Calculator Inputs
Example Data Table
| Units | Curve Type | G1 (%) | G2 (%) | L | Computed K |
|---|---|---|---|---|---|
| Metric (m) | Crest | -1.50 | +2.00 | 175 m | 50.0000 m/% |
| Imperial (ft) | Sag | +3.20 | -1.80 | 900 ft | 180.0000 ft/% |
Formula Used
Algebraic grade difference: A = G2 − G1 (in percent). Use |A| for the magnitude of grade change.
K value definition: K = L / |A|, where L is curve length and |A| is grade difference in percent.
Parabolic elevation equation: for a distance x from PVC, with grades in decimal form, Elev(x) = ElevPVC + g1·x + (A·x²)/(2·L).
Grade along the curve: g(x) = g1 + (A·x)/L. If g(x)=0 occurs within the curve, that station is a high or low point.
How to Use This Calculator
- Select Mode based on what you want to find (K, L, or grade change).
- Choose Units and Curve Type for reporting.
- Enter grades G1 and G2 in percent, plus either L or K as required.
- For a full station table, provide PVI Station and PVI Elevation, then set an interval.
- Press Calculate. Your results appear above the form.
- Use the download buttons to export results to CSV or PDF.
Note: This tool performs geometric calculations. Always confirm final design values against your local roadway standards.
Vertical Curve Article
Vertical Curve Purpose
Vertical curves connect two roadway grades with a smooth parabola. Designers compare alternatives using one number: K. This calculator finds K from length and grades, or finds length from a target K. It supports crest and sag curves in metric or imperial units, and displays results above the form.
Understanding K Value
K is defined as length divided by the absolute algebraic grade difference: K = L / |A|, where A = G2 − G1 in percent. Example: G1 = −1.50% and G2 = +2.00% gives |A| = 3.50. With L = 175 m, K = 175/3.50 = 50.00 m/%. Larger K means a gentler curve. Because K is expressed as length per percent, it scales cleanly across projects: doubling the grade change at the same K requires doubling the curve length too, in practice.
Choosing Calculation Mode
Pick a mode based on what you know. Use “Compute K” when you have G1, G2, and L. Use “Compute L” when a standard requires a minimum K. Use “Compute grade change” when K and L are fixed and you need the resulting G2; choose whether G2 is higher or lower than G1.
Reading Summary Outputs
The summary reports K, L, |A|, and the signed A value. If you enter PVI station and elevation, the tool also computes PVC and PVT stations and tangent elevations. This helps you verify where the curve starts and ends along the alignment and how it ties into adjacent tangents.
Building the Station Table
The station table uses Elev(x) = ElevPVC + g1·x + (A·x²)/(2·L), with grades in decimal form. It also reports the instantaneous grade g(x) = g1 + (A·x)/L. If g(x) becomes zero within the curve, that location is flagged as a high or low point.
Selecting an Interval
Choose an interval that matches your workflow, such as 10 m or 50 ft. Smaller intervals create a denser table for staking; larger intervals are fine for early sizing. If you omit PVI elevation, the table still lists x and grade, while elevations remain blank until elevations are provided.
Exporting for Review
Use exports to share results and keep a design record. The CSV includes inputs, key outputs, and the full table. The PDF provides a compact summary plus initial table rows. Always check final values against your local sight‑distance, comfort, and drainage requirements.
FAQs
What is the K value in a vertical curve?
K is the curve length divided by the absolute algebraic grade difference in percent: K = L/|G2−G1|. It describes how “flat” the parabola is for a given grade change.
When should I use crest versus sag?
Crest curves occur where the grade changes from uphill to downhill, while sag curves occur from downhill to uphill. Select the type for reporting and checks; the K computation itself uses grades and length.
Why does the calculator need grades in percent?
Roadway vertical grades are commonly specified as percent. Using percent keeps K in practical units like m/% or ft/%, which matches most design tables and standards.
Why are elevation values blank in the station table?
Elevation values require a reference elevation at PVC. Enter PVI station and PVI elevation so the tool can compute PVC elevation, then it can calculate Elev(x) along the curve.
How is the high or low point found?
The extreme point is where the instantaneous grade becomes zero. The calculator evaluates g(x) = g1 + (A·x)/L and flags the x location if it lies within 0 and L.
Can I export my results for a report?
Yes. Use Download CSV for full inputs, outputs, and the complete station table. Use Download PDF for a compact summary and a short preview of the station table.