Free calculator

Vertical Curve — High/Low Point & Elevations

Enter the approach and departure grades, curve length, and PVC station and elevation. The calculator returns the high or low point, the PVI and PVT, the K value, and the elevation at any station you name. Stations are entered in feet (station 10+00 = 1,000 ft); outputs are shown both ways.

y(x) = y_PVC + g₁x + (g₂ − g₁) x² / (2L) x_hp = g₁L / (g₁ − g₂) K = L / A

x	distance from the PVC, ft
g₁, g₂	approach / departure grades as decimals (enter % below; the tool converts)
A	\|g₁ − g₂\| in percent
K	rate of vertical curvature, ft per 1% grade change

Approach grade g₁ (%) Departure grade g₂ (%) Curve length L (ft) PVC station (ft) PVC elevation (ft) Station of interest (ft, optional)

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.

Worked example: crest curve high point and elevations

g₁ = +3%, g₂ = −2%, L = 600 ft. PVC at station 10+00 (1,000 ft), elevation 100.00 ft.

A = |3 − (−2)| = 5%; K = L/A = 600/5 = 120 ft per 1% grade change
High point: x_hp = 0.03 × 600/(0.03 + 0.02) = 360 ft → station 13+60, inside the curve
Elevation there: y = 100.00 + 0.03(360) − 0.05(360)²/(2 × 600) = 100.00 + 10.80 − 5.40 = 105.40 ft
Elevation at station 12+00 (x = 200 ft): y = 100.00 + 6.00 − 0.05 × 40,000/1,200 = 104.33 ft

Exam tip: grades enter the curve equation as decimals (3% = 0.03), but A is the grade change in percent — mixing the two is the classic vertical-curve miss.

Go deeper

Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.