Convert radian to angular mil
Learn how to convert
1
radian to
angular mil
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(radian\right)={\color{rgb(20,165,174)} x}\left(angular \text{ } mil\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)
\(\text{Left side: 1.0 } \left(radian\right) = {\color{rgb(89,182,91)} 1.0\left(radian\right)} = {\color{rgb(89,182,91)} 1.0\left(rad\right)}\)
\(\text{Right side: 1.0 } \left(angular \text{ } mil\right) = {\color{rgb(125,164,120)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}\left(radian\right)} = {\color{rgb(125,164,120)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}\left(rad\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(radian\right)={\color{rgb(20,165,174)} x}\left(angular \text{ } mil\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)
\(\text{Conversion Equation}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 2.0 \times \dfrac{π}{6.4 \times 10^{3}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{π \times 2.0}{6.4 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π \times 2.0}{6.4 \times 10^{3}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{6.4 \times 10^{3}}{π \times 2.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π \times 2.0}{6.4 \times 10^{3}} \times \dfrac{6.4 \times 10^{3}}{π \times 2.0} = 1.0 \times \dfrac{6.4 \times 10^{3}}{π \times 2.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}} \times {\color{rgb(166,218,227)} \cancel{6.4}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}}}{{\color{rgb(166,218,227)} \cancel{6.4}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}}} = 1.0 \times \dfrac{6.4 \times 10^{3}}{π \times 2.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.4 \times 10^{3}}{π \times 2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1018.5916358\approx1.0186 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(radian\right)\approx{\color{rgb(20,165,174)} 1.0186 \times 10^{3}}\left(angular \text{ } mil\right)\)
