Estimate elevations along a parabolic vertical curve connecting two grades.
Vertical Curve Calculator
Form
Results
Elevation of PVI
0
Elevation of EVC
0
Table of Contents
1
What is Vertical Curve?
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How to Use This Calculator
- Enter or select Elevation of BVC, Initial gradient (g1), Final gradient (g2), Length of curve.
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used
Elevation(x) = BVC elevation+g₁x+(g₂−g₁)x²/(2L)
4
Variables Explained
| Input | What it means |
|---|---|
| Elevation of BVC | Use the measured or stated value for this item, with the unit or category shown beside the field. |
| Initial gradient (g1) | Use the measured or stated value for this item, with the unit or category shown beside the field. |
| Final gradient (g2) | Use the measured or stated value for this item, with the unit or category shown beside the field. |
| Length of curve | The measured end-to-end distance of the section being calculated. |
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Worked Example
With BVC=100 m, g₁=0.02, g₂=−0.02 and L=100 m, the midpoint elevation is 100.5 m.
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Why Use This Calculator?
Use the result to put measurements on a common basis before comparing them or estimating quantities. The original measurement precision still limits the precision of the answer.
7
Common Mistakes
- Use grades as decimals in the equation; x is measured from the beginning of the curve.
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Frequently Asked Questions
When should I round a measurement?
Carry the measured values and conversion factors through the calculation first. Round the final result to a precision justified by the original measurements.
Why can a supplier’s quantity differ?
Measurement conventions, nominal sizes, density assumptions and purchase rounding can change a practical quantity. Compare the units and assumptions before comparing the numbers.
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Sources & References
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