Radians To Degrees Conversion

1 rad = 57.2957795785523 °

Want to convert from degrees to radians instead?

Disclaimer: We've spent hundreds of hours building and testing our calculators and conversion tools. However, we cannot be held liable for any damages or losses (monetary or otherwise) arising out of or in connection with their use. Full disclaimer.

How to convert radians to degrees (rad to °)

The formula for converting radians to degrees is: ° = rad × 57.2957795785523. To calculate the radian value in degrees first substitute the radian value into the preceding formula, and then perform the calculation. If we wanted to calculate 1 radian in degrees we follow these steps:

° = rad × 57.2957795785523

° = 1 × 57.2957795785523

° = 57.2957795785523

In other words, 1 radian is equal to 57.2957795785523 degrees.

Example Conversion

Let's take a look at an example. The step-by-step process to convert 7 radians to degrees is:

Understand the conversion formula: ° = rad × 57.2957795785523
Substitute the required value. In this case we substitute 7 for rad so the formula becomes: ° = 7 × 57.2957795785523
Calculate the result using the provided values. In our example the result is: 7 × 57.2957795785523 = 401.0704570498661 °

In summary, 7 radians is equal to 401.0704570498661 degrees.

Converting degrees to radians

In order to convert the other way around i.e. degrees to radians, you would use the following formula: rad = ° × 0.0174532925. To convert degrees to radians first substitute the degree value into the above formula, and then execute the calculation. If we wanted to calculate 1 degree in radians we follow these steps:

rad = ° × 0.0174532925

rad = 1 × 0.0174532925

rad = 0.0174532925

Or in other words, 1 degree is equal to 0.0174532925 radians.

Conversion Unit Definitions

What is a Radian?

A radian is a unit of angular measure that is used to quantify the size of an angle, particularly in trigonometry and calculus. One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

To better understand this definition, it's important to note that a circle has a circumference of 2π times the radius, where π is the mathematical constant pi (approximately 3.14159). Therefore, an angle of one radian is subtended by an arc that is equal in length to the radius of the circle, which is one unit in length.

When measuring angles using radians, angles are usually denoted using the radian symbol (rad), which is often omitted for simplicity. For example, an angle of 2 radians would be written as 2 rad.

What is a Degree?

A degree is a unit of measure for angles, which is used to quantify the size of an angle. One degree is defined as 1/360th of a full rotation, which is a complete revolution around a circle.

To better understand this definition, it's important to note that a circle has 360 degrees. Therefore, an angle that spans one quarter of a circle (i.e., 90 degrees) is a right angle, while an angle that spans half a circle (i.e., 180 degrees) is a straight angle.

When measuring angles, degrees are usually denoted using the degree symbol (°), which is placed after the numerical value of the angle. For example, an angle of 45 degrees would be written as 45°.