Vertical Curve Calculator
Calculate parabolic vertical curve elevations, K-value, high/low point, and minimum length for crest and sag curves using AASHTO standards.
About this calculator
A vertical curve is the parabola that smooths the transition between two road grades, and this calculator classifies it first: whenever the incoming grade g1 is greater than the outgoing grade g2, the profile is a Crest curve (the road rises then falls, like a hilltop); otherwise it's a Sag curve (a valley). K-Value — Curve Length divided by the algebraic grade difference A — is the standard measure of curvature published in AASHTO's "A Policy on Geometric Design of Highways and Streets" (the Green Book), and it scales directly with Curve Length: stretch the curve out with the same two grades and K rises in exact proportion, since A doesn't change. Min.
Length (AASHTO) is checked against a stopping sight distance formula built from Design Speed, and it grows with Design Speed for both crest and sag geometry — the crest case controls sight distance over the hill using fixed 3.5-ft driver-eye and 2.0-ft object heights, while the sag case controls headlight throw at night. The Begin (BVC) and End (EVC) Vertical Curve elevations are simple offsets from the PVI elevation using half the curve length and the entering/exiting grades, so raising the PVI Elevation raises both endpoints by the same amount. This tool assumes a standard symmetric parabola and does not model superelevation, drainage grade breaks within the curve, or stopping sight distance reductions from horizontal curvature layered on top of the profile.
Inputs
Results
Curve Type
Crest
K-Value
120
Figures current as of 2018. Source: American Association of State Highway and Transportation Officials, A Policy on Geometric Design of Highways and Streets, 7th Edition, 2018 (the "Green Book")
How to Use This Calculator
- Enter the incoming grade (G1) and outgoing grade (G2) as percentages.
- Set the Curve Length (L) in feet.
- Input the PVI Station and PVI Elevation.
- Set Design Speed to check the curve against the AASHTO minimum length for stopping sight distance.
- Review the BVC and EVC stations and elevations, and the High/Low Point location, to set grade stakes in the field.
What each input means
- Incoming Grade (g₁)
- Grade of the approaching tangent in percent. Positive = uphill, negative = downhill.
- Outgoing Grade (g₂)
- Grade of the departing tangent in percent.
- Curve Length (L)
- Total length of the vertical curve.
- PVI Station
- Station of the Point of Vertical Intersection (PVI).
- PVI Elevation
- Elevation at the PVI.
- Design Speed
- Design speed for minimum curve length calculation per AASHTO.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersIncoming Grade (g₁) = 3, Outgoing Grade (g₂) = -2, Curve Length (L) = 600, PVI Station = 5000 = 6 input(s) provided
- Calculate Curve TypeCurve TypeCrest = Crest
- Calculate K-ValueK-Value = K120 = 120
- Calculate Grade DifferenceGrade Difference = A5 = 5
- Calculate Min. LengthMin. Length557 = 557
Figures and sources
- AASHTO stopping sight distance criteria for minimum crest and sag vertical curve length (2018) — American Association of State Highway and Transportation Officials, A Policy on Geometric Design of Highways and Streets, 7th Edition, 2018 (the "Green Book")
Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
What determines whether this is a Crest or Sag curve?
It's purely the relationship between the two grades: if the incoming grade g1 is larger than the outgoing grade g2, the road is transitioning from climbing to descending (or descending less steeply), which the calculator classifies as Crest. Any other relationship — g2 equal to or greater than g1 — is classified as Sag.
Why does a longer Curve Length raise the K-Value?
K-Value is Curve Length divided by the algebraic grade difference A, and A only depends on the two grades, not the length. So stretching the curve length while holding both grades fixed increases K in direct, exact proportion — doubling Curve Length doubles K-Value.
Why does raising Design Speed increase the minimum curve length?
Higher design speeds require longer stopping sight distances, and the AASHTO formula this calculator uses scales the minimum curve length with the square of the stopping sight distance. A curve that's adequate at 35 mph can fail the AASHTO minimum at 65 mph even though the two grades never changed. This is the same stopping-sight-distance based minimum-length criterion published in AASHTO's "A Policy on Geometric Design of Highways and Streets" (the Green Book), the standard reference U.S. highway agencies use for vertical curve design.
Does this calculator account for superelevation or drainage breaks?
No — it models a standard symmetric parabolic vertical curve only. Superelevation transitions, mid-curve drainage grade breaks, and combined horizontal-vertical sight distance effects all require additional geometric design checks beyond what this calculator performs.
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