# Convert degree / (hour • second) to radian / square minute

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

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{degree}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } minute}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{degree}{hour \times second}\right) = {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{radian}{square \text{ } minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{degree}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{square \text{ } minute}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{7.2 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6 \times 10^{3}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{π}{7.2 \times {\color{rgb(255,204,153)} \cancelto{10}{10^{4}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}$$
$$\text{Simplify}$$
$$\dfrac{π}{7.2 \times 10.0} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6} = \dfrac{π}{7.2 \times 10.0}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{3.6}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6} \times \dfrac{3.6}{1.0} = \dfrac{π}{7.2 \times 10.0} \times \dfrac{3.6}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{3.6}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 3.6}{7.2 \times 10.0 \times 1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{π \times 3.6}{7.2 \times 10.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.1570796327\approx1.5708 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{degree}{hour \times second}\right)\approx{\color{rgb(20,165,174)} 1.5708 \times 10^{-1}}\left(\dfrac{radian}{square \text{ } minute}\right)$$