Parts per million calculations are used for measuring small concentrations in a solution, solid and gas or the number of defects in manufacturing. The basic formula for PPM starts with dividing the weight or number of defects by the volume and then multiplying the result by 1,000,000. This formula is used by people in the agricultural industry for fertilizer calculations, by water treatment professionals, in swimming pool chlorine calculations, and in laboratories by chemists and others.

## The Basic Formula

The basic formula is weight (or number of defects) divided by volume multiplied by 1,000,000 – or w/v x 1,000,000. For example, if you have 100 defective products in 10,000 manufactured pieces, divide 100 by 10,000 to arrive at the result of 0.01 or 1 percent of the total. Then, multiply 0.01 by 1,000,000 to achieve the answer of 10,000 defective parts per million parts produced.

## Solid Calculations

To calculate the PPM of one solid mixed with another, you compare the mass of the two substances. Divide the mass of the first solid in milligrams by the mass of the second solid in kilograms. (A kilogram is one million milligrams.) Using the example of 200 mg of gold mixed with 2.5 kg of iron:

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200 milligrams/2.5 kilograms = 80 ppm

There are 80 parts of gold per million parts of iron in this example.

## Liquid Calculations

For liquid calculations, use the formula ppm = pounds/1m gallons or ppm = milligrams/liter. (Where one liter is the volume equivalent of one kilogram.) In swimming pool chlorine calculations, for example, the parts per million are measured in milligrams of chlorine per liter of water. Using the example of 47 milligrams of chlorine in 17 liters of water:

47 milligrams/17 liters = 2.765 ppm

There are 2.765 parts of chlorine per liter of water. This type of calculation allows you to measure liquid constituents in small amounts.

## Water Quality and Treatment

The PPM calculation is used by water treatment professionals when adding chemicals to water to ensure it is safe to drink. The measurement is the mass of a chemical per unit volume of water. When you read a water treatment facility’s water quality reports, you might see ppm, mg/L or ug/L. The last item refers to the number of micrograms per a liter of water – 1 milligram = 1,000 micrograms.

## Parts Per Billion

Sometimes the formula may be expressed in parts per billion instead of parts per million. In this example, 1 part per million = 1,000 parts per billion or 1PPM = 1,000 PPB. Another way to express PPM and PPB looks like this. PPM = (10^{6}) and PPB = (10^{9}) or (10^6) and (10^9).