# Convert arc minute to full circle

Learn how to convert 1 arc minute to full circle step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(arc \text{ } minute\right)={\color{rgb(20,165,174)} x}\left(full \text{ } circle\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(radian\right)$$
$$\text{Left side: 1.0 } \left(arc \text{ } minute\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(rad\right)}$$
$$\text{Right side: 1.0 } \left(full \text{ } circle\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(radian\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(rad\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(arc \text{ } minute\right)={\color{rgb(20,165,174)} x}\left(full \text{ } circle\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(radian\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times 2.0 \times π$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times 2.0$$
$$\text{Simplify}$$
$$\dfrac{1.0}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times 2.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2.0 = \dfrac{1.0}{1.08 \times 10^{4}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2.0}\right)$$
$${\color{rgb(20,165,174)} x} \times 2.0 \times \dfrac{1.0}{2.0} = \dfrac{1.0}{1.08 \times 10^{4}} \times \dfrac{1.0}{2.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.0}}} = \dfrac{1.0 \times 1.0}{1.08 \times 10^{4} \times 2.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.08 \times 10^{4} \times 2.0}$$
Rewrite equation
$$\dfrac{1.0}{10^{4}}\text{ can be rewritten to }10^{-4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-4}}{1.08 \times 2.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000462963\approx4.6296 \times 10^{-5}$$
$$\text{Conversion Equation}$$
$$1.0\left(arc \text{ } minute\right)\approx{\color{rgb(20,165,174)} 4.6296 \times 10^{-5}}\left(full \text{ } circle\right)$$