# Horizontal Curves Definitions and Formulas

### Horizontal Curve Formulas

$$L = 100\frac{I^{\circ}}{D^{\circ}}$$

$$L = RI_{\text{radians}}$$

$$L = \frac{RI 2 \pi}{360^{\circ}}$$

$$ R = \frac{5729.578}{D}$$

$$ T = R\tan\frac{I}{2}$$

$$ LC = 2R\sin\frac{I}{2}$$

$$ E = T\tan\frac{I}{4}$$

$$ M = E\cos\frac{I}{2}$$

There are MANY of these formulas thanks to geometry and trigonometry. This is only a small sampling so that you can view and get related to them when you are away from your reference materials.

### Horizontal Curve Definitions

LC or C – Long chord

D – Degree of Curve

E – External Distance

I – Intersection Angle

L – Length of Curve

M or HSO – Middle Ordinate or Horizontal Sightline Offset

R – Radius of Curve

PC – Point of Curvature

PI – Point of Intersection

PT – Point of Tangency

T – tangent distance between PC and PI, PI to PT

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