# Horizontal Curve Formulas

## Horizontal Curve Formulas

D = Degree of Curve, Arc Definition

1° = 1 Degree of Curve

2° = 2 Degrees of Curve

P.C. = Point of Curve

P.T. = Point of Tangent

P.I. = Point of Intersection

I = Intersection Angle, Angle between two tangents

L = Length of Curve, from P.C. to P.T.

T = Tangent Distance

E = External Distance

R = Radius

L.C. = Length of Long Chord

M = Length of Middle Ordinate

c = Length of Sub-Chord

k = Length of Arc for Sub-Chord

d = Angle of Sub-Chord

R = | L.C. | T = R tan(I/2) = | L.C. | |

2 sin(I/2) | 2 cos(I/2) |

L.C. | = R sin (I/2) | D1° = R = 5,729.58 | D2° = | 5,729.58 | D = | 5,729.58 | |||

2 | 2 | R |

M = R [1 - cos(I/2)] = R - R cos(I/2)

E + R | = sec(I/2) | R - M | = cos(I/2) | |

R | R |

c = 2R sin(d/2) | d = | kD | |

100 |

L.C. = 2R sin(I/2) | E = R [sec(I/2) - 1] = R sec(I/2) - R |

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