1. Nomenclature
A vertical curve is used to provide a smooth transition between two different grade lines, Figure B1.

Figure B1 Adding a Vertical Curve 
The parts of the curve, Figure B2, are:
Figure B2 Curve Parts 
PVI  Point of Vertical Intersection (aka PI) 
BVC  Begin Vertical Curve (aka, BC, PVC, PC) 
EVC  End Vertical Curve (aka EC, PVT, PT) 
L  Curve Length 
Distances, including the curve length, are horizontal, not along the grade lines or curve.
An equal tangent vertical curve is used. This places BVC and EVC equidistant from the PVI, Figure B3.
Figure B3 Equal Tangent Vertical Curve 
The curve is tangent to the grade lines at both ends to provide a smooth transition between the grade lines and curve.
The stations and elevations of the BVC and EVC are determined from Equationa B1 and B2:
Equation B1  Equation B2 
Because grade ratio and percent differ by a factor of 100 as do distances in feet or stations, care must be taken to use the correct form of each in Equations B1 and B2. If g is in %, then L must be in stations, if g is a ratio, then L is in feet.