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

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

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{degree}{square \text{ } minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{degree}{square \text{ } minute}\right) = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{radian}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{degree}{square \text{ } minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{6.48 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{6.48 \times 10^{5}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{60.0}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{6.48 \times 10^{5}} \times \dfrac{60.0}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{6.48 \times 10^{5} \times 1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{6.48 \times 10^{5}}$$
Rewrite equation
$$\dfrac{1.0}{10^{5}}\text{ can be rewritten to }10^{-5}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-5} \times π \times 60.0}{6.48}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0002908882\approx2.9089 \times 10^{-4}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{degree}{square \text{ } minute}\right)\approx{\color{rgb(20,165,174)} 2.9089 \times 10^{-4}}\left(\dfrac{radian}{minute \times second}\right)$$

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