headlight sight distance, drainage, comfort, and undercrossing clearance. That is why design K tables have separate crest and sag columns.
How to Calculate K from Curve Length and Grades
To calculate K from a known curve length, first compute the algebraic grade difference:
A = G2 - G1 |A| = abs(A) K = L / |A|For example, if G1 = +3.00%, G2 = -1.00%, and L = 200 m, then A = -4.00%, |A| = 4.00%, and K = 50 m/%. The negative sign tells you the curve is a crest curve; the K-value itself uses the absolute grade change.
How to Calculate Required Curve Length from K
If a standard, agency table, or design note gives a target K-value, the required curve length is:
L = K x |A|For a 4 percent grade break and a required K of 40 m/%, the curve length is 160 m. In US customary work, the same calculation applies with K in ft/% and length in feet. Do not mix metric K-values with feet-based stationing unless the value has been converted.
AASHTO-Style K-Value Checks by Design Speed
The calculator includes an AASHTO-style design-speed check. It converts mph to km/h when needed, looks up the reference K for crest or sag curves, interpolates between table rows, and compares the provided K against the reference value. The built-in table is intended for quick checks and education; final design should always follow the governing edition and local road authority.
| Speed (km/h) | Crest K (m/%) | Sag K (m/%) | SSD (m) |
|---|---|---|---|
| 50 | 7 | 13 | 65 |
| 60 | 11 | 18 | 85 |
| 70 | 17 | 23 | 105 |
| 80 | 26 | 30 | 130 |
| 90 | 39 | 38 | 160 |
| 100 | 53 | 45 | 185 |
| 110 | 74 | 55 | 220 |
| 120 | 95 | 63 | 250 |
When K-Value Alone Is Not Enough
K-value is a compact and useful design parameter, but it is not the whole vertical alignment. A complete roadway design may also require PVC/PVI/PVT stationing, elevations, drainage checks, clearance checks, comfort criteria, coordination with horizontal alignment, and full stopping sight distance verification. Use the full Vertical Curve Calculator when you need more geometry than a focused K-value check.
Formula Reference
| Output | Formula | Notes |
|---|---|---|
| Algebraic grade difference | A = G2 - G1 | Signed percent |
| Absolute grade difference | |A| = abs(G2 - G1) | Used in K and length |
| K-value | K = L / |A| | Length per 1% grade change |
| Required length | L = K x |A| | Same length unit as K |
| PVC station | PVC = PVI - L/2 | Equal-tangent curve |
| PVT station | PVT = PVI + L/2 | Equal-tangent curve |
| High/low point offset | x = -G1 x L / A | Valid only when 0 < x < L |
Related Roadway and Surveying Calculators
- Vertical Curve Calculator for full PVC/PVI/PVT geometry, high/low point, and SSD checks.
- Horizontal Curve Calculator for tangent length, curve length, and superelevation checks.
- Slope Calculator for percent grade, angle, rise, and run.
- Road Grade Calculator for roadway grade and elevation checks.
- Superelevation Calculator for curve banking and side-friction checks.
- Distance & Bearing Calculator for coordinate-pair distance and bearing checks.
Frequently Asked Questions
What does K mean in vertical curve design?
K is the curve length divided by the absolute percent grade change. It expresses how many meters or feet of curve are provided per 1 percent change in grade.
How do you calculate K-value for a crest curve?
Use K = L / |G2 - G1|. The curve is a crest curve when G2 - G1 is negative, meaning the grade decreases through the vertical curve.
How do you calculate K-value for a sag curve?
The formula is the same: K = L / |G2 - G1|. The curve is a sag curve when G2 - G1 is positive, meaning the grade increases through the curve.
What is the formula for vertical curve length?
When K and grade difference are known, use L = K x |A|. Make sure K and L use the same length unit.
Why are sag and crest K-values different?
Crest curves are usually controlled by sight distance over the curve, while sag curves are often controlled by headlight sight distance and comfort. Different controls produce different K requirements.
Does a higher K-value mean a smoother curve?
Usually yes. A higher K spreads the grade change over a longer distance, creating a flatter and more gradual vertical curve.