What is the Difference Between Radian and Degree?

The main difference between radian and degree lies in their representation and application. Here are the key differences:

1. Measurement unit: A degree is a unit of measurement for circles, spheres, and angles. A radian is also a unit of measurement for angles.
2. Full circle: A full circle has 360 degrees, while its radian measure is only half of it, which is 180 degrees or one pi radian.
3. Application: Degrees are widely used in the measurement of circles and angles, while radians are not as widely used for these purposes. Radians are more commonly used in rotational motion equations and when dealing with rates of change, such as in calculus.
4. Conversion: There are approximately 180 degrees in a radian, and one radian is equal to 57 degrees.

In summary, degrees are more commonly used for measuring angles and circles, while radians are typically used in rotational motion equations and calculus.

Comparative Table: Radian vs Degree

Here is a table comparing the difference between radian and degree measurements for some common angles:

Both degrees and radians are used to measure angles, but they represent different units of measurement. One complete anticlockwise revolution can be represented by 2π radians or 360° (in degrees). To convert an angle from degrees to radians, the value has to be multiplied by π/180. For example, to convert 180° to radians, you would use the following formula:

$$\frac{180° \times \pi}{180°} = \pi$$

To convert an angle from radians to degrees, the value has to be multiplied by 180/π. For example, to convert π/12 radians to degrees, you would use the following formula:

$$\frac{12° \times 180}{π} = 15°$$