Vertical Curve Design Calculator — PVIs & Parabolic Curves
Chain PVIs together, one after another, and each interior PVI gets a parabolic vertical curve where the two grades meet. Step forward and back through the chain with the arrows to see G1, G2, PVC/PVT, K, A, the middle ordinate and the high/low point recalculate live — then query the finished elevation anywhere along the whole alignment.
PVI Chain
Curve Data — PVI 2
Elevations along the alignment
Results
About this vertical curve design calculator
This tool designs the vertical alignment of a road as a chain of points of vertical intersection. It is built for highway and design engineers, road designers and surveyors setting out a profile, checking a proposed grade line, or verifying that curves satisfy sight distance requirements. You add PVIs one after another; the first is the alignment start and the last is the end, and every PVI in between receives a parabolic vertical curve of the length you set.
What it calculates for each curve
- Entering and exiting grades, G1 and G2
- Algebraic difference of grades,
A = G2 − G1 - Curve length L and the rate of vertical curvature
K = L / A - Middle ordinate,
MO = A × L / 800 - PVC and PVT station and elevation
- High point on a crest curve, or low point on a sag curve
- Curve type, crest or sag, and a pass or fail check against minimum K
Sight distance checking
Set the design speed and the tool compares your design K against the AASHTO minimum K for stopping sight distance at that speed, separately for crest and sag curves. The Crest K Table and Sag K Table buttons open the full design control tables for 20 to 130 kph. The metric values used are AASHTO's last published SI table from 2001, which carries the same stopping sight distance criteria — 2.5 second perception-reaction time and 3.4 m/s² deceleration — as the current edition.
Querying elevations
Once the profile is defined you can read the finished elevation at any single station, at a fixed interval to the end of the alignment, or across a start-to-end range at a chosen interval. Results work across the whole chain, on straight tangents and inside curves alike, and each row reports whether the point falls on a tangent or within a curve. Output can be copied as CSV or printed as a PDF.
Where this fits in design
Vertical curve design pairs with horizontal alignment: the plan geometry sets the curve radii and superelevation, while the profile sets the grades and the crest and sag curves between them. Low points on sag curves also drive drainage, since that is where surface water collects and where inlets are needed.
Frequently asked questions
What is a vertical curve in road design?
A vertical curve is the parabolic transition placed where two grades meet on a road profile, at a point of vertical intersection. It smooths the change in gradient so vehicles are not subjected to an abrupt break, and it is sized so drivers retain adequate stopping sight distance through the change.
What is the difference between a crest curve and a sag curve?
A crest curve occurs where the algebraic difference in grades is negative, so the profile rises then falls and the curve has a high point. A sag curve occurs where the difference is positive, so the profile falls then rises and the curve has a low point. Crest curves are governed by sight distance over the crest; sag curves are typically governed by headlight sight distance, comfort and drainage.
How is the K value of a vertical curve calculated?
K is the curve length divided by the algebraic difference in grades,
K = L / A, where A is expressed in percent. It represents the
horizontal distance in metres needed to achieve a one percent change in gradient,
so a higher K means a flatter, longer curve. Minimum K values for each design
speed come from stopping sight distance requirements.
What are PVC, PVI and PVT?
PVI is the point of vertical intersection, where the two tangent grades would meet if extended. PVC is the point of vertical curvature, where the curve begins, and PVT is the point of vertical tangency, where it ends. For a symmetrical parabolic curve the PVC and PVT each lie half the curve length either side of the PVI.
What is the middle ordinate of a vertical curve?
The middle ordinate is the vertical offset between the PVI and the curve itself at
the midpoint, calculated as A × L / 800. It is the maximum
departure of the parabola from the intersecting tangents and is useful for setting
out and for checking clearance at the crest or sag.
How do I find the high or low point on a vertical curve?
The turning point lies where the gradient of the curve becomes zero, at a distance from the PVC equal to the entering grade multiplied by the curve length divided by the algebraic difference in grades. The calculator locates this station and its elevation automatically, which matters for drainage design because the low point of a sag is where water will collect.
Which K values does the AASHTO check use?
The tool compares your design K against AASHTO minimum K values for stopping sight distance at the selected design speed, for crest and sag curves separately. The metric values used are AASHTO's last published SI table from 2001, which carries the same stopping sight distance criteria — a 2.5 second perception-reaction time and 3.4 m/s² deceleration — used in the current edition.
Related engineering tools
Designing the rest of the same alignment: