J in kWh Umrechner - Joule in Kilowattstunde

Conversion derivation

Express both J and kWh 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 kWh in the base unit

   $$1\mathrm{kWh}=3,600,000\mathrm{J}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{J}& =\frac{1\cancel{\mathrm{J}}}{3,600,000\cancel{\mathrm{J}}}\times 1\mathrm{kWh}\\ & =\frac{1}{3,600,000}\mathrm{kWh}\\ & =2.77777778\times 10^{-7}\mathrm{kWh}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{kWh}& =\frac{3,600,000\cancel{\mathrm{J}}}{1\cancel{\mathrm{J}}}\times 1\mathrm{J}\\ & =\frac{3,600,000}{1}\mathrm{J}\\ & =3,600,000\mathrm{J}\end{array}$$