Conversion of Angle units

Introducing the Different Units of Angle

The standard unit of angle is referred to as degree, symbolized by the ° symbol, and is derived from the Latin term “Gradus” which means step. This is divide into two other units, which are minutes and seconds of arc, symbolized by the single apostrophe ‘ and double apostrophe ” or ‘’, respectively. Radian and gradians are also used to constitute angle measurements, with the radian being much more popularly used due to its definitions in relation to the unit circle, and the gradian still having a place in the modern metric systems to measure angles.

The History of the Different Units ofAngle

Angle measurements have been accounted for since the Ancient Babylon era, with the earliest known cuneiform tablets displaying the astronomical calculations of sexagesimal system, as well as the use of special protractors to measure angles accurately. The degree, being the most interchanged unit of angle measurement, initially required for the Babylonians to measure the 360 parts of a circle by using a divide-and-conquer method.

Interesting Facts and Uses of the Different Units ofAngle

The units of angles are used in a diverse range of fields such as, mathematics, physics, engineering, and geometry. The 360 degree circles helps mathematicians mathematically differentiate between circles, which are three-dimensional objects, and angles, which are two dimensional objects. Radians also plays a large role in mathematical equations in that, it serves as a useful tool when dividing a circle into equal parts while also allowing mathematicians to define relationships and equivalencies amongst circles and angles to a far greater degree.

Examples of Reference or Record Values in Different Units of Angle

Here is a list of 10 examples of the reference and record values of different units of angle measurements:

• 0° = Straight angle
• 1 Radian = Quarter of a circle
• 90° = Right angle
• 60° = Regular hexagon
• 45° = Isosceles triangle
• 1/20 Gradian = Compass rosette
• 1° = Fretting angle
• 57°17′43″ = Olivary angle
• 180° = Full circle
• 91°59′59″ = Smallest non-zero angle

How to Convert Different Units of Angle

The best approach to convert different units of angle is to understand the various conversions between each unit, and then use simple mathematical methods such as addition and subtraction to calculate the target angle in the desired unit. The main conversions are:

• 1 Radian = 57.29578 degrees
• 1 Degree = 0.01745329 Radians
• 1 Gradian = 0.9 degrees
• 1 Degree = 60 Minutes
• 1 Minute = 60 Seconds