# 1ppm – Have You Ever Wondered What 1ppm Means?

*Stive has BEng Hons 1st Cl Electronics w/masters level modules from the O.U. and is retired from 45+ years in various fields of electronics.*

## Why ppm - What Is It? What Does it Mean?

1ppm literally means “one Part-Per-Million(-parts)” and could be described as either “one part-in-a-million(-parts)” or “1 part-in-one-million(-parts)”.

ppm as a standalone symbol without any numerals means parts-per-million (plural)

Many people can grasp what that means – that the liquid or solid in question, be it element, compound, substance, mixture, mineral, or other, contains one ‘foreign’ part for each 999,999 major or base parts of the material. So it is the one part in a million parts or particles.

It could also be used for gases, such as air, but the ‘foreign bodies’ in air usually are specified as ‘per volume of air’ (usually 1m^{3}), not ppm, and are also described by their physical size. The specifications for integrated circuit cleanrooms are good examples of this description.

If the 1ppm is unwanted then the base material is said to be contaminated with an unwanted foreign body or contaminant such as dust or other particle, for example, in a chocolate factory.

If the 1ppm is purposefully added then the base material has been infused or doped, such as the materials used in the manufacture of transistors and integrated circuits.

## Why use ppm and not Per Cent (%)?

Cent is a Latin root word meaning 100.

Some examples of its usage are the coinage cent, so-called because there are 100 in a dollar, and similarly centavos with pesos, centimes with francs. Other examples are century which means 100 years and, of course, the Roman Centurion, a commander of one hundred legionaries and support staff.

Earlier variations of per cent include percent (as a single word), per cent. (with a period or full stop, ‘.’), per-cent (hyphenated) and per centum (a legal term), but the modern term is per cent.

Per cent (%) literally means per-one-hundred and could easily have been designated as pph which could stand for parts-per-hundred.

And therein lies the simple relationship between percent (pph) and ppm – that ppm is actually a very much smaller amount and is in fact only 1/10,000^{th} of one percent or 0.0001% and would be too small to envisage and hence required its own designation.

__Symbol__

ppm is the common 'symbol' used, albeit initials and not a real symbol such as % (per cent) or ‰ (mille/mil). Although it is a frequently used and reasonably well known symbol, it is not a part of the S.I. system of measurement symbols.

Due to the parameter being quantity-per-quantity it is a ratio and therefore has no units of measurement.

## From % to ppm, Visually – For those who understand clearer by “seeing”, rather than the math.

% (pph) | ‰ (ppt) | pptt | ppht | ppm | |
---|---|---|---|---|---|

Accepted Name | per cent | mille / mil | n/a | n/a | ppm |

Suggested Name to Assist Understanding | parts per hundred | parts per thousand | parts per ten thousand | parts per hundred thousand | parts per million |

1% as a Fraction | 1% | 1/10 % | 1/100 % | 1/1000 % | 1/10,000 % |

1% as a Decimal Fraction | 1 % | 0.1 % | 0.01 % | 0.001 % | 0.0001 % |

## ppm Specifications

It is possible to easily calculate how many ppm-items there are in an ‘amount’, given the amount and the ppm specification.

It is often easier to explain with examples, as follows...

Take, for example, the crystal clock in your laptop, tablet, pad or smart phone. If it runs at 3.7GHz and is specified at +/-20ppm then the calculation is performed similar to percentage calculations.

If it were +/-20%, then 3.7Ghz+/-20% = 3.7x10^{9} x 20/100 = 740x10^{6} or 740MHz

Similarly with +/-20ppm, 3.7GHz+/-20ppm = 3.7x10^{9} x 20/1000000 = 74x10^{3} or 74kHz

Thus, a 3.7GHz crystal clock with a +/-20ppm specification (spec.) can be allowed to drift +/-74kHz or +/-74,000Hz (Hz means Hertz, which are the single or unit parameters of frequency).

Taking this a step further, we can calculate the upper and lower limits of the drift as follows –

3.7x10^{9} + 74x10^{3} = 3700 x10^{6} + 0.074 x10^{6} = 3700.074x10^{6} for the upper limit

3.7x10^{9} – 74x10^{3} = 3700 x10^{6} – 0.074 x10^{6} = 3699.926x10^{6} for the lower limit

__mg/kg__

In the world of chocolate, for example, the contaminant ppm specification can be easily quoted as mg/kg, or milligram-per-kilogram, because a milligram is 1/1000^{th} of a gram and a kilogram is 1000 grams and hence the mg is 1ppm of a kg.

The major contaminants in the chocolate and candy world are usually lead and cadmium and the specifications are often quoted as low as 0.1ppm which is exceedingly low.

**mg/L**

The liquids’ contaminants specifications can be quoted as mg/L and as 1L weighs 1kg then this is also 1ppm. They are sometimes quoted as fractions of ppm/Litre.

## ppm Conversions

It is possible to convert between ppm and % and vice versa.

For example, __convert 1ppm to an equivalent percentage value –__

1ppm can be written as 1/1000000. And n% can be written as n/100.

Such that 1/1000000 = n/100

Hence 100/1000000 = n.

Hence n = 0.0001

Therefore 1ppm = 0.0001%

And conversely, __convert 1% into ppm –__

n ppm can be written as n/1000000. And 1% can be written as 1/100.

So that n/1000000 = 1/100

Hence n = 1000000/100

Hence n = 10,000

Therefore 1% = 10,000ppm

__Other Conversions__

__% to Decimal Fractions__

Simply divide the given % figure by 100

Hence 25% becomes 25/100 which then further becomes 0.25 as a decimal fraction

__% to Fractions__

Simply write down the given % figure over 100

Hence 25% becomes 25/100

But now, do not reduce it to a one-line decimal fraction, as above.

Instead, reduce it to the lowest possible simple fraction.

Hence 25/100 is equivalent to ¼ as a simple fraction.

Therefore 25% = ¼

**© 2019 Stive Smyth**