ug to mg Converter - Microgram to Milligram

Conversion derivation

Express both ug and mg in the same base unit kg (kilogram), then cancel the shared base unit.

1. 1

   Rewrite ug in the base unit

   $$1\mathrm{ug}=1\times 10^{-9}\mathrm{kg}$$
2. 2

   Rewrite mg in the base unit

   $$1\mathrm{mg}=0.000001\mathrm{kg}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{ug}& =\frac{1\times 10^{-9}\cancel{\mathrm{kg}}}{0.000001\cancel{\mathrm{kg}}}\times 1\mathrm{mg}\\ & =\frac{1\times 10^{-9}}{0.000001}\mathrm{mg}\\ & =0.001\mathrm{mg}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{mg}& =\frac{0.000001\cancel{\mathrm{kg}}}{1\times 10^{-9}\cancel{\mathrm{kg}}}\times 1\mathrm{ug}\\ & =\frac{0.000001}{1\times 10^{-9}}\mathrm{ug}\\ & =1,000\mathrm{ug}\end{array}$$