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Vertical Curve Design

Vertical Alignment Design on Tangent and Parabolic Curves Calculator

Calculate parabolic vertical-curve elevations, tangent points and K values from a chain of intersection points.

Chain PVIs together, one after another, and each interior PVI gets a parabolic vertical curve where the two grades meet. Step forward and back through the chain with the arrows to see G1, G2, PVC/PVT, K, A, the middle ordinate and the high/low point recalculate live — then query the finished elevation anywhere along the whole alignment.

by Shahid Pervaiz: pervaiz.shahid@gmail.com
Not saved to a file yet

PVI Chain

PVI 1 is the alignment start point and the last PVI is the end point — neither carries a curve. Every PVI in between gets a vertical curve of the length you set.
PVI 2 of 4 focused

Curve Data — PVI 2

Recalculates automatically as you edit or step through the PVI chain. The design K is checked against AASHTO's minimum for the design speed set above.

Elevations along the alignment

Works across the whole chain — straight tangents and curves alike.
Compute at

Results

Method & practical use

Understand the result.

Calculate parabolic vertical-curve elevations, tangent points and K values from a chain of intersection points.

How to use this tool

  1. Select the geometry or design case and confirm the displayed units.
  2. Replace sample inputs with the project values, then calculate or review the live result.
  3. Check the method, assumptions and output; save or print the calculation with its input record.

Units & method

Stations, elevations and lengths in m; grades in %; K in m/%.

For a symmetrical parabola, z(x) = zPVC + g1x + (g2 − g1)x²/(2L), with decimal grades. K = L/|g2 − g1| uses grades in percent. The page includes legacy SI K values; their full edition-specific table remains to be checked against the licensed source. They are not a compliance certificate.

Worked examples

Illustrative inputs for checking the method; these are not project records.

Crest parabola

PVC elevation 100 m, length 100 m, entering grade +2% and exiting grade -2%. At x = 50 m, z = 100 + (0.02)50 + (-0.04)50²/(2 × 100) = 100.500 m.

Sag parabola

PVC elevation 100 m, length 100 m, entering grade -2% and exiting grade +2%. At x = 50 m, z = 100 + (-0.02)50 + (0.04)50²/(2 × 100) = 99.500 m.

Frequently asked questions

What does this tool calculate or track?

Calculate parabolic vertical-curve elevations, tangent points and K values from a chain of intersection points.

Which units and assumptions should I use?

Stations, elevations and lengths in m; grades in %; K in m/%. For a symmetrical parabola, z(x) = zPVC + g1x + (g2 − g1)x²/(2L), with decimal grades. K = L/|g2 − g1| uses grades in percent. The page includes legacy SI K values; their full edition-specific table remains to be checked against the licensed source. They are not a compliance certificate.

Can I save or share the result?

Use the save, export and print controls shown in this workspace. Where CSV export is available, the exported data can be opened in a spreadsheet. Browser print can save a PDF.

Continue your workflow

How to use the Vertical Curve Design Calculator

Everything runs in your browser — nothing is uploaded. If you are new to the tool, follow these steps in order.

1

See what the tool can do

Press Load Sample Data. It loads a short example alignment: a start point, a crest curve, a sag curve and an end point. Then scroll down the page:

  • Road name, design speed and decimal places — the design speed sets the AASHTO minimum K used in the checks.
  • PVI Chain — one card per PVI with its station, elevation and curve length. PVI 1 is the start and the last PVI is the end; every PVI in between gets a vertical curve. Use + Add PVI and Remove last PVI to change the chain.
  • Curve Data — for the selected PVI: grades G1 and G2, A, L, K, PVC/PVT and the high or low point, checked against AASHTO minimum K. Step through the curves with « Prev PVI and Next PVI ». View Crest K Table and View Sag K Table show the AASHTO tables.
  • Elevations along the alignment — choose At any station, At fixed interval or For some range, then press Compute. Copy as CSV copies the results table for pasting into Excel, and Reset clears the results.

Load Sample Data replaces your PVI chain (it asks first). Save your own work first (step 4).

When you open the tool it already holds sample values, and a yellow bar says You are looking at sample data. The bar goes away as soon as you type your own values or load a saved project.

2

See how the data file looks

Press ↓ Export Table (.csv). It downloads the PVI chain as a CSV file that opens in Excel:

ColumnWhat to enterExample
PVISequence number (for reference only)2
RoleStart, Interior or End (for reference only)Interior
StationChainage as km+m or plain metres0+300 or 300
ElevationPVI elevation in metres103.500
Curve LVertical curve length in metres; use 0 for the start and end PVIs120
3

Enter your own data and import it

Replace the sample rows with your own PVIs, one row per PVI in increasing station order, keeping the heading row. Save it in Excel as CSV (Comma delimited), then press ↑ Import Table (.csv) and choose the file.

  • You need at least 3 PVIs: a start, at least one interior PVI and an end.
  • Station and Elevation columns are required. Curve L is optional (taken as 0 if missing), and the PVI and Role columns can be left out.
  • Columns are found by their heading names, so keep the words Station, Elevation and Curve in the headings.
  • Import replaces the whole PVI chain. Road name, design speed and decimal places are kept.

For a few PVIs it is quicker to type straight into the PVI cards on the page.

4

Save your project and open it later

💾 Save Project (.json) saves the road name, design speed, decimal places and the full PVI chain in one file, named like vertical_curve_<road name>.json. 📁 Load Project opens that file again, on any computer.

The note beside the Save button tells you whether you have unsaved changes or when you last saved. If you try to close or leave the page with unsaved changes, the browser asks you to confirm first.

The CSV holds only the PVI chain; the .json project file holds the whole project. Use it for backups and for sharing with colleagues. Don't edit it by hand.

This tool does not autosave. Save your project before closing the page.

5

Print, PDF and report

  • 🖨 Print / Save as PDF prints the PVI chain, the curve data with the AASHTO K check for every curve, and the elevations from your last Compute. To get a PDF, choose Save as PDF as the printer in the print dialog.
  • 📄 Generate Report opens a complete design report in a new tab: project, design criteria, method and formulas, PVI chain, detailed curve data, the profile drawing and the elevations table. It has its own Print / Save as PDF button. If nothing opens, allow pop-ups for this site.
6

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