🛣️ Vertical Curve Calculator
Calculate vertical curve dimensions
Entering grade (use negative for downgrade)
Exiting grade (use negative for downgrade)
Point of Vertical Curvature
Elevation at Point of Vertical Curvature
How to Use This Calculator
Enter Approach and Departure Grades
Input approach grade (entering grade) and departure grade (exiting grade) as percentages. Use positive for upgrade, negative for downgrade. For example, +2% = upgrade, -2% = downgrade.
Enter Curve Length
Input curve length in feet. This is the length of the vertical curve transition between the two grades. Typical lengths: 100-1000 feet depending on speed and grade change.
Enter Station and Elevation (Optional)
Optionally enter PVC (Point of Vertical Curvature) station and elevation to calculate elevations at PVI and PVT, and high/low point if applicable.
Calculate and Review
Click "Calculate Vertical Curve" to see rate of curvature (K), curve type (crest or sag), algebraic difference, elevations, and high/low point. Use this for road design.
Formula
Rate of Curvature (K) = L / |g2 - g1|
Algebraic Difference = |g2 - g1|
High/Low Point Distance = L × g1 / (g1 - g2)
External Distance (E) = (L × |g1 - g2|) / 8
Example 1: Approach = 2%, Departure = -2%, Length = 500 ft
Step 1: Algebraic Difference = |(-2) - 2| = 4%
Step 2: K = 500 / 4 = 125 ft/%
Step 3: Curve Type: Crest Curve (g1 > g2)
Step 4: External Distance = (500 × 4) / 8 = 250 feet
Step 5: High/Low Point = 500 × 0.02 / (0.02 - (-0.02)) = 10 / 0.04 = 250 feet from PVC
Example 2: Approach = -2%, Departure = 2%, Length = 500 ft
Step 1: Algebraic Difference = |2 - (-2)| = 4%
Step 2: K = 500 / 4 = 125 ft/%
Step 3: Curve Type: Sag Curve (g1 < g2)
About Vertical Curve Calculator
The Vertical Curve Calculator is an essential tool for civil engineers, surveyors, and road designers who need to calculate vertical curve dimensions for road design. This calculator implements vertical curve formulas to determine rate of curvature (K), curve type (crest or sag), elevations, and high/low points for smooth grade transitions in road construction.
When to Use This Calculator
- Road Design: Calculate vertical curves for road grade transitions
- Grade Transitions: Design smooth transitions between different road grades
- Elevation Calculation: Calculate elevations along vertical curves
- High/Low Points: Determine high/low points for drainage and sight distance
- Educational Use: Learn and understand vertical curve calculations
Why Use Our Calculator?
- ✅ Complete Calculations: Shows K value, curve type, elevations, and high/low points
- ✅ Accurate Formulas: Uses standard vertical curve equations
- ✅ Elevation Analysis: Calculates elevations at PVC, PVI, PVT, and high/low points
- ✅ Easy to Use: Simple inputs for grades, length, and station data
- ✅ Time Savings: Instant calculations eliminate manual math
Understanding Vertical Curves
Basic Principle: Vertical curves provide smooth transitions between different road grades. Rate of curvature (K) = Curve Length / Algebraic Difference of Grades. K value determines curve steepness: higher K = gentler curve, lower K = steeper curve. K is used in road design standards for sight distance and comfort.
Curve Types: Crest curves (sag curves) occur when approach grade is greater than departure grade (going over a hill). Sag curves (dip curves) occur when approach grade is less than departure grade (going into a valley). Both types use the same formulas but have different applications for sight distance and drainage.
K Values: Typical K values: 50-200 ft/% for low-speed roads, 200-500 ft/% for high-speed roads. Higher K values provide gentler curves and better sight distance. Minimum K values are specified by design standards (AASHTO, state DOTs).
Tips for Best Results
- Accurate Grades: Enter approach and departure grades accurately
- Correct Length: Use appropriate curve length for speed and grade change
- Verify K Values: Check calculated K against design standards
- Check High/Low Points: Verify high/low points for drainage and sight distance
- Use Standards: Follow applicable design standards (AASHTO, local codes)
Frequently Asked Questions
How do I calculate vertical curve K value?
Rate of Curvature (K) = Curve Length / Algebraic Difference of Grades. For example, Length = 500 ft, Approach = 2%, Departure = -2%: Algebraic Difference = |(-2) - 2| = 4%, K = 500 / 4 = 125 ft/%. K value determines curve steepness: higher K = gentler curve. The calculator does this automatically.
What is the difference between crest and sag curves?
Crest curves (sag curves) occur when approach grade is greater than the departure grade (going over a hill, like +2% to -2%). Sag curves (dip curves) occur when approach grade is less than the departure grade (going into a valley, like -2% to +2%). Both use the same formulas but have different applications for sight distance and drainage.
What is a typical K value for roads?
Typical K values: 50-200 ft/% for low-speed roads (30-50 mph), 200-500 ft/% for high-speed roads (55-70 mph). Higher K values provide gentler curves and better sight distance. Minimum K values are specified by design standards (AASHTO, state DOTs). Use appropriate K for your design speed and grade change.
How do I find the high/low point on a vertical curve?
High/Low Point Distance = Curve Length × Approach Grade / (Approach Grade - Departure Grade). For example, Length = 500 ft, Approach = 2%, Departure = -2%: Distance = 500 × 0.02 / (0.02 - (-0.02)) = 10 / 0.04 = 250 feet from PVC. The calculator shows high/low point automatically if it's within the curve.
Do I need PVC station and elevation?
PVC station and elevation are optional but useful for calculating elevations at PVI (Point of Vertical Intersection) and PVT (Point of Vertical Tangency), and high/low point elevation. If you only need K value and curve type, PVC data is not required. If you need elevations along the curve, enter PVC station and elevation.