Vertical Curve Design Calculator

Plan vertical profiles using reliable roadway design inputs. Review stations, grades, elevations, and curvature outputs. Generate practical summaries for surveying, drafting, checking, and reporting.

Enter Design Inputs

Example Data Table

This sample illustrates a crest-curve setup using typical roadway design values.

Input Item Example Value
Curve typeCrest
Entering grade, g1+2.50%
Leaving grade, g2-1.20%
Curve length, L180 m
PVI station1+250.00
PVI elevation154.80 m
Station interval20 m
Required sight distance120 m

Formula Used

Algebraic grade difference
A = g2 − g1
PVC and PVT stations
PVC = PVI − L/2
PVT = PVI + L/2
PVC elevation
EPVC = EPVI − (g1/100)(L/2)
Elevation at distance x from PVC
E(x) = EPVC + (g1/100)x + [(A/100)x²]/(2L)
Grade at any point
g(x) = g1 + A(x/L)
Offset from initial tangent
Offset = [(A/100)x²]/(2L)
High or low point location
x = −g1L/A, when A ≠ 0 and 0 ≤ x ≤ L
K-value
K = L / |A|
Crest stopping sight distance check
For shorter curves: L = AS² / [200(√h1 + √h2)²]
For longer curves: L = 2S − [200(√h1 + √h2)²]/A
Sag headlight sight distance check
For shorter curves: L = AS² / [200(h + S tan φ)]
For longer curves: L = 2S − [200(h + S tan φ)]/A

Grades are entered in percent, lengths in meters, and elevations in meters. The page uses a symmetric parabolic vertical curve model.

How to Use This Calculator

  1. Choose whether you want a crest or sag design check.
  2. Enter the incoming and outgoing grades in percent.
  3. Provide the total vertical curve length.
  4. Enter the PVI station and PVI elevation.
  5. Choose the station interval for generated output rows.
  6. Optionally enter a required sight distance for checking adequacy.
  7. Adjust eye, object, headlight, and beam-angle values if needed.
  8. Press the calculate button to display the summary above the form.
  9. Use the CSV or PDF buttons to export the computed report.

Frequently Asked Questions

1. What is a vertical curve in roadway design?

A vertical curve smoothly connects two different roadway grades. It improves ride quality, visibility, drainage behavior, and overall geometric continuity along the alignment.

2. What is the difference between crest and sag curves?

A crest curve bends downward and usually controls daytime stopping sight distance. A sag curve bends upward and often depends on nighttime headlight sight distance.

3. Why is the algebraic grade difference important?

The algebraic grade difference defines curvature severity. Larger values create sharper profile changes and usually require longer curves for comfort and visibility.

4. What does the K-value represent?

The K-value is the curve length divided by the absolute grade difference. Engineers use it to compare vertical curve smoothness and design quality quickly.

5. Why might the selected type disagree with the result?

The actual curve shape comes from the signs of g1 and g2. If those grades form the opposite shape, the calculator follows the numeric inputs.

6. How is the highest or lowest point found?

The turning point occurs where the grade becomes zero. If that zero-grade location falls inside the curve length, the calculator reports its station and elevation.

7. Can this tool help with sight distance checks?

Yes. Enter a required sight distance and the calculator estimates a minimum curve length using common crest or sag design relationships.

8. Are the exported CSV and PDF files useful for reports?

Yes. The exports include the summary values and generated station table, making them practical for design review, documentation, and quick sharing.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.