**Known values: **Curvature radius H^{~}R (positive for concave, negative for convex vertical curve), grade in **S _{1} **and grade out

**S**(positive for ascending , negative for descending slopes), elevation of start point A of vertical curve

_{2}**H**

_{A}**Solution:** Elevation of point K at a distance **x **from curve start point A **y _{K}**, grade value at point K

**S**

_{K}The vertical distance of point K from point A is calculated:

**y _{K} = (S_{1}/100)*x + x^{2}/(2*H)**

The elevation of point K is calculated:

**H _{K} = H_{A} + y_{K}**

Grade **S _{K}** at point K calculation:

**S _{K} = S_{1} + (x/H)*100**

Where:

S_{1} = grade in value at start point A of vertical curve

x = horizontal distance of point K from point A

H = curvature radius at peak of vertical curve (where grade s = 0%)

H_{A} = elevation of start point A of vertical curve