# Convert second of arc to gradian

Learn how to convert 1 second of arc to gradian step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(second \text{ } of \text{ } arc\right)={\color{rgb(20,165,174)} x}\left(gradian\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(radian\right)$$
$$\text{Left side: 1.0 } \left(second \text{ } of \text{ } arc\right) = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}\left(rad\right)}$$
$$\text{Right side: 1.0 } \left(gradian\right) = {\color{rgb(125,164,120)} \dfrac{π}{2.0 \times 10^{2}}\left(radian\right)} = {\color{rgb(125,164,120)} \dfrac{π}{2.0 \times 10^{2}}\left(rad\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(second \text{ } of \text{ } arc\right)={\color{rgb(20,165,174)} x}\left(gradian\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{2.0 \times 10^{2}}}} \times {\color{rgb(125,164,120)} \left(radian\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{2.0 \times 10^{2}}} \cdot {\color{rgb(125,164,120)} \left(rad\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{2.0 \times 10^{2}}} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{6.48 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{2.0 \times 10^{2}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{6.48 \times {\color{rgb(99,194,222)} \cancelto{10^{3}}{10^{5}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{2.0 \times {\color{rgb(99,194,222)} \cancel{10^{2}}}}$$
$$\text{Simplify}$$
$$\dfrac{1.0}{6.48 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.0} = \dfrac{1.0}{6.48 \times 10^{3}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{2.0}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.0} \times \dfrac{2.0}{1.0} = \dfrac{1.0}{6.48 \times 10^{3}} \times \dfrac{2.0}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{2.0}}}{{\color{rgb(99,194,222)} \cancel{2.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 2.0}{6.48 \times 10^{3} \times {\color{rgb(255,204,153)} \cancel{1.0}}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{2.0}{6.48 \times 10^{3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 2.0}{6.48}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.000308642\approx3.0864 \times 10^{-4}$$
$$\text{Conversion Equation}$$
$$1.0\left(second \text{ } of \text{ } arc\right)\approx{\color{rgb(20,165,174)} 3.0864 \times 10^{-4}}\left(gradian\right)$$