Calculator Inputs
Use either known curve length or known K value. The calculator will solve the missing design value.
Example Data Table
| Case | Curve Type | g1 (%) | g2 (%) | L (m) | A (%) | K (m/%) |
|---|---|---|---|---|---|---|
| Example 1 | Crest | 2.500 | -1.500 | 120.000 | 4.000 | 30.000 |
| Example 2 | Sag | -3.000 | 1.000 | 160.000 | 4.000 | 40.000 |
| Example 3 | Crest | 1.800 | -0.600 | 96.000 | 2.400 | 40.000 |
Formula Used
A = |g2 - g1|
K = L / A
L = K × A
BVC station = PVI station - L / 2
EVC station = PVI station + L / 2
Elevation(x) = Elevation at BVC + (g1 / 100) × x + [(g2 - g1) × x²] / (200 × L)
In this calculator, grades are entered in percent, such as 2.5 or -1.5. The K value expresses how many length units are provided per one percent of grade change. Larger K values produce flatter, smoother vertical curves.
How to Use This Calculator
- Select whether you want to solve for K from a known length, or solve for length from a known K value.
- Choose the curve type, then enter the entering and exiting grades.
- Enter either the curve length or the K value, depending on your selected mode.
- Provide the PVI station and PVI elevation so the calculator can generate stations and profile elevations.
- Set a step interval to control how many profile points are listed in the data table and graph.
- Press Calculate to show the result above the form, create the Plotly graph, and generate export options.
Frequently Asked Questions
1) What is the K value in a vertical curve?
The K value is the curve length divided by the algebraic grade difference. It shows how quickly the roadway changes grade. A larger K value means a flatter and smoother vertical curve.
2) Why is algebraic grade difference important?
Algebraic grade difference measures the total change between the entering and exiting grades. It is required because K depends directly on that difference, not only on the curve length.
3) Can this calculator be used for crest and sag curves?
Yes. The same K formula works for both crest and sag curves. The sign and direction of the grades determine whether the turning point becomes a high point or a low point.
4) What happens if both grades are the same?
If the entering and exiting grades are equal, the algebraic grade difference becomes zero. In that case, there is no meaningful vertical curve rate change, so the K value cannot be computed.
5) What does the plotted graph show?
The graph shows the vertical curve profile together with the two tangent lines. This makes it easier to understand the curve shape, the grade transition, and the effect of a larger or smaller K value.
6) Why are PVI station and elevation included?
Those values let the calculator locate the BVC and EVC stations and compute actual curve elevations. Without them, you could find K, but you could not build a profile table.
7) Is this calculator useful for roadway design checks?
Yes. It is useful for quick design checks, concept comparisons, and educational work. Final design should still follow the governing standards, visibility requirements, and project criteria.
8) Can I export the results for reports?
Yes. The calculator provides CSV and PDF download options after a result is created. These exports help you save summary values and profile data for documentation or review.