km to nm Converter - Kilometer to Nanometer

Conversion derivation

Express both km and nm in the same base unit m (meter), then cancel the shared base unit.

1. 1

   Rewrite km in the base unit

   $$1\mathrm{km}=1,000\mathrm{m}$$
2. 2

   Rewrite nm in the base unit

   $$1\mathrm{nm}=1\times 10^{-9}\mathrm{m}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{km}& =\frac{1,000\cancel{\mathrm{m}}}{1\times 10^{-9}\cancel{\mathrm{m}}}\times 1\mathrm{nm}\\ & =\frac{1,000}{1\times 10^{-9}}\mathrm{nm}\\ & =1\times 10^{12}\mathrm{nm}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{nm}& =\frac{1\times 10^{-9}\cancel{\mathrm{m}}}{1,000\cancel{\mathrm{m}}}\times 1\mathrm{km}\\ & =\frac{1\times 10^{-9}}{1,000}\mathrm{km}\\ & =1\times 10^{-12}\mathrm{km}\end{array}$$