Vertical Curve Calculator
Find the K-value of a vertical highway curve.
The K-value defines the rate of vertical curvature for road design.
How the Math Works
The Vertical Curve Calculator uses the formula K = L ÷ |G₂ − G₁| to determine the K-value of a vertical highway curve. Here, L represents the length of the curve, while G₁ and G₂ are the grades (slopes) at the beginning and end of the curve, respectively. The absolute value ensures the difference in grades is positive, which is essential for accurate curvature measurement. This K-value is a critical parameter that quantifies the rate of vertical curvature, helping engineers design safe and comfortable road transitions.
Practical Applications
To apply this calculation, first measure or obtain the curve length (L) and the entering and exiting grades (G₁ and G₂) from road design specifications. Subtract G₁ from G₂ and take the absolute value of the result. Then divide the curve length by this grade difference to find the K-value. For example, if a curve is 200 meters long with grades of 3% and -2%, the K-value would be 200 divided by |(-2) - 3|, resulting in K = 40. This value helps determine if the curve meets design standards for vehicle stability and passenger comfort.
Day-to-Day Use
While most drivers may not calculate K-values daily, this formula directly impacts their daily commute experience. Road engineers use these calculations to design smoother highway transitions between uphill and downhill sections, reducing the need for sudden braking or acceleration. Properly calculated vertical curves prevent dangerous sight line obstructions and ensure comfortable rides, making your daily drive safer and more predictable. When you notice a gradual, well-designed hill crest or dip on the highway, that's a direct result of K-value calculations ensuring your safety and comfort.
Worked example
3% to −2% over 500 ft → K 100.
FAQ
Design speed?
Minimum K increases with design speed — check highway standards for your jurisdiction.