Vertical Curve Calculator
Use this vertical curve calculator to estimate elevation along a roadway transition. It can find a point elevation on a crest or sag curve, or the elevation at the PVI. This page also keeps the formula, examples, FAQs, and references close by so you can check the result with confidence.
What This Vertical Curve Calculator Helps You Do
For a symmetric vertical curve, elevation changes with the initial grade, the final grade, the curve length, and the point distance along the curve. Review the formula and examples below if you want to see how the result is derived.
This page is meant to give you a fast answer, but it also helps you double-check the math before you make a decision. Start with the inputs that you already know, run the calculation, and then compare the output with the formula, examples, and FAQs below so you can see whether the answer fits the situation you are modeling.
If the result looks off, the usual causes are a unit mismatch, a missing decimal, the wrong scenario, or a value that needs to be entered as a rate instead of a total. The notes on this page are designed to make those checks easy without forcing you to leave the calculator and search for context elsewhere.
- Use the calculator first for a quick estimate.
- Use the formula to understand how the result is built.
- Use the examples to compare common use cases.
- Use the references when the answer depends on a standard or assumption.
Common Checks
A quick result is useful, but the best result is one that still makes sense when you look at it a second time. If you are comparing scenarios, try changing one input at a time so you can see which variable has the biggest impact on the final answer. That makes it much easier to spot whether the calculation matches your expectations.
It also helps to keep the context of the problem in mind. A calculator can tell you the math, but you still need to decide whether the input represents a total, a rate, an average, or a category-specific assumption. When in doubt, start with a simple example from the page and scale up from there.
- Check that every unit matches the rest of the problem.
- Keep rates, totals, and averages separate.
- Adjust one variable at a time when testing scenarios.
- Use the smallest realistic input first, then scale upward.
Scenario Planning
This calculator is especially useful when you want a quick answer before you commit time, money, or effort. Try one baseline input set, then change a single number and compare the result so you can see how sensitive the answer is to that variable.
That makes the page useful for more than just arithmetic. It becomes a small decision aid that helps you compare options, test assumptions, and explain the final number with confidence when you need to share it with someone else.
Result
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How to Calculate Vertical Curve Calculator
- Enter the BVC elevation: Use the elevation where the vertical curve begins.
- Enter the grades: Use the initial and final grade magnitudes for the curve.
- Set the curve length: Enter the horizontal length between the BVC and the EVC.
- Choose the point: Enter the horizontal distance when you want the elevation at a point on the curve.
Vertical Curve Calculator Formula
| Variable | Meaning | Unit |
|---|---|---|
| E_BVC | Elevation at the beginning of vertical curve | m |
| g1 | Initial grade | % |
| g2 | Final grade | % |
| L | Curve length | m |
| x | Distance from BVC | m |
Worked Examples
- BVC elevation: 100 m
- Initial grade: 2%
- Final grade: 1%
- Distance: 50 m
Result: Crest curve elevation = 100.88 m
A gentle crest curve usually changes elevation slowly.
- BVC elevation: 95 m
- Initial grade: 3%
- Length: 200 m
Result: PVI elevation = 98 m
The PVI is found halfway along the curve for a symmetric setup.
- BVC elevation: 110 m
- Initial grade: 1%
- Final grade: 3%
- Distance: 80 m
Result: Sag curve elevation = 112.28 m
A sag curve rises more quickly as the final grade increases.
- BVC elevation: 150 m
- Length: 400 m
- Distance: 120 m
Result: Crest curve elevation = 152.88 m
Longer curves make the change in elevation easier to spread out.
How to Interpret Your Results
| Range | Meaning | Action |
|---|---|---|
| Short curve | Sharper transition | Check comfort, drainage, and sight distance. |
| Moderate curve | Common roadway transition | Verify the grades at both ends. |
| Long curve | Gentle elevation change | Use the point elevation to confirm profile continuity. |
Frequently Asked Questions
References
Last reviewed: March 2026