How this calculator works
A quadratic profile changes grade at a constant rate along horizontal distance. The PVI is the intersection of the two tangents and is generally off the curve. The table replaces a plot and always includes both endpoints. This geometry does not check stopping sight distance or drainage.
Formula
z(x) = zBVC + g1 x + (g2-g1)x^2/(2L), with grades as decimal ratios; grade(x) = g1 + (g2-g1)x/L; extreme x = -g1 L/(g2-g1).
Worked example
For BVC elevation 100 m, length 100 m and grades +2% to -2%, the midpoint is 100.5 m high, while the tangent PVI elevation is 101 m. EVC returns to 100 m.
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Frequently asked questions
What does BVC mean?
Beginning of vertical curve. EVC is its end, and PVI is the intersection of the entry and exit tangents.
Can I use unequal tangent lengths?
No. This page assumes equal tangent lengths of L/2 on each side of the PVI.
Why is no high point shown?
An interior extreme exists only when the grade crosses zero within the curve.