Vertical Curve Calculator

Civil Engineering & AASHTO Highway Geometric Standards

The AASHTO Green Book governs vertical alignment design using equal-tangent parabolic curves.

Primary Parabolic Curve Formulas

• Algebraic Difference in Grades: A = |g_2 - g_1| [\%]

• Rate of Vertical Curvature (K): K = (L) / (A)

• PVC (BVC) Station & Elevation:

PVC_sta = PVI_sta - (L) / (2), PVC_elev = PVI_elev - ((g_1) / (100))((L) / (2))

• PVT (EVC) Station & Elevation:

PVT_sta = PVI_sta + (L) / (2), PVT_elev = PVI_elev + ((g_2) / (100))((L) / (2))

• High / Low Turning Point Distance from PVC:

x = (g_1 × L) / (g_1 - g_2)

• Parabolic Elevation Equation at distance x from PVC:

y(x) = PVC_elev + ((g_1) / (100))x + (g_2 - g_1) / (200 L) x^2

How to Use This Calculator

Enter your Initial Grade (g₁) % (e.g. 3.0 in %), Final Grade (g₂) % (e.g. -2.0 in %), Vertical Curve Length (L) (e.g. 600.0 in ft), PVI Station (Feet, e.g. 1000 for 10+00) (e.g. 1000.0 in ft), and PVI Elevation (Feet) (e.g. 100.0 in ft). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Vertical Curve Calculator

Input variables:

initialGradeG1Percent — Initial Grade (g₁) %

finalGradeG2Percent — Final Grade (g₂) %

curveLengthFeet — Vertical Curve Length (L)

pviStation — PVI Station (Feet, e.g. 1000 for 10+00)

pviElevationFeet — PVI Elevation (Feet)

Computed outputs:

rateOfVerticalCurvatureK — Rate of Curvature (K-Value)

algebraicDifferencePercent — Algebraic Grade Difference (A)

pvcStationAndElevation — PVC / BVC (Sta & Elev)

pvtStationAndElevation — PVT / EVC (Sta & Elev)

turningPointStationAndElevation — High / Low Turning Point (Sta & Elev)

Mathematical relationships extracted from calculation logic:

a = Math.abs(g2 - g1)

pvcSta = pviSta - (l / 2)

pvcElev = pviElev - ((g1 / 100) * (l / 2))

pvtSta = pviSta + (l / 2)

pvtElev = pviElev + ((g2 / 100) * (l / 2))

sta100 = Math.floor(s / 100)

xTurn = safeDiv(g1 * l, g1 - g2)

turnSta = pvcSta + xTurn

turnElev = pvcElev + ((g1 / 100) xTurn) + safeDiv((g2 - g1) Math.pow(xTurn, 2), 200 * l)

Standard: NIST / ISO mathematical definitions

Worked Example

A 600-foot vertical crest curve transitioning from a +3% climb to a -2% descent has a K-value of 120, peaking at Station 10+60 at an elevation of 96.40 feet.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.