# Sine Bar

10 inch and 100 mm sine bars

A sine bar is a tool used to measure angles in metalworking.

It consists of a hardened, precision ground body with two precision ground cylinders fixed at the ends. The distance between the centers of the cylinders is precisely controlled, and the top of the bar is parallel to a line through the centers of the two rollers. The dimension between the two rollers is chosen to be a whole number (for ease of later calculations) and forms the hypotenuse of a triangle when in use. The image shows a 10 inch and a 100 mm sine bar, however, in the U.S., 5 inch sine bars are the most commonly used.

When a sine bar is placed on a level surface the top edge will be parallel to that surface. If one roller is raised by a known distance, usually using gauge blocks, then the top edge of the bar will be tilted by the same amount forming an angle that may be calculated by the application of the sine rule.

• The hypotenuse is a constant dimension — (100 mm or 10 inches in the examples shown).
• The height is obtained from the dimension between the bottom of one roller and the table’s surface.
• The angle is calculated by using the sine rule. Some engineering and metalworking reference books contain tables showing the dimension required to obtain an angle from 0-90 degrees, incremented by 1 minute intervals.
$\sin \left(angle \right) = {opposite \over hypotenuse}$

Angles may be measured or set with this tool.