Per mille

‰
‰
Per mille
In Unicode	U+2030 ‰ PER MILLE SIGN (&permil;)
Related
See also	U+0025 % PERCENT SIGN; U+2031 ‱ PER TEN THOUSAND SIGN (Basis point)

The phrase per mille (from Latin per mīlle 'in each thousand')^[1] indicates parts per thousand.^[2] The associated symbol is ‰, similar to a per cent sign % but with an extra zero in the divisor.

Major dictionaries do not agree on the spelling,^[1]^[2]^[3] giving other options of per mil,^[2] per mill,^[1]^[3] permil,^[1]^[4] permill,^[1] permille.^[5]^[6]

The word promille is the cognate in Dutch, German, Finnish and Swedish, and is sometimes seen as a loanword in English with the same meaning as per mille.^[7]^[4]

The symbol is included in the General Punctuation block of Unicode at U+2030 ‰ PER MILLE SIGN.^[5] There is also an Arabic-Indic per mille sign at U+0609 ؉ ARABIC-INDIC PER MILLE SIGN.

Examples

Blood alcohol concentration

Promille and permille are likely best known as shorthand terms for Blood Alcohol Concentration, where 1 promille corresponds to 1 gram of alcohol per liter of blood.^[8] Promille is used in the legal limits of blood-alcohol content for driving a road vehicle in some countries: for example: 0.5‰ or 0.8‰.^[9]

Cost per mille

Sales and marketing

Cost per mille (CPM), the price of 1000 units, may be used for views of banner and display advertising, and for emails delivered by email service providers.

Insurance

In UK insurance usage, the cost per mille is the rate per £1000 of insured value.^[10] In India, the premium per mille is the rate expressed as thousandths of the sum assured.^[11]

Gradients

Gradients (in some countries in Europe) may be expressed as mm/m or m/km, and written with the per mille symbol.^[12]

Isotope ratios

Per mille may be used to express stable-isotope ratios—for example: "δ¹³C was measured at −3.5‰"

Taxation

Charity fraction

In Italy, it is possible to nominate a charity or charities to receive "five per mille" (5‰) of personal taxation payments.^[13]

Property tax

Property taxation rates may be expressed as the millage rate (U.S.) or mill rate (Canada), from mill (currency), one thousandth of a dollar.

Quantile

Permille may also be used to express a 1000-quantile ("999th permille"),^[14]^[15] but this usage is rare and largely obsolete. Modern publications instead use fractional percentiles ("99.9th percentile").^[16]

Salinity

Seawater salinity is often expressed per mille. Average marine salinity is about 35 parts per thousand or 35‰ (3.5%).^[17]

Related units

Percentage point difference of 1 part in 100
Percentage (%) 1 part in 100
Basis point (bp) difference of 1 part in 10,000
Permyriad (‱) 1 part in 10,000
Per cent mille (pcm) 1 part in 100,000

Notes

References

^ ^a ^b ^c ^d ^e "per mil". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
^ ^a ^b ^c "per mille". Cambridge Dictionary. Business English. Cambridge: Cambridge University Press. Retrieved 2020-06-08. per mille adverb (also per mil)
^ ^a ^b "per mill". Oxford Dictionaries: The American Dictionary. Archived from the original on August 9, 2013. Retrieved 2014-08-01.
^ ^a ^b Heinz Gamsjäger; John W. Lorimer; Pirketta Scharlin; David G. Shaw (2008). "Glossary of terms related to solubility". Pure Appl. Chem. 80 (2): 233–276. doi:10.1351/pac200880020233. (Page 258)
^ ^a ^b Unicode. "General Punctuation". 2014. Accessed 5 Aug 2014.
^ "per mille". Longman Business Dictionary. Retrieved 2020-07-01.
^ "Promille in English". Cambridge German – English Dictionary. Cambridge University Press. Retrieved 24 September 2023.
^ "Promille vs BAC: the difference and how much promille is 1 BAC". AlcoSafe. Retrieved 24 September 2023.
^ "Blood alcohol level (BAL)". Health Research Board (Ireland).
^ Jonathan Law; John Smullen (eds.). "Per mille". A Dictionary of Finance and Banking (4 ed.).
^ "Avoidable loss due to imprudent underwriting of Group Personal Accident Policy" (PDF). Comptroller and Auditor General of India. March 2019.
^ Michael W. Sayers; Thomas D. Gillespie; William D.O. Paterson (January 1986). "Directives pour la mesure de l'uni des routes et l'étalonnage des appareils" (PDF) (in French). World Bank. p. 2. L'indice IRI est une mesure de l'uni des routes standardisée, apparentée aux mesures obtenues à l'aide des appareils de type-réponse. Les unités recommandées sont : les mètres par kilomètres (m/km) = millimètres par mètres (mm/m) = pente x 1000.
^ "Five per thousand—how does it work and how is it calculated?". N26 (bank). 22 June 2021. Retrieved 19 November 2023.
^ Walker, Helen Mary; Lev, Joseph (1969). Elementary Statistical Methods. Holt, Rinehart and Winston. ISBN 978-0-03-081130-2.
^ Valentijn, Floris Arnold (21 September 2022). Senescent cell accumulation & Research-based undergraduate education (Thesis). Utrecht University. doi:10.33540/1121.
^ Knoppert, Sebastiaan N; Keijzer-Veen, Mandy G; Valentijn, Floris A; van den Heuvel-Eibrink, Marry M; Lilien, Marc R; van den Berg, Gerrit; Haveman, Lianne M; Stokman, Marijn F; Janssens, Geert O; van Kempen, Sven; Broekhuizen, Roel; Goldschmeding, Roel; Nguyen, Tri Q (December 2023). "Cellular senescence in kidney biopsies is associated with tubular dysfunction and predicts CKD progression in childhood cancer patients with karyomegalic interstitial nephropathy". The Journal of Pathology. 261 (4): 455–464. doi:10.1002/path.6202. PMID 37792603.
^ "Per mille". Glossary of Meteorology. American Meteorological Society. 2022.