Prototype railroads in North America measure curves by degree of curvature, not radius. The degree of curvature is measured by in the field by the offset of a 100 foot chord.

**For a prototype curve:**

R=Radius of the curve

D=Degree of curvature

R=50/sin(D/2)

So for a 4 degree 30 minute curve:

R= 50/sin(4 deg 30 min/2)

R= 50/sin(2 deg 15 min)

R= 50/.0392

R= 1275 feet

**To convert to HO radius in inches:**

Rho= (R/87)x12

Rho= (1275/87)x12

Rho= (14.655)x12

Rho= 175 inches

Typical mainline curves are in the 2-6 degree range. Sharp curves are those above 10 degrees.

In the United Kingdom and most countries that belonged to the former British Empire, prototype curves are commonly measured by radius. In pre-metric times, the radius was often measured in chains.

1 chain = 22 yards = 66 feet.