Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a unit of measurement of a plane angle. It helps us describe how much something turns or rotates. One full turn, like a complete spin in a circle, is divided into 360 equal parts, and each part is called a degree.

This way of measuring angles is very common in everyday life. For example, a straight line makes an angle of 180 degrees, while a right angle, like the corner of a book, measures 90 degrees. Degrees are easy to use and understand, which is why they are often taught in schools and used in many fields.

Although the degree is not an SI unit—the official system of units used by scientists—the SI brochure mentions it as an accepted unit. Scientists often use a different unit called the radian, but degrees remain popular because they are straightforward and widely known. Since a full rotation equals 2π radians, one degree is the same as ⁠π/180⁠ radians, linking the two systems of measurement.

History

We don't know exactly why ancient people chose the degree to measure angles. One idea is that it is connected to the number of days in a year, which is close to 360. Early astronomers noticed that the sun appeared to move about one degree each day along its path in the sky. Some old calendars, like the Persian calendar and the Babylonian calendar, had 360 days, possibly because they used a sexagesimal (base-60) number system.

Another idea is that the Babylonians divided the circle into parts based on the angles of an equilateral triangle, and then split those parts into 60 smaller pieces, following their base-60 system. Later, Greek scientists like Aristarchus of Samos and Hipparchus used this system, dividing a circle into 360 degrees, each containing 60 smaller units called arc minutes.

The number 360 was also chosen because it is easily divided. It has many factors, which makes it useful for dividing the world into time zones and for other practical purposes.

Subdivisions

A degree can be split into smaller parts for more precise measurements. One degree equals 60 minutes, and one minute equals 60 seconds. These smaller parts are called minutes and seconds of arc. For example, 40.1875° can also be written as 40° 11′ 15″ using this system.

Maritime maps often use degrees and minutes to help with navigation. The older system of using thirds, fourths, and so on is rarely used today. Some people also use millidegrees and microdegrees for even smaller measurements.

Alternative units

See also: Measuring angles

In much of higher mathematics, angles are often measured in radians instead of degrees. This is because radians make the rules of trigonometry simpler and more natural. A full circle, or one complete turn (360°), equals 2_π_ radians. This means that 180° is the same as π radians, and one degree equals π⁄180 radians.

Historically, some countries tried to use a decimal system for angles, calling the new unit grade or grad. In this system, a right angle was 100 grades, and a full circle was 400 grades. Although this system did not catch on widely, it is still used in some fields today. Another unit, called an angular mil, is used mainly in military contexts and has several slightly different definitions.