Convert radian to half circle
Learn how to convert
1
radian to
half circle
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(radian\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)
\(\text{Left side: 1.0 } \left(radian\right) = {\color{rgb(89,182,91)} 1.0\left(radian\right)} = {\color{rgb(89,182,91)} 1.0\left(rad\right)}\)
\(\text{Right side: 1.0 } \left(half \text{ } circle\right) = {\color{rgb(125,164,120)} π\left(radian\right)} = {\color{rgb(125,164,120)} π\left(rad\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(radian\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} π}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)
\(\text{Conversion Equation}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times π\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times π\)
Switch sides
\({\color{rgb(20,165,174)} x} \times π = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times π \times \dfrac{1.0}{π} = 1.0 \times \dfrac{1.0}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{π}}} = 1.0 \times \dfrac{1.0}{π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.3183098862\approx3.1831 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(radian\right)\approx{\color{rgb(20,165,174)} 3.1831 \times 10^{-1}}\left(half \text{ } circle\right)\)
