Convert cycle / square hour to radian / square second

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

Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{cycle}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{cycle}{square \text{ } hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{6}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{6}}\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{radian}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 1.0\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 1.0\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{cycle}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{6}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{6}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{6}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{6.48 \times 10^{6}} = {\color{rgb(20,165,174)} x} \times 1.0$$
$$\text{Simplify}$$
$$\dfrac{π}{6.48 \times 10^{6}} = {\color{rgb(20,165,174)} x}$$
Switch sides
$${\color{rgb(20,165,174)} x} = \dfrac{π}{6.48 \times 10^{6}}$$
Rewrite equation
$$\dfrac{1.0}{10^{6}}\text{ can be rewritten to }10^{-6}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-6} \times π}{6.48}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000004848\approx4.8481 \times 10^{-7}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{cycle}{square \text{ } hour}\right)\approx{\color{rgb(20,165,174)} 4.8481 \times 10^{-7}}\left(\dfrac{radian}{square \text{ } second}\right)$$