The Measurement of Angles: An Introduction

Ways and means of measuring angles began in antiquity.

The rotational measure of angles can be traced to various ancient civilizations in the geographical regions of Mesopotamia (between the Tigris and Euphrates rivers), Egypt and the Indus River basin (located in Pakistan). However, it is the Babylonians (circa 1700 B.C.) who are credited with the introduction of the degree unit of rotational measurement. They were the ones who subdivided a full rotation into 360 angular parts and called each of them an angle of one degree.  The division was not arbitrary. It was derived using their number system which had a base of 60. (In contrast, our decimal system has a base of 10.)

The “Grand Conjunctions” of planets in our solar system are still a matter of small angular measurements in tenths of a degree between their lines of sight from earth. See “Jupiter & Saturn Conjunction – December 21, 2020” for both the science and the history of these astronomical events which occur about every 20 years when Jupiter “overtakes” Saturn in its orbit about the sun from our perspective on earth. Streamed live from the McDonald Observatory at 6:00 pm CST on December 21, 2020. This was one of the closest grand conjunctions of these large gas planets in our solar system seen since 1226, measuring 6 minutes of arc or approximately 1/10th of a degree.

This type of angular measurement was adopted by various cultures in that region and over time made its way to the farthest reaching climes of the Roman Empire, which extended to its northern edge, the Antonine Wall, located in what is now central Scotland. It is rather interesting to note that very close (relatively speaking) to that most northern frontier, approximately 3400 years later, an English mathematician, Roger Cotes (1682-1716) added a new dimension to the measurement of angles. He introduced the concept of, what is now termed, the radian measure of angles, though he did not coin the nomenclature itself. The advantage of radian measure was that it was an arc length along a circle and, therefore, could be regarded as a linear measure of an angle because the arc could be flattened along a horizontal axis. This revolutionized the study of the trigonometric functions and led to a visual depiction of their graphs in the Cartesian plane.

Last Updated by SAS October 07, 2026, 16:00:34