How do I find the high point?

Distance from the start = L × |g₁| ÷ |A|. At that point the grade is zero and the curve turns.

If the exiting grade is lower than the entering grade, it is a crest; if higher, a sag. The height of the turning point differs between them.

Vertical Curve Calculator

By Zencalcy Editorial TeamLast reviewed September 2026About us

Road profiles join grades with a parabola so the transition is smooth. The K value — curve length divided by the algebraic grade change — sets the shape, and the high or low point sits where the grade crosses zero.

Vertical Curve Calculator

Elevations and high/low point on a vertical curve.

Configuration

Entering grade (%)
Exiting grade (%)
Curve length (ft)
Start station (ft)
Start elevation (ft)

Enter values and calculate

How to use this calculator

Enter the entering and exiting grades in percent.
Enter the curve length and the starting station and elevation.
Read K, the turning point and the elevation at the end of the curve.

Formula

K = L ÷ |A| turning point = L × |g₁| ÷ |A| elevation = E₀ + g₁x + (A ÷ 2L) x²

A is the algebraic difference between exiting and entering grades, keeping signs. Stations and elevations are in the same units as the grades are applied. K in feet per percent is the value used in design tables for stopping sight distance.

Symbol	Meaning
g₁, g₂	Entering and exiting grades, percent.
L	Curve length.
K	Rate of vertical curvature.

Worked example

Example: +3% to −2% over 500 ft starting at 100.00

A is −5, so K = 100 and the high point is 300 ft into the curve at elevation 104.50.

Continue with the Angle Cut Calculator, Angle of Depression Calculator, Bolt Circle Calculator, or the Bowl Segment Calculator — or browse more layout & geometry and all construction calculators.

Vertical Curve Calculator FAQ

Length of curve per percent of grade change. It is the design parameter for sight distance: a larger K gives a gentler curve.

Sources & methodology

Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.

Reference material used to build and check this calculator: