Protractors

Protractors are measuring instruments used to determine angles. The most common forms are semicircular and circular devices marked with degree scales. A typical semicircular protractor is 180 degrees with a baseline along 0 and 180 degrees, while a circular protractor can measure angles across the full 360 degrees. Protractors are often made from transparent plastic, though metal varieties exist, and many include a ruler along the edge to assist in drafting.

Two main features distinguish protractors: the scales and the alignment features. Most protractors have outer and inner scales to accommodate reading angles in two directions. The center hole or point serves as the vertex. To measure an angle, place the protractor's center at the vertex, align the baseline with one ray, and read where the other ray crosses the scale. Reading can involve choosing the outer scale or inner scale depending on which yields the intended direction.

Specialized types raise precision and convenience. Vernier protractors add a secondary scale for readings finer than one degree. Digital protractors provide an electronic display of the measured angle. Large-format protractors are used in drafting and surveying, while compact models serve education and basic geometry.

History and etymology. The term protractor derives from the Latin protractus, meaning drawn out or extended. Modern protractors became common in engineering drawing and mathematics education in the 18th–19th centuries, with variations supporting higher precision and specialized applications.

Limitations and tips. Protractors are subject to parallax errors when read from an angle. For best results, read the scale at eye level and ensure the baseline is properly aligned with one ray. They are simple, inexpensive tools for educational contexts and for basic angle measurement in design and construction.