erg to kJ Converter - Erg to Kilojoule

Conversion derivation

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

1. 1

   Rewrite erg in the base unit

   $$1\mathrm{erg}=1\times 10^{-7}\mathrm{J}$$
2. 2

   Rewrite kJ in the base unit

   $$1\mathrm{kJ}=1,000\mathrm{J}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{erg}& =\frac{1\times 10^{-7}\cancel{\mathrm{J}}}{1,000\cancel{\mathrm{J}}}\times 1\mathrm{kJ}\\ & =\frac{1\times 10^{-7}}{1,000}\mathrm{kJ}\\ & =1\times 10^{-10}\mathrm{kJ}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{kJ}& =\frac{1,000\cancel{\mathrm{J}}}{1\times 10^{-7}\cancel{\mathrm{J}}}\times 1\mathrm{erg}\\ & =\frac{1,000}{1\times 10^{-7}}\mathrm{erg}\\ & =1\times 10^{10}\mathrm{erg}\end{array}$$