How to Use the Road Curve Length and Tangent Calculator
Where two tangent alignments meet, a circular curve carries the roadway through the deflection. Radius and intersection angle are the only two inputs needed to define that curve, and everything else follows from them. This calculator returns the five standard circular curve elements used on plan sheets plus the degree of curve.
Curve length equals the radius times the deflection angle in radians, and the tangent distance from the point of intersection back to the point of curvature equals R tan(Δ/2). External distance measures from the PI to the midpoint of the curve, the middle ordinate measures from the long chord to the curve, and the long chord connects the PC to the PT.
American highway practice also describes curves by degree of curve. Under the arc definition used by AASHTO for highways, D equals 5,729.578 divided by the radius, which is the central angle subtended by a 100 ft arc. A 1,000 ft radius is therefore a 5 degree 43 minute 46 second curve, and the curve length can be checked as 100Δ/D.
Tangent distance drives right of way. A larger radius gives a flatter, more comfortable curve but pushes the PC and PT farther from the intersection point, which is often the limiting factor in built-up corridors. Design also adds spiral transitions and applies the minimum radius tied to design speed and maximum superelevation, so treat these values as the circular curve geometry alone.
Frequently Asked Questions
It is the central angle subtended by a 100 ft arc of the curve under the arc definition, equal to 5,729.578 divided by the radius. A sharper curve has a larger degree of curve, so a 5° curve is flatter than a 10° curve.
External distance runs from the point of intersection to the midpoint of the curve, so it governs clearance and right of way near the PI. Middle ordinate runs from the middle of the long chord to the curve and is the value used when laying the curve out in the field.