Horizontal Curve Calculator

A horizontal curve is a segment of a road or railway that changes the direction of the alignment smoothly. It is critical for maintaining vehicle stability and safety. Using this calculator, you can determine key curve parameters like curve length, long chord, middle ordinate, and external distance.

The curve length (L) is calculated using the formula:
L = (π × Radius × Deflection Angle) / 180
Enter the radius (R) in meters and deflection angle (Δ) in degrees into the calculator, and it will automatically compute the curve length for you.

The long chord is the straight-line distance between the beginning and end of the curve. Formula: LC = 2 × Radius × sin(Δ/2). Input the radius and deflection angle, and the calculator will display the long chord automatically.

Middle Ordinate (M) is the maximum distance from the midpoint of the long chord to the curve. It helps in checking the road layout and alignment accuracy. Formula: M = Radius × (1 - cos(Δ/2)).

External Distance (E) is the distance from the intersection point of tangents to the curve. Formula: E = Radius × (sec(Δ/2) - 1). Enter R and Δ in the calculator to get this value instantly.

Optional inputs include Superelevation (e), Design Speed (V), Lane Width (W), and Side Friction Factor (f). These parameters help in more advanced road design calculations for safety and comfort.

1. Enter the Radius (R) of your curve in meters.
2. Enter the Deflection Angle (Δ) in degrees.
3. Optionally, enter Superelevation (e), Design Speed (V), Lane Width (W), and Side Friction Factor (f).
4. Select the Curve Type: Circular or Compound.
5. Click “Calculate Curve” and view results: Curve Length, Long Chord, Middle Ordinate, External Distance, and optional inputs.
6. Use these results to design your road or railway alignment accurately.

Yes, this calculator can be used for any horizontal curve, including roads, highways, or railways. Ensure the radius and deflection angle are input correctly for accurate results.

Middle Ordinate and External Distance are critical for verifying curve accuracy in the field and ensuring the alignment meets design specifications. These values also help in setting out the curve using surveying instruments.