# Convert ESU of charge to EMU of charge

Learn how to convert 1 ESU of charge to EMU of charge step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(ESU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(EMU \text{ } of \text{ } charge\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(coulomb\right)$$
$$\text{Left side: 1.0 } \left(ESU \text{ } of \text{ } charge\right) = {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}\left(coulomb\right)} = {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}\left(C\right)}$$
$$\text{Right side: 1.0 } \left(EMU \text{ } of \text{ } charge\right) = {\color{rgb(125,164,120)} 10.0\left(coulomb\right)} = {\color{rgb(125,164,120)} 10.0\left(C\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(ESU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(EMU \text{ } of \text{ } charge\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10.0}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10.0} \cdot {\color{rgb(125,164,120)} \left(C\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10.0} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}$$
$$\text{Conversion Equation}$$
$$3.33564 \times 10^{-10} = {\color{rgb(20,165,174)} x} \times 10.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 10.0 = 3.33564 \times 10^{-10}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{10.0}\right)$$
$${\color{rgb(20,165,174)} x} \times 10.0 \times \dfrac{1.0}{10.0} = 3.33564 \times 10^{-10} \times \dfrac{1.0}{10.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10.0}}} = 3.33564 \times 10^{-10} \times \dfrac{1.0}{10.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{3.33564 \times 10^{-10}}{10.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 3.33564 \times 10^{-11}\approx3.3356 \times 10^{-11}$$
$$\text{Conversion Equation}$$
$$1.0\left(ESU \text{ } of \text{ } charge\right)\approx{\color{rgb(20,165,174)} 3.3356 \times 10^{-11}}\left(EMU \text{ } of \text{ } charge\right)$$