Angle Converter
Degree
Definition: A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees.
History/origin: The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun advanced roughly one degree in the sky each day.
Current use: Degrees are widely used in geometry, trigonometry, geography (latitude and longitude), astronomy, and everyday engineering applications.
Gradian
Definition: The gradian (also known as the gon, grad, or grade) is a unit of measurement of an angle, defined as one hundredth of the right angle. In other words, there are 100 gradians in a quarter circle and 400 gradians in a full circle.
History/origin: The unit originated in France in connection with the metric system during the French Revolution. The goal was to replace the base-60 system of degrees with a decimal (base-100) system to simplify calculations.
Current use: Gradians are primarily used in some fields of surveying, civil engineering, and mining, particularly in parts of Europe, because it simplifies the addition and subtraction of right angles.
Degree to Gradian Conversion Table
| Degree [deg] | Gradian [grad] |
|---|---|
| 0.01 deg | 0.01111111 grad |
| 0.1 deg | 0.11111111 grad |
| 1 deg | 1.11111111 grad |
| 2 deg | 2.22222222 grad |
| 3 deg | 3.33333333 grad |
| 5 deg | 5.55555556 grad |
| 10 deg | 11.11111111 grad |
| 20 deg | 22.22222222 grad |
| 50 deg | 55.55555556 grad |
| 100 deg | 111.11111111 grad |
| 1000 deg | 1111.11111111 grad |
How to Convert Degree to Gradian
1 deg = 1.11111111 grad
1 grad = 0.9 deg
Example: convert 15 deg to grad:
15 deg = 15 × 1.11111111 grad = 16.66666667 grad
Did You Know?
- A full circle is divided into 360 degrees. This system likely originated from ancient Babylonians who used a base-60 number system.
- Gradians, also known as gons, divide a right angle into exactly 100 parts, making it much easier to calculate right angles in surveying.