# Is 1% m/m the same as 1% w/w?

Hydrocortisone cream seems to be sold as 1% w/w, but my cream is 1% m/m, which is confusing. Are they the same units or the same concentrations?

“[M]ass is the amount of "matter" in an object (though "matter" may be difficult to define), whereas weight is the force exerted on an object by gravity.” (Wikipedia quoting [de Silva, G.M.S. (2002), Basic Metrology for ISO 9000 Certification, Butterworth-Heinemann, 214p.]

Well-known relationship:

$$W = m \times g$$

where W is weight, m is mass and g is the acceleration of gravity.

Because g is a constant that cancels out in a ratio, mass/mass and weight/weight are identical.

Likewise, the ratios % m/m and % W/W are identical.

• Indeed m/m would be more appropriate. Thumb up for the pharmacists. – Alchimista Jan 21 at 10:39

The symbol “w/w” is more often used in chemistry, whereas its equivalent “m/m” is favored in pharmaceutical industry. For instance, European Pharmacopoeia in section 1.2. Other provisions applying to general chapters and monographs suggests the following methods for expressing concentration [1, p. 4]:

Expression of content. In defining content, the expression ‘per cent’ is used according to circumstances with one of 2 meanings:

– per cent m/m (percentage, mass in mass) expresses the number of grams of substance in 100 g of ﬁnal product;
– per cent V/V (percentage, volume in volume) expresses the number of millilitres of substance in 100 mL of final product.

The expression ‘parts per million’ (or ppm) refers to mass in mass, unless otherwise specified.

Please note, however, that this is a somewhat flawed definition: neither of physical quantities such as “mass” or “volume” should be called or referred to as to “number of grams” or “number of millilitres”, respectively. Also, neither w/w, V/V or m/m, despite their widespread usage, are considered correct by the BIPM [2, p. 149]:

### 5.4.2 Quantity symbols and unit symbols

Unit symbols must not be used to provide specific information about the quantity and should never be the sole source of information on the quantity. Units are never qualified by further information about the nature of the quantity; any extra information on the nature of the quantity should be attached to the quantity symbol and not to the unit symbol.

For example:

The maximum electric potential difference is $$U_\mathrm{max} = \pu{1000 V}$$ but not $$U = \pu{1000 V_\mathrm{max}}.$$ The mass fraction of copper in the sample of silicon is $$w(\ce{Cu}) = \pu{1.3E−6}$$ but not $$\pu{1.3E−6 w/w}.$$

Considering the aforementioned guidelines, the hydrocortisone (HCT) content should ideally be depicted as $$w(\text{HCT}) = 1\,\%$$ to avoid ambiguity.

### References

1. Council of Europe; European Directorate for the Quality of Medicines & Healthcare. European Pharmacopoeia 8.0; European Directorate for the Quality of Medicines & Healthcare, Council of Europe: Strasbourg, 2013. ISBN 978-92-871-7525-0.
2. BIPM. Le Système International d’unitès / The International System of Units (“The SI Brochure”), 9th ed.; Bureau international des poids et mesures: Sèvres, 2019. (PDF)