# ppm - calculation and conversion

ppm is an abbreviation of parts per million. ppm is used to describe very low concentrations. In this page, you will know how to calculate ppm and how to convert ppm into ％.

Contents

## What is ppm?

ppm is an abbreviation of "parts per million." This is equivalent to 10^{-6}. ppm is the same kind of unit as ％ (％ is equivalent to 10^{-2}).

ppm is mainly used to describe very low concentrations of substances in environment.

For example, ppm is used to measure the concentration of CO_{2} in the air. If there is 1 mL of CO_{2} in 1 m^{3} of the air, then the concentration of CO_{2} is 1 ppm (= 1 mL/m^{3} = 1 cm^{3}/m^{3}).

When ppm is used to measure the very low concentartions of substances in water, ppm is approximately equal to mg/L because 1 L of solution is approximately 1 kg in very weak water.

## How to calculate ppm

One mg of chlorine is dissolved in 1 L of water. Calculate the concentration of chlorine (C_{Cl2}).

Answer

\begin{align*} \text{C}_{\text{Cl}_\text{2}} &= \frac{\text{m}_\text{solute}}{\text{m}_\text{solution}} \times 10^6 \,\text{ppm} \\ &= \frac{1 \,\text{mg}}{1 \,\text{kg}} \times 10^6 \,\text{ppm} \\ &= \frac{1 \times 10^{-3} \,\text{g}}{1 \times 10^3 \,\text{g}} \times 10^6 \,\text{ppm} \\ &= 1 \,\text{ppm} \end{align*}

When you calculate in ％, you will use

Concentration = Ratio × 100 %

In similar way, you can calculate in ppm as follows.

Concentration = Ratio × 1,000,000 ppm

### Calculate a content from ppm

Calculate the volume of CO_{2} in 1 L of air. The concentartion of CO_{2} is 400 ppm.

Answer

ppm means parts per million. So you can substitute 10^{-6} for ppm.

\begin{align*} \text{V}_{\text{CO}_\text{2}} &= \text{V}_\text{total} \times \text{ratio} \\ &= 1 \,\text{L} \times 400 \,\text{ppm} \\ &= 1 \,\text{L} \times \left( 400 \times 10^{-6} \right) \\ &= 4.00 \times 10^{-4} \,\text{L} \\ &= 0.400 \,\text{mL} \end{align*}

## How to convert ppm into ％

ppm shows that the value is multiplied 1 million (10^{6}), and ％ shows that the value is multiplied 1 hundred (10^{2}).

So in order to convert ppm into ％, you will multiply 10^{-4} (0.0001) by the value. On the contrary, in order to convert ％ into ppm, you will multiply 10^{4} (10000) by the value.

Following list is example of conversion.

- $ \hphantom{0000} 1 \,\text{ppm} = 0.0001 \hphantom{}\,\% $
- $ \hphantom{000} 10 \,\text{ppm} = 0.001 \hphantom{0}\,\% $
- $ \hphantom{00} 100 \,\text{ppm} = 0.01 \hphantom{00}\,\% $
- $ \hphantom{0} 1000 \,\text{ppm} = 0.1 \hphantom{000}\,\% $
- $ \hphantom{} 10000 \,\text{ppm} = 1 \hphantom{0000.}\,\% $

For example, the concentration of CO_{2} in the air is about 400 ppm, and this is converted into 0.04 ％.