# Convert radian / square second to cycle / (minute • second)

Learn how to convert 1 radian / square second to cycle / (minute • second) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{radian}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{minute \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 1.0\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 1.0\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{cycle}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{30.0}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{30.0}\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{radian}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{minute \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{30.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{30.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{30.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{π}{30.0}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{π}{30.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{π}{30.0} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{30.0}{π}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{π}{30.0} \times \dfrac{30.0}{π} = 1.0 \times \dfrac{30.0}{π}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{30.0}}}{{\color{rgb(99,194,222)} \cancel{30.0}} \times {\color{rgb(255,204,153)} \cancel{π}}} = 1.0 \times \dfrac{30.0}{π}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{30.0}{π}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx9.5492965855\approx9.5493$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{radian}{square \text{ } second}\right)\approx{\color{rgb(20,165,174)} 9.5493}\left(\dfrac{cycle}{minute \times second}\right)$$