# Convert EMU to ESU

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

## Calculation Breakdown

Set up the equation
$$1.0\left(EMU\right)={\color{rgb(20,165,174)} x}\left(ESU\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(farad\right)$$
$$\text{Left side: 1.0 } \left(EMU\right) = {\color{rgb(89,182,91)} 10^{9}\left(farad\right)} = {\color{rgb(89,182,91)} 10^{9}\left(F\right)}$$
$$\text{Right side: 1.0 } \left(ESU\right) = {\color{rgb(125,164,120)} 1.1126 \times 10^{-12}\left(farad\right)} = {\color{rgb(125,164,120)} 1.1126 \times 10^{-12}\left(F\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(EMU\right)={\color{rgb(20,165,174)} x}\left(ESU\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{9}} \times {\color{rgb(89,182,91)} \left(farad\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.1126 \times 10^{-12}}} \times {\color{rgb(125,164,120)} \left(farad\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10^{9}} \cdot {\color{rgb(89,182,91)} \left(F\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.1126 \times 10^{-12}} \cdot {\color{rgb(125,164,120)} \left(F\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{9}} \cdot {\color{rgb(89,182,91)} \cancel{\left(F\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.1126 \times 10^{-12}} \times {\color{rgb(125,164,120)} \cancel{\left(F\right)}}$$
$$\text{Conversion Equation}$$
$$10^{9} = {\color{rgb(20,165,174)} x} \times 1.1126 \times 10^{-12}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 1.1126 \times 10^{-12} = 10^{9}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{1.1126 \times 10^{-12}}\right)$$
$${\color{rgb(20,165,174)} x} \times 1.1126 \times 10^{-12} \times \dfrac{1.0}{1.1126 \times 10^{-12}} = 10^{9} \times \dfrac{1.0}{1.1126 \times 10^{-12}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.1126}} \times {\color{rgb(99,194,222)} \cancel{10^{-12}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.1126}} \times {\color{rgb(99,194,222)} \cancel{10^{-12}}}} = 10^{9} \times \dfrac{1.0}{1.1126 \times 10^{-12}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{9}}{1.1126 \times 10^{-12}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-12}}\text{ can be rewritten to }10^{12}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{12} \times 10^{9}}{1.1126}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{21}}{1.1126}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx8.9879561388 \times 10^{20}\approx8.988 \times 10^{20}$$
$$\text{Conversion Equation}$$
$$1.0\left(EMU\right)\approx{\color{rgb(20,165,174)} 8.988 \times 10^{20}}\left(ESU\right)$$