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Use our Vertical Curve calculator to find curve length, K-value, grade, elevation, and key points with clear steps and easy formulas.
A Vertical Curve calculator helps you solve road grade curves fast. It can save time and reduce math errors.
Our calculator makes vertical curve work simple. You can find the curve length, K-value, and grade change. You can also find key points and elevations.
This tool works for both crest and sag curves. It uses the standard parabolic vertical curve method.
You don't need to do hard math by hand. Just enter your values and let the tool do the work.
The result is clear and easy to check. This makes the tool useful for road design, civil work, and study.
The main vertical curve formula uses two road grades. These are the initial grade (G1) and final grade (G2).
Algebraic grade difference:
A = |G2 − G1|
If you know the curve length, use:
K = L ÷ A
If you know the K-value, use:
L = K × A
Here:
For elevation at any point:
E(x) = E(PVC) + (G1 ÷ 100) × x + [(G2 − G1) × x²] ÷ (200 × L)
For grade at any point:
g(x) = G1 + [(G2 − G1) × x] ÷ L
The zero-grade point can be found with:
x = −G1 × L ÷ (G2 − G1)
A positive-to-negative grade change forms a crest curve. A negative-to-positive change forms a sag curve.
Think of a crest curve like going over a small hill. A sag curve feels like passing through a dip.
Step 1: Enter the Initial Grade
Enter the starting road grade as G1. Use a positive value for an uphill grade.
Step 2: Enter the Final Grade
Enter the ending road grade as G2. Use a negative value for a downhill grade.
Step 3: Enter Curve Length or K-Value
Enter the curve length if you know it. You can also enter the K-value instead.
The calculator will find the missing value.
Step 4: Add Station Data
You can enter the PVI station if you need station results. The tool can then find the PVC and PVT stations.
Step 5: Add Elevation Data
Enter the known elevation at the PVC or PVI. This lets the calculator find curve elevations.
Step 6: Add a Point of Interest
You can enter a distance from the PVC. The tool will find the grade and elevation at that point.
Step 7: Check Your Results
The calculator shows the main results in one place. You'll see the curve type, curve length, K-value, grades, elevations, and key points.
Let's use a simple road example.
Suppose:
G1 = +4%
G2 = −2%
L = 600 ft
PVI = 10+00
Elevation at PVC = 100 ft
Point of interest = 200 ft from PVC
A = |G2 − G1|
A = |−2 − 4|
A = 6%
So, the grade change is 6%.
K = L ÷ A
K = 600 ÷ 6
K = 100 ft/%
G2 − G1 = −2 − 4
G2 − G1 = −6%
The grade falls from +4% to −2%. So, this is a crest curve.
Half of the curve length is:
L ÷ 2 = 600 ÷ 2
L ÷ 2 = 300 ft
PVC = PVI − 300 ft
PVC = 10+00 − 300 ft
PVC = 7+00
PVT = PVI + 300 ft
PVT = 10+00 + 300 ft
PVT = 13+00
x = −G1 × L ÷ (G2 − G1)
x = −4 × 600 ÷ (−2 − 4)
x = 400 ft from PVC
So, the high point is 400 ft from the PVC.
High Point Station = 7+00 + 400 ft
High Point Station = 11+00
The point is 200 ft from the PVC.
E(x) = E(PVC) + (G1 ÷ 100) × x + [(G2 − G1) × x²] ÷ (200 × L)
E(x) = 100 + (4 ÷ 100) × 200 + [(−6) × 200²] ÷ (200 × 600)
E(x) = 100 + 8 − 2
E(x) = 106 ft
So, the elevation at 200 ft is 106 ft.
g(x) = G1 + [(G2 − G1) × x] ÷ L
g(x) = 4 + [(−6) × 200] ÷ 600
g(x) = 4 − 2
g(x) = +2%
So, the grade at the point is +2%.
This example shows how a Vertical curve calculator with steps can save time. You can check each result with the same formulas.
You can also build a simple vertical curve tool in Excel. The same formulas work in Excel cells.
For algebraic grade difference:
=ABS(G2-G1)
For K-value:
=L/A
For curve length:
=K*A
For grade at a point:
=G1+((G2-G1)*x)/L
For elevation at a point:
=EPVC+(G1/100)*x+((G2-G1)x^2)/(200L)
For zero-grade point:
=-G1*L/(G2-G1)
These are useful Vertical curve calculator Excel formula options. They can help you build a custom road design sheet.
A Vertical Curve calculator makes curve math much easier. It helps you find key values with less effort.
You can use it for crest curves and sag curves. You can also find K-values, curve length, grades, elevations, and stations.
The tool is useful for students and civil engineering work. It also helps you check your manual calculations.
If you need a quick answer, you don't have to start from scratch. Enter your data, follow the steps, and check the results.
A Vertical Curve calculator finds key values for a vertical road curve. It can calculate curve length, K-value, grade, elevation, and key stations.
The main grade change formula is:
A = |G2 − G1|
For curve length, use:
L = K × A
For K-value, use:
K = L ÷ A
A crest curve connects a higher grade to a lower grade. For example, a change from +4% to −2% creates a crest curve.
A sag curve connects a lower grade to a higher grade. For example, a change from −3% to +2% creates a sag curve.
Use this formula:
x = −G1 × L ÷ (G2 − G1)
The result gives the distance from the PVC.
Yes. The same formulas work with metric units. Just use meters for all length values.
It shows the math behind the result. You can see each formula and calculation step. This makes the answer easier to understand and check.
Yes. You can use Excel formulas for grade change, K-value, curve length, elevation, and zero-grade point. The Vertical curve calculator Excel formula can also help you create a custom spreadsheet.
Students, civil engineers, road designers, and learners can use it. It can help with highway and road geometry work.