Work out vertical curve elevation instantly with clear inputs, formula shown and shareable results.
A parabolic vertical curve changes grade at a constant rate, so elevation relative to the curve start is g1 x + (g2 - g1) x² / (2L). The offset term is the departure from the incoming tangent. The high or low point occurs where the grade reaches zero, at -g1 L / (g2 - g1) from the start, and the K value, length per percent of grade change, is how curves are specified in design standards.
Parabolic curve
Elevation change = g1 x + (g2 - g1) x² / (2 L)
Turning point
x = -g1 L / (g2 - g1); K = L / |algebraic grade difference|
Preliminary estimate only. Vertical alignment design must satisfy the sight distance, comfort and drainage criteria of the applicable highway design standard.
Elevation change = g1 x + (g2 - g1) x² / (2 L). A parabolic vertical curve changes grade at a constant rate, so elevation relative to the curve start is g1 x + (g2 - g1) x² / (2L).
A parabola gives a constant rate of grade change, which produces constant vertical acceleration and is far easier to set out by offsets from the tangent.
This calculator takes 4 inputs: Incoming grade, Outgoing grade, Curve length, Distance from the start of the curve. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.