ppm to molec/cm³ Converter - Parts per million to Molecules per cubic centimeter

Conversion derivation

Express both ppm and molec/cm³ in the same base unit mol/L (molar), then cancel the shared base unit.

1. 1

   Rewrite ppm in the base unit

   $$1\mathrm{ppm}=0.000001mol/L$$
2. 2

   Rewrite molec/cm³ in the base unit

   $$1molec/c{\mathrm{m}}^3=1.66053907\times 10^{-27}mol/L$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{ppm}& =\frac{0.000001\cancel{mol/L}}{1.66053907\times 10^{-27}\cancel{mol/L}}\times 1molec/c{\mathrm{m}}^3\\ & =\frac{0.000001}{1.66053907\times 10^{-27}}molec/c{\mathrm{m}}^3\\ & =6.02214076\times 10^{20}molec/c{\mathrm{m}}^3\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1molec/c{\mathrm{m}}^3& =\frac{1.66053907\times 10^{-27}\cancel{mol/L}}{0.000001\cancel{mol/L}}\times 1\mathrm{ppm}\\ & =\frac{1.66053907\times 10^{-27}}{0.000001}\mathrm{ppm}\\ & =1.66053907\times 10^{-21}\mathrm{ppm}\end{array}$$