Highways Horizontal Curve Calculator

Enter the intersection angle, degree of curve, and point of intersection in the input boxes below. Use the calculate button to get the properties of horizontal curve using survey horizontal curve calculator.

Highways Horizontal Curve

To calculate Highways Horizontal Curve :

  • Intersection Angle

  • Degree of Curve


  • Point of Intersection





  • Radius

  • Tangent

  • Length

  • External

  • Long Chord

  • Point of curve

  • Point of Tangent


Along with elevation point vertical curve, horizontal curve is second important factor in highway design. These curves are semicircles that provide constant turning rate to driver.

Our curve calculator is very useful for surveying and transport engineers can use it without any hesitation.

In the next sections, we will explain horizontal curves, formulas to get the properties of horizontal curves, and method to find those geometrical properties without using horizontal tangent calculator.

What is horizontal curve in road?

horizontal curve offers a switch between two tangent strips of roadway. It allows a vehicle to negotiate a turn at a steady rate rather than a sharp cut. The design of the curve is reliant on the projected design speed for the roadway, as well as other factors including drainage and friction.

Horizontal Curve

Horizontal curve formulas

Horizontal curve has several geometric properties. Each property has separate formula. You can find formula for each property of horizontal curves.

R = 5729.58 / D

T = R * tan (A/2)

L = 100 * (A/D)

LC = 2 * R *sin (A/2)

E = R ((1/ (cos (A/2))) - 1))

PC = PI – T

PT = PC + L

M = R (1 - cos (A/2))


P.C. refers to the point of curve,

P.T. refers to the point of tangent,

D refers to the degree of curve,

P.I. represents the point of intersection,

L is the length of curve, from P.C. to P.T.,

T is the tangent distance,

A refers to the angle between two tangents, intersection Angle,

E refers to the external distance,

M is the length of middle ordinate,

R is radius,

c is the length of sub-chord, and

L.C. refers to the length of long chord.

How to calculate horizontal curve properties?

In this section, we will find the properties of horizontal curve without using circular curve calculator. Follow the steps below to find the properties discussed in the above section.


If the intersection angle is 30°, degree of curve is 2°, and point of intersection is 4000, find the horizontal curve radius, tangent, length, external, long chord, point of curve and point of tangent?


Step 1: Identify and write down the values.

A = 30°

D = 2°

P.I. = 4000

Step 2: Use the formulas given above to find each property.

R = 5729.58 / D

R = 5729.58/2°

R = 2,864.79

T = R * tan (A/2)

T = 2,864.79*tan (30°/2)

T = 767.62

L = 100 * (A/D)

L = 100* (30°/2°)

L = 1500

LC = 2 * R *sin (A/2)

LC = 2* 2864.79 * sin (30°/2)

LC = 1,482.92

E = R ((1/ (cos (A/2))) - 1))

E = 2864.79 ((1/ (cos (30°/2))) - 1))

E = 101.06

PC = PI – T

PC = 4000 - 767.62

PC = 3232.38 è 32+32.38

PT = PC + L

PT = (32+32.38) + 1500

PT = 4732.38 è 47+32.38

Use our simple curve calculator above to verify the values.


  1. Fundamentals of Transportation/Horizontal Curves - Wikibooks.