Revolutions To Radians Conversion

1 rev = 6.28318530685963 rad

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How to convert revolutions to radians (rev to rad)

The formula for converting revolutions to radians is: rad = rev × 6.28318530685963. To calculate the revolution value in radians first substitute the revolution value into the preceding formula, and then perform 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

In other words, 1 revolution is equal to 6.28318530685963 radians.

Example Conversion

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

Understand the conversion formula: rad = rev × 6.28318530685963
Substitute the required value. In this case we substitute 9 for rev so the formula becomes: rad = 9 × 6.28318530685963
Calculate the result using the provided values. In our example the result is: 9 × 6.28318530685963 = 56.54866776173667 rad

In summary, 9 revolutions is equal to 56.54866776173667 radians.

Converting radians to revolutions

In order to convert the other way around i.e. radians to revolutions, you would use the following formula: rev = rad × 0.1591549431. To convert radians to revolutions first substitute the radian value into the above formula, and then execute 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

Or in other words, 1 radian is equal to 0.1591549431 revolutions.

Conversion Unit Definitions

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.

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.