# Convert radian / second to revolution / second

Learn how to convert 1 radian / second to revolution / second step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{radian}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{radian}{second}\right) = {\color{rgb(89,182,91)} 1.0\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} 1.0\left(\dfrac{rad}{s}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{revolution}{second}\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{rad}{s}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{radian}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}$$
$$\text{Conversion Equation}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 2.0 \times π$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times π \times 2.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times π \times 2.0 = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{π \times 2.0}\right)$$
$${\color{rgb(20,165,174)} x} \times π \times 2.0 \times \dfrac{1.0}{π \times 2.0} = 1.0 \times \dfrac{1.0}{π \times 2.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}}} = 1.0 \times \dfrac{1.0}{π \times 2.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{π \times 2.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.1591549431\approx1.5915 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{radian}{second}\right)\approx{\color{rgb(20,165,174)} 1.5915 \times 10^{-1}}\left(\dfrac{revolution}{second}\right)$$