Radians To Revolutions Conversion

rad

1 rad = 0.1591549431 rev

Want to convert from revolutions to radians instead?

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How to convert radians to revolutions (rad to rev)

The formula for converting radians to revolutions is: rev = rad × 0.1591549431. To calculate the radian value in revolutions first substitute the radian value into the preceding formula, and then perform the calculation. If we wanted to calculate 1 radian in revolutions we follow these steps:

rev = rad × 0.1591549431

rev = 1 × 0.1591549431

rev = 0.1591549431

In other words, 1 radian is equal to 0.1591549431 revolutions.

Example Conversion

Let's take a look at an example. The step-by-step process to convert 9 radians to revolutions is:

1. Understand the conversion formula: rev = rad × 0.1591549431
2. Substitute the required value. In this case we substitute 9 for rad so the formula becomes: rev = 9 × 0.1591549431
3. Calculate the result using the provided values. In our example the result is: 9 × 0.1591549431 = 1.4323944879 rev

In summary, 9 radians is equal to 1.4323944879 revolutions.

Converting revolutions to radians

In order to convert the other way around i.e. revolutions to radians, you would use the following formula: rad = rev × 6.28318530685963. To convert revolutions to radians first substitute the revolution value into the above formula, and then execute the calculation. If we wanted to calculate 1 revolution in radians we follow these steps:

rad = rev × 6.28318530685963

rad = 1 × 6.28318530685963

rad = 6.28318530685963

Or in other words, 1 revolution is equal to 6.28318530685963 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 Revolution?

A revolution is a unit of angular measure that is equal to one complete turn around a circle, which is 360 degrees or 2π radians.
To better understand this definition, it's important to note that a circle is divided into 360 degrees or 2π radians. Each revolution is a full rotation around the circle, completing a full 360-degree cycle or 2π radians. When measuring angles using revolutions, angles are usually denoted using the revolution symbol (rev), which is placed after the numerical value of the angle. For example, an angle of 2 revolutions would be written as 2 rev or 720°.
Revolutions are not commonly used as a unit of angular measure in everyday life, but they are used in some fields such as mechanical engineering and robotics, where they are used to measure the rotation of motors, gears, and other moving parts. In addition, revolutions are sometimes used in astronomy to describe the rotation of celestial bodies, such as planets and stars.

Radians To Revolutions Conversion Table

Below is a lookup table showing common radians to revolutions conversion values.

Radian (rad)Revolution (rev)
1 rad0.1591549431 rev
2 rad0.3183098862 rev
3 rad0.4774648293 rev
4 rad0.6366197724 rev
5 rad0.7957747155 rev
6 rad0.9549296586 rev
7 rad1.1140846017 rev
8 rad1.2732395448 rev
9 rad1.4323944879 rev
10 rad1.591549431 rev
11 rad1.7507043741 rev
12 rad1.9098593172 rev
13 rad2.0690142603 rev

Other Common RadianConversions

Below is a table of common conversions from radians to other angle units.

ConversionResult
1 radian in degrees57.2957795785523 °
1 radian in quadrants0.636619772365513 quadrant