Degree (°)
A unit of angle equal to 1/360 of a full rotation
The Degree (°) is a unit of angle rooted in ancient and modern traditions of geometry and measurement. The division of a circle into 360 degrees is attributed to ancient Babylonian astronomers who used a base-60 number system. Radians — a more mathematically natural unit — became standard in calculus and physics because they simplify formulas involving trigonometric functions. The Degree is used in specific contexts where its properties make it the most convenient choice for the task at hand.
Accurate angle measurement is critical in engineering, science, commerce, and everyday life. Using the correct unit and applying conversions precisely prevents errors that can be costly or dangerous in professional applications.
Conversion Table
| Unit | Symbol | 1 ° = |
|---|---|---|
| Radian | rad | 0.0174533 rad |
| Gradian | grad | 1.11111 grad |
| Arcminute | ′ | 60 ′ |
| Arcsecond | ″ | 3600 ″ |
Conversions Involving Degree
Common Uses of the Degree
- •Surveying — measuring bearing angles and slope gradients
- •Navigation — expressing compass headings and course changes
- •Mechanical design — specifying cam angles, gear pressure angles, and joint rotations
- •Physics and engineering — setting up trigonometric calculations
- •Astronomy — measuring the angular separation between celestial objects
Did You Know?
Ancient Babylonians divided the circle into 360 degrees around 1500 BC, possibly because 360 is close to the number of days in a year and is highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, and 180). This 4,000-year-old convention survives to this day. The Degree represents an alternative approach to expressing angular measurement.