J to eV Converter - Joule to Electron Volt

Conversion derivation

Express both J and eV in the same base unit J (joule), then cancel the shared base unit.

1. 1

   Rewrite J in the base unit

   $$1\mathrm{J}=1\mathrm{J}$$
2. 2

   Rewrite eV in the base unit

   $$1\mathrm{eV}=1.60217663\times 10^{-19}\mathrm{J}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{J}& =\frac{1\cancel{\mathrm{J}}}{1.60217663\times 10^{-19}\cancel{\mathrm{J}}}\times 1\mathrm{eV}\\ & =\frac{1}{1.60217663\times 10^{-19}}\mathrm{eV}\\ & =6.24150907\times 10^{18}\mathrm{eV}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{eV}& =\frac{1.60217663\times 10^{-19}\cancel{\mathrm{J}}}{1\cancel{\mathrm{J}}}\times 1\mathrm{J}\\ & =\frac{1.60217663\times 10^{-19}}{1}\mathrm{J}\\ & =1.60217663\times 10^{-19}\mathrm{J}\end{array}$$