us to ns Converter - Microsecond to Nanosecond

Conversion derivation

Express both us and ns in the same base unit s (second), then cancel the shared base unit.

1. 1

   Rewrite us in the base unit

   $$1\mathrm{us}=0.000001\mathrm{s}$$
2. 2

   Rewrite ns in the base unit

   $$1\mathrm{ns}=1\times 10^{-9}\mathrm{s}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{us}& =\frac{0.000001\cancel{\mathrm{s}}}{1\times 10^{-9}\cancel{\mathrm{s}}}\times 1\mathrm{ns}\\ & =\frac{0.000001}{1\times 10^{-9}}\mathrm{ns}\\ & =1,000\mathrm{ns}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{ns}& =\frac{1\times 10^{-9}\cancel{\mathrm{s}}}{0.000001\cancel{\mathrm{s}}}\times 1\mathrm{us}\\ & =\frac{1\times 10^{-9}}{0.000001}\mathrm{us}\\ & =0.001\mathrm{us}\end{array}$$