How to Use Vertical Curve Calculator
The Vertical Curve Calculator computes all key alignment points for a parabolic vertical curve.
- Enter the PVI Data — Type the PVI station (chainages such as 2+400 or 2400 m), the PVI elevation, the incoming grade g1 (%), and the outgoing grade g2 (%).
- Enter the Curve Length L — Input the total parabolic curve length in metres or feet. The Vertical Curve Calculator derives EPVC and EPVT positions automatically.
- Read the Key Points — The result panel shows EPVC station and elevation, EPVT station and elevation, K value, and the high/low point (if one exists within the curve).
- Generate an Elevation Table — Enter a station interval to produce a table of road elevations at regular points along the curve for earthwork volume calculations or stakeout.
Formula & Theory — Vertical Curve Calculator
The Vertical Curve Calculator applies the standard equal-tangent parabola equations:
A = g2 − g1 (algebraic grade difference, %)
K = L / |A|
Station_EPVC = Station_PVI − L/2
Elevation_EPVC = Elevation_PVI − (g1/100) × (L/2)
Station_EPVT = Station_PVI + L/2
Elevation_EPVT = Elevation_PVI + (g2/100) × (L/2)
Elevation at station x from EPVC:
y = y_EPVC + (g1/100) × x + A / (200 × L) × x²
High/low point (when g1 and g2 have opposite signs):
x_hl = −g1 × L / A| Symbol | Meaning | Unit |
|---|---|---|
| g1, g2 | Entering and leaving grades | % |
| A | Algebraic grade difference g2−g1 | % |
| L | Curve length | m or ft |
| K | Rate of grade change | m/% or ft/% |
| PVI | Point of vertical intersection | — |
| EPVC | Entry point of vertical curve | — |
| EPVT | Exit point of vertical curve | — |
AASHTO Minimum K Values (Stopping Sight Distance)
| Design speed | Crest K min | Sag K min |
|---|---|---|
| 50 km/h | 7 | 9 |
| 80 km/h | 26 | 23 |
| 100 km/h | 51 | 37 |
| 120 km/h | 99 | 54 |
Use Cases for Vertical Curve Calculator
The Vertical Curve Calculator supports civil engineers, students, and surveyors:
- Highway and road design — Preliminary curve layout and grade review for new or reconstructed roads; check K values against AASHTO or local design standards.
- Civil engineering coursework — Students work through vertical alignment design problems step by step and verify hand calculations instantly.
- Municipal road assessment — Check existing road curves against current design standards during pavement rehabilitation planning.
- Land development grading — Design smooth driveway and parking-lot grade transitions that meet accessibility requirements.
- Railway track geometry — Vertical curve design for rail alignments uses the same parabola equations with different K-value limits.
- Cross-checking manual calculations — Surveyors and designers verify elevations and stakeout data before field work.