# Simple Circular Curve

Written by Jerry Ratzlaff on . Posted in Surveying Engineering

Simple circular curve is a curve that does not cross itself.

## Simple Circular Curve formula

 $$\large{ c = 2 \; r \; sin \; \frac{ \theta }{ 2 } }$$ $$\large{ E = r \; sec \; \frac{ \theta }{ 2 } \;-\; r }$$ $$\large{ l = \frac{ \pi \; r \; \theta }{ 180 } }$$ $$\large{ M = r \;-\; r \; cos \; \frac{ \theta }{ 2 } }$$ $$\large{ T = r \; tan \; \frac{ \theta }{ 2 } }$$

### Where:

$$\large{ \theta }$$ = angle

$$\large{ BT }$$ = back tangent

$$\large{ c }$$ = chord length

$$\large{ E }$$  = external distance

$$\large{ FT }$$ = forward tangent

$$\large{ l }$$  = length of curve

$$\large{ M }$$  = middle ordinate

$$\large{ \pi }$$ = Pi

$$\large{ PC }$$ = point on curve

$$\large{ PI }$$ = point of intersection

$$\large{ PT }$$  = point on tangent

$$\large{ r }$$  = radius of curve

$$\large{ T }$$ = subtangent