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Vertical Curve Elevation Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Equal-tangent parabolic vertical curve. Last verified 15 June 2026.

The vertical curve elevation calculator computes elevations at specified stations along a parabolic vertical curve used in road design. Enter the PVI (Point of Vertical Intersection) station and elevation, the incoming grade g1 and outgoing grade g2 as percentages, the total curve length L, and a station distance from the BVC where you want the elevation. The calculator returns the BVC, EVC, and intermediate elevations using the standard equal-tangent parabolic curve formula. This is the foundational calculation in highway vertical alignment design.

Elevation at Point of Vertical Intersection
Positive = uphill entering curve. e.g. 3 for +3%
Negative = downhill leaving curve. e.g. -2 for -2%
Total parabolic curve length (same unit as elevations)
0 = BVC, L = EVC, values between give intermediate elevations
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Vertical curve parabola formula

BVC elevation = PVI elevation - g1 * (L/2) / 100
EVC elevation = PVI elevation + g2 * (L/2) / 100
y(x) = BVC elevation + (g1/100)*x + (g2-g1)/(200*L) * x^2
High/low point: x = -g1*L / (g2-g1)

Grades g1 and g2 are in percent. L is curve length. x is the distance from BVC. The formula applies to equal-tangent parabolic vertical curves.

Curve type identification

  • Crest curve (sag in profile): g1 positive and g2 negative (or g2 less than g1). Sight distance controls minimum length.
  • Sag curve (valley in profile): g1 negative and g2 positive (or g2 greater than g1). Headlight distance and rider comfort control minimum length.
  • The algebraic difference A = |g2 - g1| in percent governs how sharp the curve feels.
  • K value = L / A gives curve sharpness: K = 44 is typical minimum for 60 mph design speed on a crest (AASHTO).

Vertical curve elevation calculator: frequently asked questions

What is a vertical curve in road design?

A vertical curve is a parabolic transition connecting two tangent grades on a road profile. It provides a smooth change in grade for driver comfort and sight distance. The most common vertical curves in highway design are equal-tangent parabolic curves.

What is a PVI in vertical curve design?

PVI stands for Point of Vertical Intersection, the point where the two tangent grades intersect if extended. The vertical curve begins at the BVC (Beginning of Vertical Curve), passes through the PVI, and ends at the EVC (End of Vertical Curve).

What is the rate of grade change (r)?

The rate of grade change r = (g2 - g1) / L, where g1 and g2 are the incoming and outgoing grades in percent and L is the curve length in feet (or meters). It determines how rapidly the slope changes along the curve.

How do I find the high or low point of a vertical curve?

The high or low point occurs where the grade is zero. Distance from BVC to high/low point: x = -g1 / r = -g1 * L / (g2 - g1). This is only on the curve if x is between 0 and L. The elevation at the high/low point: y = BVC elevation + g1*x + r*x^2/2.

What is sight distance and how does it relate to curve length?

Sight distance is the length of road visible to a driver, which must exceed the required stopping or passing sight distance. For crest vertical curves (going over a hill), the minimum curve length is determined by sight distance requirements in AASHTO Green Book standards.

Official sources

Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.