# Convert cycle / square second to revolution / square second

Learn how to convert 1 cycle / square second to revolution / square second step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{cycle}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{square \text{ } second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{cycle}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{revolution}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{cycle}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{square \text{ } second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$2.0 \times π = {\color{rgb(20,165,174)} x} \times 2.0 \times π$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x}$$
Switch sides
$${\color{rgb(20,165,174)} x} = 1.0$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 1$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{cycle}{square \text{ } second}\right) = {\color{rgb(20,165,174)} 1}\left(\dfrac{revolution}{square \text{ } second}\right)$$