Vertical Curve Calculator
Evaluate a simple parabolic vertical curve from beginning elevation, entering and leaving grades, and horizontal curve length in metres or feet.
Evaluate the elevation and grade along a simple parabolic vertical curve joining two straight profile grades. Supply the beginning elevation and horizontal curve length, then inspect a selected offset and a table of intermediate points.
How to use this tool
- Choose one common metre or foot unit for stationing, elevation and length.
- Enter the beginning station, beginning elevation and positive horizontal curve length.
- Enter signed grades in percent, positive uphill in the direction of increasing station.
- Choose an offset within the curve and review elevation, local grade and any zero-grade point.
Formula
z(x) = z₀ + g₁x/100 + (g₂ − g₁)x²/(200L)
Local grade is g₁ + (g₂ − g₁)x/L. Grades are percentage numbers, while x and L are horizontal distances. K = L / |g₂ − g₁| has units of distance per percentage point. The zero-grade point, when it lies within the curve, is at x = −g₁L/(g₂ − g₁).
Example
Start at 100 m elevation, with L = 200 m, entering grade +2% and leaving grade −2%. At x = 100 m the elevation is 101 m and grade is zero. The curve ends at 100 m elevation, and K is 50 m/%.
Frequently asked questions
Is a zero-grade point always inside the curve?
No. When grades retain the same nonzero sign, the profile can remain monotonic. The tool only reports a zero-grade location when it falls inside the entered interval.
What happens when both grades are equal?
The quadratic term vanishes and the profile is a straight tangent. K has a zero denominator, so the tool marks it undefined instead of reporting a finite curve value.
Can the K value approve a road profile?
No. It describes this geometry. Sight distance, headlights, comfort, drainage and local minimum-length criteria require additional inputs and a separate design check.
Sources
Last updated: 2026-10-30