Vertical Curve Calculator

Use the vertical curve calculator to calculate elevations of points on a vertical curve.

Curve typecrestA = -5%, K = 80

K value80length per per cent of grade change — codes set minimums by design speed

BVCstation 800, elevation 94

PVIstation 1,000, elevation 100

EVCstation 1,200, elevation 96

Middle ordinate2.5 fthow far the curve sits below or above the PVI: A L ÷ 8

High pointstation 1,040, elevation 97.6240 ft past the BVC

Elevation at station 1,00097.5200 ft past the BVC

Grade there0.5%

Offset from the incoming tangent-2.5 ft

Curve length400 ft

Grade change-5 percentage points

The formula

y = g₁x + (g₂ − g₁)x² ÷ (2L); the turning point is at x = −g₁L ÷ (g₂ − g₁)

A parabola, not an arc

Highway vertical curves are parabolic rather than circular, because a parabola gives a constant rate of grade change — the vehicle’s vertical acceleration stays steady, which is what makes the curve feel smooth.

The K value is the design shorthand: curve length divided by the algebraic grade change in per cent. Standards set minimum K values by design speed, because on a crest K controls sight distance over the hill, and in a sag it controls how far the headlights reach.

Note the middle ordinate is A L ÷ 8, so the curve passes exactly halfway between the PVI and the chord joining the tangent ends.