Advanced Vertical Curve Calculator
Enter roadway grades, curve length, PVI station, and PVI elevation. Results appear above the form after calculation.
Example Data Table
| Input | Example Value | Meaning |
|---|---|---|
| G1 | 2.5% | Incoming tangent grade |
| G2 | -1.5% | Outgoing tangent grade |
| L | 600 ft | Total vertical curve length |
| PVI Station | 15+00 | Point of vertical intersection |
| PVI Elevation | 248.75 ft | Elevation at tangent intersection |
Formula Used
The calculator uses the parabolic vertical curve equation. Grades are converted from percent to decimal values.
BVC Station = PVI Station - L / 2
EVC Station = PVI Station + L / 2
BVC Elevation = PVI Elevation - G1 × L / 2
EVC Elevation = PVI Elevation + G2 × L / 2
For any distance x from BVC:
Elevation = BVC Elevation + G1x + ((G2 - G1) / (2L))x²
The grade at any point is:
Grade at x = G1 + ((G2 - G1) / L)x.
The K value is:
K = L / |G2 - G1|, where grade difference is in percent.
How to Use This Calculator
- Select feet or meters for the project units.
- Enter incoming grade G1 and outgoing grade G2 as percentages.
- Enter the total curve length, PVI station, and PVI elevation.
- Add a station interval for the generated elevation table.
- Enter a custom station if you need one specific point checked.
- Add a required K value if you want a design check.
- Press the calculate button to view curve results.
- Use CSV or PDF buttons to save the report.
Vertical Curve Planning Guide
What a Vertical Curve Does
A vertical curve connects two roadway grades. It creates a smooth change between them. This improves comfort, visibility, and drainage. The curve may be a crest curve. It may also be a sag curve. A crest curve rises and then falls. A sag curve falls and then rises. Both types use the same basic parabolic model.
Why Accurate Inputs Matter
Small grade errors can change field elevations. A wrong station can also shift the whole curve. The PVI station marks the tangent intersection. The BVC starts the curve. The EVC ends the curve. The curve length controls how quickly the grade changes. A longer curve gives a softer transition. A shorter curve gives a sharper transition.
Understanding the Results
The calculated table shows each station along the curve. It includes distance from BVC, curve elevation, tangent elevation, offset, and grade. The offset shows the difference between the tangent and curve. The calculator also finds the high point or low point when it lies inside the curve. This is useful for drainage review.
Using K Value Checks
The K value is the curve length divided by the absolute grade difference. Designers use it to compare curve smoothness. A higher K value means a flatter rate of grade change. The optional required K input helps compare a project target with the calculated curve. It gives a quick pass or review message.
Exporting the Report
The export tools help with records and review. CSV is useful for spreadsheets. PDF is useful for sharing. Keep the report with design notes. Check all final values against local standards before construction.
Frequently Asked Questions
What is a vertical curve?
A vertical curve is a smooth parabolic transition between two roadway grades. It helps vehicles move comfortably between slopes.
What does PVI mean?
PVI means point of vertical intersection. It is where the incoming and outgoing tangent grades meet.
What are BVC and EVC?
BVC is the beginning of the vertical curve. EVC is the end of the vertical curve.
What is G1?
G1 is the incoming tangent grade before the curve begins. Enter it as a percentage.
What is G2?
G2 is the outgoing tangent grade after the curve ends. Enter it as a percentage.
What is K value?
K value equals curve length divided by absolute grade difference. It describes the rate of vertical curvature.
Can this calculator find the high point?
Yes. It finds the high point or low point when the grade becomes zero inside the curve.
Can I export the curve table?
Yes. You can download the calculated table as CSV or PDF for records and review.