What Is a Road Horizontal Curve Calculator?

A road horizontal curve calculator turns a design speed and the available lateral resistance into the radius a curve needs, and then into the dimensions a surveyor or designer sets out in the field: degree of curve, tangent length, curve length, middle ordinate, external distance and long chord. It also runs the reverse check, reporting the maximum speed a curve of the entered radius actually supports on the stated superelevation and friction, so a design can be tested rather than assumed.

Horizontal curves are where a road is most likely to be driven faster than its geometry allows. The geometry is a compromise between three quantities — speed, superelevation and friction — and any one of them can be pushed beyond its limit by a designer working to a cost constraint or by a driver ignoring the posted limit.

How It Works

The design relationship sets centrifugal demand against resistance: the term V² divided by R is the lateral acceleration the curve demands, and superelevation plus side friction supply it. AASHTO writes the balance as R = V² divided by 15 times the sum of e and f in US customary units, and as R = V² divided by 127 times the same sum in metric with speed in km/h and radius in metres. Rearranged the other way, the superelevation required at a known radius is the lateral demand minus the friction the pavement can supply, which is the check that identifies a curve whose bank is too shallow for its speed.

The layout dimensions come from the central angle. Tangent length is the radius times the tangent of half the angle; the external distance is the radius times the secant of half the angle minus one, giving the clearance needed at the point of intersection; the middle ordinate is the radius times one minus the cosine of half the angle, which is the largest gap between chord and arc and therefore the sightline offset that must be kept clear; and the long chord spans the tangent points. The degree of curve is the central angle subtended by a 100 foot or 100 metre arc — 5,729.578 divided by the radius in feet, or 1,746.375 divided by the radius in metres — and the curve length follows as the radius times the central angle in radians.

Design speed then becomes a question with two answers rather than one. The first is the radius needed for the speed you intend. The second, which this calculator reports directly, is the speed the radius you have can actually carry — and the gap between them is what a designer has to close before the alignment is built.

Understanding Your Results

The primary card is the radius in the units you selected, with the degree of curve and the maximum speed it supports underneath. The three-stat bar adds the tangent length, the curve length and the middle ordinate, which between them define where the curve starts, how long it runs and how far back an obstruction has to be.

The breakdown table lists the units in use, the speed, radius and central angle, all five layout dimensions, the split of lateral demand between superelevation and friction, the superelevation the curve actually requires, the maximum design speed the geometry supports and the margin between that figure and the design speed. The summary panel repeats the headline dimensions and prints the verdict line.

Treat friction as the honest input here. A new, dry, well-textured pavement can develop lateral friction above 0.35 at low speed, but the value falls with speed and falls further with wet weather, polished aggregate and worn tyres. Designing close to a friction limit of 0.15 leaves nothing for the day the pavement is wet, which is why the required superelevation figure matters more than the radius when a curve is being assessed rather than designed. Long vehicles also matter: a large truck not only occupies more of the lane through a sharp curve but also tracks inside it, and its higher centre of gravity reduces the rollover threshold, which is what curve widening requirements and off-tracking checks are for.