Horizontal Curve Calculator : Examples / Formula

Our horizontal curve calculator helps determine key geometric elements and safety parameters for road design horizontal curves.

When you have a curve with a radius of 500 feet and a delta angle of 45 degrees at 60 mph, the calculator would process these parameters to determine curve elements like tangent length, arc length, and required superelevation.

How to Use Horizontal Curve Calculator

• Enter Radius: Input the curve radius in feet
• Input Delta Angle: Enter the central angle in degrees
• Set Design Speed: Specify the design speed in mph
• Define Superelevation: Enter the superelevation percentage

The calculator will compute the curve parameters using advanced formulas

Horizontal Curve Formula

Radius (R) = 15 * (V²) / (e + f)

Where:

• V = Design speed in mph
• e = Superelevation rate
• f = Side friction factor

Tangent Length Formula:

T = R * tan(Δ/2)

Arc Length Formula:

L = R * Δ (in radians)

Minimum Radius Formula:

Rmin = V²/(15(e + f))

If we have a 30° deflection angle and a radius of 1000 feet:

L = (30 π 1000) / 180 = 523.6 feet

How to Find Horizontal Radius?

• Determine the design speed based on road classification
• Select appropriate superelevation rate (typically 4-6% for highways)
• Find the friction factor from design tables
• Apply the radius formula

For a 500ft radius curve with 45° delta, calculations would be:

T = 500 × tan(45°/2) = 207.11 ft
L = 500 × (π × 45°/180°) = 392.70 ft

What are Typical Parameters?

• Low Speed: Radius: 100-300 ft, Superelevation: 4-6%
• Medium Speed: Radius: 300-1000 ft, Superelevation: 6-8%
• High Speed: Radius: >1000 ft, Superelevation: 8-12%
• Urban Streets: Radius: 150-500 ft, Superelevation: 2-4%
• Rural Highways: Radius: 500-2000 ft, Superelevation: 6-8%

Horizontal Curve Examples

For an urban street curve, we consider a design speed of 30 mph, with a deflection angle of 45°. Using a superelevation of 0.04, this yields a calculated radius of 400 feet and a curve length of 314.2 feet.

Moving to our rural highway curve, we increase the design speed to 65 mph to accommodate faster-moving traffic. With a deflection angle of 25° and superelevation of 0.06, we calculate a radius of 2,865 feet and a curve length of 1,250.8 feet.

For our mountain road curve, we must consider challenging terrain conditions. Using a design speed of 40 mph and a significant deflection angle of 90°, we implement a higher superelevation of 0.08 to help vehicles navigate the sharp turn. This results in a calculated radius of 575 feet and a curve length of 904.8 feet.

The freeway transition curve demands the highest design standards for safety at high speeds. With a design speed of 70 mph and a modest deflection angle of 15°, we use a superelevation of 0.06. These parameters give us a calculated radius of 3,320 feet and a curve length of 869.3 feet, providing an almost imperceptible transition for drivers.

In our local road curve example demonstrates calculations for residential areas. Using a design speed of 25 mph and a deflection angle of 60°, combined with a superelevation of 0.04, we determine a radius of 250 feet and a curve length of 261.8 feet.

What is a Horizontal Curve?

Horizontal curves are geometric elements used to provide a gradual transition between two tangent sections of roadway. They’re like a road’s signature – uniquely defining its path and safety characteristics.