# Convert half circle to rotation

Learn how to convert 1 half circle to rotation step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(half \text{ } circle\right)={\color{rgb(20,165,174)} x}\left(rotation\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(radian\right)$$
$$\text{Left side: 1.0 } \left(half \text{ } circle\right) = {\color{rgb(89,182,91)} π\left(radian\right)} = {\color{rgb(89,182,91)} π\left(rad\right)}$$
$$\text{Right side: 1.0 } \left(rotation\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(radian\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(rad\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(half \text{ } circle\right)={\color{rgb(20,165,174)} x}\left(rotation\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} π} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(radian\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} π} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} π} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}$$
$$\text{Conversion Equation}$$
$$π = {\color{rgb(20,165,174)} x} \times 2.0 \times π$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{π}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times 2.0$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 2.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2.0 = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2.0}\right)$$
$${\color{rgb(20,165,174)} x} \times 2.0 \times \dfrac{1.0}{2.0} = \times \dfrac{1.0}{2.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.0}}} = \dfrac{1.0}{2.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{2.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 5 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(half \text{ } circle\right) = {\color{rgb(20,165,174)} 5 \times 10^{-1}}\left(rotation\right)$$