Convert arc second to radian

Learn how to convert 1 arc second to radian step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(arc \text{ } second\right)={\color{rgb(20,165,174)} x}\left(radian\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)

\(\text{Left side: 1.0 } \left(arc \text{ } second\right) = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(rad\right)}\)

\(\text{Right side: 1.0 } \left(radian\right) = {\color{rgb(125,164,120)} 1.0\left(radian\right)} = {\color{rgb(125,164,120)} 1.0\left(rad\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(arc \text{ } second\right)={\color{rgb(20,165,174)} x}\left(radian\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{π}{6.48 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times 1.0\)

\(\text{Simplify}\)

\(\dfrac{π}{6.48 \times 10^{5}} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = \dfrac{π}{6.48 \times 10^{5}}\)

Rewrite equation

\(\dfrac{1.0}{10^{5}}\text{ can be rewritten to }10^{-5}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{-5} \times π}{6.48}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx0.0000048481\approx4.8481 \times 10^{-6}\)