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 do not 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.

Some old calendars, like the Persian calendar and the Babylonian calendar, had 360 days, possibly because they used a sexagesimal (base-60) number system.

Later, Greek scientists like Aristarchus of Samos and Hipparchus used this system, dividing a circle into 360 degrees.

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 exact 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 higher math, angles are often measured in radians instead of degrees. This makes the rules of trigonometry simpler. 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.

Some countries once 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. This system did not become popular, but it is still used in some places today. Another unit, called an angular mil, is used mostly in military contexts.