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Parabolic Vertical Curve Calculator — result sheet
Estimate grade change, K value, grade, and elevation at a station on a simple parabolic vertical alignment.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A = g₂−g₁ in percentage points; K = L/|A|; g(x) = g₁ + (A/100)x/L; elevation y(x) = y₀ + (g₁/100)x + (A/100)x²/(2L).
The model treats the alignment as a parabolic vertical curve between two entered grades. It reports a point on that ideal curve and a conventional K-style length-per-percent change; it is not a roadway design approval or sight-distance calculation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Elevation at curve start — m; minimum -1000000; maximum 1000000
- Curve length — m; minimum 1.0E-6; maximum 1000000
- Initial grade — %; minimum -1000; maximum 1000
- Final grade — %; minimum -1000; maximum 1000
- Station from curve start — m; minimum 0; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Elevation at curve start | 100 |
| Curve length | 120 |
| Initial grade | -2 |
| Final grade | 3 |
| Station from curve start | 60 |
Grade change = 5 percentage points, K = 24 m/%, station grade = 0.5%, and station elevation = 99.55 m.
Assumptions and limits
- Grades are signed percentages and the entered station lies between the curve start and end.
- The vertical alignment follows one symmetric parabolic grade transition over the entered length.
- Sight distance, design speed, drainage, superelevation, cross section, earthwork, surveying uncertainty, and jurisdictional standards are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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