Convert gradian to radian

Learn how to convert 1 gradian to radian step by step.

Calculation Breakdown

Set up the equation

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

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

\(\text{Left side: 1.0 } \left(gradian\right) = {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}\left(rad\right)}\)

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

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

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

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

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{π}{2.0 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times 1.0\)

\(\text{Simplify}\)

\(\dfrac{π}{2.0 \times 10^{2}} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = \dfrac{π}{2.0 \times 10^{2}}\)

Rewrite equation

\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times π}{2.0}\)

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

\({\color{rgb(20,165,174)} x}\approx0.0157079633\approx1.5708 \times 10^{-2}\)