======================================== progress report on metrication of the UK ======================================== by Andrew Main (Zefram) 2006-03-31 abstract -------- The state of metrication in the UK is surveyed, with a view to resolving the remaining uses of non-metric units. Many such situations are identified, and the correct metric units indicated. table of contents ----------------- 0. introduction 0.0. motivation 0.1. acknowledgements 0.2. principles 1. uses of non-metric units in UK public life 1.0. travel 1.1. cars 1.2. domestic utilities 1.3. body measurements 1.4. health 1.5. popular science 1.6. economics 1.7. technical products 1.8. quantities of goods 1.9. time 1.10. music 1.11. miscellaneous 2. notable uses of metric units in UK public life 3. conclusion 4. references 0. introduction =============== 0.0. motivation --------------- The UK has been very gradually switching from the predominant use of Imperial units of measurement to the metric system since 1864. This paper does not address the issue of whether this was a good idea. The case for metrication in the UK is explored in great depth in [VBM]; opposing views can be found in [DESTRUCT], [ANTIMETRIC], and [BWMA]. In this paper it is assumed that the completion of the ongoing metrication is desirable. This paper therefore surveys public life in the UK to see how far the metrication process has yet to go. Analyses of metrication tend to focus on only a few types of measurement, and examine the details of switching those few to metric units. This paper aims to comprehensively cover all types of currently non-metric measurement, but for the most part does not address the practicalities of conversion. 0.1. acknowledgements --------------------- I am grateful to Benjohn Barnes, Mike Crowe, Neal Hughes, Steve Marvell, Anthony Milbourne, and Christopher Soanes for discussion on a draft of this work. 0.2. principles --------------- For the purposes of this survey, metric units consist of three categories of unit: (a) coherent SI units (e.g., metre, pascal); (b) where there is no appropriate SI unit, suitable units from other authorities (e.g., bit, neper); (c) semi-coherent derived units that differ from the coherent unit by a factor of a power of ten (e.g., litre, bar); (d) incoherently-derived units that are of a naturally meaningful size for the situation (e.g., shannon, circle). It is assumed that the reader is familiar with the general principles of the metric system, including particularly the system of unit prefixes [SI-PREFIX]. Where a linear conversion is possible, conversion factors are given. All conversions specified with the "=" sign are exact. Where the exact conversion cannot be expressed as a terminating decimal fraction, an approximate decimal fraction is given, indicated with the "~" sign. Digits are grouped, with the groups separated by "_". An important aspect of the metric system is that measurements are given as a single number, using decimal fractions and a single unit. Where measurements are given using multiple units added together (e.g., "five feet and eleven inches") this is specifically pointed out, referred to as using "mixed" units. Mixed-unit measurements are much more problematic than unmixed use of non-metric units, because they must be converted to unmixed form before any calculation (including conversion to a metric unit) can be performed on them. In some cases, not only is the wrong unit being used, but the phenomenon is being described in a silly way. For example, the brightness of light bulbs is technically known as "luminous flux", and is properly measured in lumens, but it's more common to describe the brightness in terms of the power rating of an incandescent filament bulb of similar brightness. Such cases of measuring the wrong unit are discussed in the sections below, but by the nature of the situation no conversion factor can be given. Conversion in such situations is non-linear. 1. uses of non-metric units in UK public life ============================================= 1.0. travel ----------- Long geographical distances in miles. Maps universally have dual scales, but road distance signs are exclusively in miles. The latter is probably what drives common usage. Correct metric unit: metre; 1 mile = 1.609_344 km. Travel speeds in miles per hour. All road speed limits are set and indicated in miles per hour, and this is tied in with distances being in miles. The usage of miles per hour when discussing trains and planes probably follows the road usage. Correct metric unit: metre per second; 1 mph = 447.04 mm/s. Short road distances in yards. This is purely a matter of road signs. Correct metric unit: metre; 1 yard = 914.4 mm. Height and width restrictions for road vehicles in mixed feet and inches. Correct metric unit: metre; 1 foot = 304.8 mm, 1 inch = 25.4 mm. There is substantial (but not universal) dual labelling, and on private property some metric-only labelling. In nautical and aviation contexts, distances in nautical miles. Actually there are two variants of the nautical mile that are in use in the UK: the international nautical mile and the UK nautical mile. Correct metric unit: metre; 1 international nautical mile = 1.852 km, 1 UK nautical mile = 1.853 km. The nautical mile approximates the distance subtended by one arcminute of geocentric coordinates, which can be convenient when planning great circle routes. A similar relation is available with the metre if angles are measured in the metric manner: one metre approximates the distance subtended by 25 nanocircles (40 metres corresponds to 1 microcircle). In nautical and aviation contexts, speeds in knots. Correct metric unit: metre per second; 1 international knot = (1_852/3_600) m/s ~ 514.4 mm/s, 1 UK knot = (1_853/3_600) m/s ~ 514.7 mm/s. This follows the use of nautical miles for distances. Aircraft altitudes in feet. Correct metric unit: metre; 1 foot = 304.8 mm. Much of the world measures aircraft altitudes in metres, so international pilots are already familiar with this. Latitude and longitude coordinates in mixed arcdegrees, arcminutes, and arcseconds. Correct metric unit: circle; 1 arcdegree = (1/360) cr ~ 2.778 mcr, 1 arcminute = (1/21_600) cr ~ 46.30 ucr, 1 arcsecond = (1/1_296_000) cr ~ 771.6 ncr. Headings and bearings in arcdegrees. Correct metric unit: circle; 1 arcdegree = (1/360) cr ~ 2.778 mcr. 1.1. cars --------- Engine power in horsepower. Correct metric unit: watt; 1 horsepower = 745.699_871_582_270_22 W. Engine crankshaft rotation rate in revolutions per minute. Correct metric unit: hertz; 1 RPM = (1/60) Hz ~ 16.67 mHz. An incidental effect of the change to hertz is that it may become necessary to be more explicit about the quantity being measured (which is good practice in any case). Whereas "RPM" only ever refers to a physical rotation, "Hz" can refer to any type of cyclic phenomenon. Specifically, the engine cycle rate and crankshaft rotation rate can both be measured in hertz; in a four-stroke engine there are two crankshaft rotations per engine cycle. Fuel economy in miles per gallon. Correct metric unit: metre per litre; 1 mpg = (1_609.344/4.546_09) m/l ~ 354.0 m/l. Alternatively we could switch to stating fuel consumption, as is done in continental Europe, for which the correct metric unit is litre per metre. 1.2. domestic utilities ----------------------- Electrical and gas energy usage in kilowatt hours. Correct metric unit: joule; 1 kW h = 3.6 MJ. Water supply pressure in metres of water. Correct metric unit: pascal; 1 mH2O = 9.806_65 kPa. 1.3. body measurements ---------------------- Human heights in mixed feet and inches. Correct metric unit: metre; 1 foot = 304.8 mm, 1 inch = 25.4 mm. Human body mass in mixed stones, pounds, and (of babies) ounces. Correct metric unit: kilogram; 1 stone = 6.350_293_18 kg, 1 pound = 453.592_37 g, 1 ounce = 28.349_523_125 g. Most clothes sizes in inches. Correct metric unit: metre; 1 inch = 25.4 mm. Also, usually the size of the clothing is given, rather than the measurements of the body for which it is suitable, so the consumer must allow for the slack required. The new labelling standard EN 13402 [EN-13402] addresses both these issues, mandating that body measurements be indicated in centimetres. Shoe sizes, dress sizes, and ring sizes on sui generis numeric and letter scales. Should be labelled with the body measurements for which they are designed, in metres. The new standard EN 13402 [EN-13402] addresses this. Horse heights in mixed hands and inches. Correct metric unit: metre; 1 hand = 101.6 mm, 1 inch = 25.4 mm. 1.4. health ----------- Human blood pressure in millimetres of mercury. Correct metric unit: pascal; 1 mmHg = 133.322_387_415 Pa. Human heart rate in beats per minute. Correct metric unit: hertz; 1 BPM = (1/60) Hz ~ 16.67 mHz. Energy content of food in kilocalories. Correct metric unit: joule; 1 kcal = 4.184 kJ. The mandatory food nutrition labels show both units, but all discussion of nutrition uses kilocalories exclusively. This is seen even on gym machines that display the total energy expended. Furthermore, the kilocalorie is usually incorrectly stated as "calorie". Gym machines that show energy expenditure rate (power) do so in kilocalories per hour, incorrectly stated as "calories per hour". Correct metric unit: watt; 1 kcal/h = (4_184/3_600) W ~ 1.162 W. Some are dual unit, however. 1.5. popular science -------------------- Interstellar distances in light years. Correct metric unit: metre; 1 light year = 9.460_730_472_580_8 Pm. Energy content of highly energetic events in nominal equivalent tons of TNT. Correct metric unit: joule; 1 nominal ton of TNT = 4.184 GJ. Earthquake magnitudes on the moment magnitude scale. Correct metric unit: joule; conversion is non-linear. Acidity on the pH scale. Should be stated as concentration of H^+ ions in moles per litre; conversion is non-linear. Temperatures (especially ambient temperatures of human-habitable locations, but also in other contexts) in degrees Celsius. Correct metric unit: kelvin; conversion is non-linear. The magnitude of the units is actually equal, and the difference is in where the zero point is. An ice-point-relative temperature of 0 Cel is equivalent to a thermodynamic temperature of 273.15 K. 1.6. economics -------------- Commodity prices for precious metals are quoted per "ounce" (actually troy ounce). Correct metric unit: kilogram; 1 troy ounce = 31.103_476_8 g. Internationally the kilogram is already used in addition to the troy ounce. Commodity prices for oil are quoted per barrel. Correct metric unit: litre; 1 oil barrel = 158.987_294_928 l. Stock and price index changes in (arbitrary) index points. Correct metric unit: neper; conversion is non-linear. The neper is the unit for measuring ratios, including proportional changes. Sometimes an index change is given as a percentage, which is better than the raw index points, but percentage changes don't add up properly. Nepers can be added. Interest rates are specified in terms of equivalent annual proportional change. Correct metric unit: neper per second; conversion is non-linear. 1.7. technical products ----------------------- Luminous flux from interior lighting products is often stated in terms of equivalent incandescent bulb power (in watts). Correct metric unit: lumen; conversion is non-linear. This is important now that incandescent bulbs are being displaced by flourescents and other more efficient technologies. If the misusage of watts continues, it'll get awfully confusing when people grow up unfamiliar with incandescent bulbs: "Mummy, why is the 23 watt flourescent labelled "100 watt"?". Bulbs of all types now often include a proper luminous flux rating in lumens, but the power consumption and equivalent incandescent power are the most prominent ratings. Information capacity of digital storage media in octets, invariably incorrectly named "bytes". Correct metric unit: bit; 1 octet = 8 bit. Additionally, with RAM it is common to misuse the SI prefixes, for example using "kilo-" to mean 1024. The corresponding IEC binary-based prefixes [BIN-PREFIX] should be used: "kibi-" properly means 1024. Hard disks are usually labelled with correct use of SI decimal-based prefixes. Display screen sizes in inches (length of the diagonal). Correct metric unit: metre; 1 inch = 25.4 mm. Display/printer resolution in dots per inch. Correct metric unit: square root pixel per metre; 1 dot per inch = (1/25.4) px^(1/2)/mm ~ 39.37 px^(1/2)/m. Battery charge in ampere hours. Correct metric unit: coulomb; 1 A h = 3.6 kC. 1.8. quantities of goods ------------------------ Gemstone sizes are stated in carats. Correct metric unit: kilogram; 1 carat = 200 mg. Land areas in acres. Correct metric unit: are; 1 acre = 40.468_564_224 a. Draught ale, cider, etc., in pints. Correct metric unit: litre; 1 pint = 568.261_25 ml. Pre-packaged drinks sold in the same outlets are labelled in metric units, and wine and spirits are also sold in metric measures. 1.9. time --------- Sub-day time durations in mixed hours, minutes, and seconds. Correct metric unit: second; 1 h = 3.6 ks, 1 min = 60 s. This is seen in all manner of sports events, cookery, news reporting, telephone bills, and other places. This use of mixed units complicates the use of time durations in combination with any other measurements, such as to determine the speed of a runner. Because time is such a frequently-required quantity, and very frequently combined with other quantities, this has enormous effects. Super-day time durations in days, months, or years (usually unmixed). For geological time periods this is confusing because the modern day and year lengths do not match the historical day and year lengths. In any case, as units of duration these are poorly defined. Generally, calendar units should be used only when discussing actual calendar dates, not for general specification of time durations. 1.10. music ----------- Music tempo in beats per minute. Correct metric unit: hertz; 1 BPM = (1/60) Hz ~ 16.67 mHz. In music analysis, pitch intervals are precisely specified in cents. Correct metric unit: shannon (a.k.a. "octave"); 1 cent = (1/1_200) Sh ~ 833.3 uSh. The cent, being 1/100 of a semitone, only makes sense from the point of view of Western music's twelve-note scale. The octave, however, is a nearly universal concept. 1.11. miscellaneous ------------------- Wind speeds in miles per hour. Correct metric unit: metre per second; 1 mph = 447.04 mm/s. Horse race distances in mixed miles, furlongs, and yards. Correct metric unit: metre; 1 mile = 1.609_344 km, 1 furlong = 201.168 m, 1 yard = 914.4 mm. Racing enthusiasts are already familiar with races run in metric distances, because of races in Dubai televised on British channels. Typographic measurements in points. Correct metric unit: metre; 1 point = (25.4/72.27) mm ~ 351.5 um. Actually there are several versions of the typographic point; this conversion factor is for the most popular. Knitting needle diameters are often (but not always) given on a sui generis numeric scale. The diameter should be specified using the metre; conversion is non-linear. It would actually make more sense to specify the circumference than the diameter, because it is the circumference that directly determines stitch size. Angles in arcdegrees. Correct metric unit: circle; 1 arcdegree = (1/360) cr ~ 2.778 mcr. Wire diameters on a sui generis numerical scale. The diameter should be specified using the metre, or cross-sectional area in square metres; conversion is non-linear. Some construction materials are described by non-metric sizes. For example, dimensional lumber may have its cross-sectional size described approximately in inches, though by law its linear extent must be priced using the metre. Being only approximate descriptions, rather than precise measurements, these would be particularly easy to change to metric equivalents: "two by four" (inches) lumber could be equally well described as "five by ten" (centimetres). 2. notable uses of metric units in UK public life ================================================= Most goods are packaged and priced using metric quantities. There is some dual labelling, which will be phased out by 2010. However, some vendors make the non-metric labelling more prominent than the metric labelling, and a few illegally fail to provide any metric labelling. Construction plans use exclusively metric units. Most construction materials are sized in metric units. Vehicle tyre pressure is given in bars. However, it's also given in pounds-force per square inch. Nutrition labelling is in metric units, except that energy value is dual labelled (in kilocalories as well as kilojoules). Body mass index is always calculated in kilograms per square metre, though this unit is usually not stated. The national grid, used by most maps, is metric-based. Ordnance Survey maps all have metric scales and show elevations in metres. Education is solely in metric units, and has been for decades. Currency was decimalised in 1971, and so is compatible with the metric system. ISO (metric-based) paper sizes are used universally. The energy density of gas supplied domestically is given in megajoules per cubic metre. However, the unit is not actually stated on the bill; instead it is given as a dimensionless number, and the equations used to calculate with it use numbers rather than quantities. Relative power and volume are stated in decibels. However, the neper is a more proper metric unit than the bel, and is more likely to become an official SI unit. In any case, the bel is very misunderstood. Air pressure is stated in millibars. This is a metric unit, but it would be more properly referred to as "hectopascal". Electrical parameters are universally stated in volts, amperes, ohms, watts, and hertz. Radiation equivalent doses are universally stated in millisieverts. Thermal resistivity of cloth is stated in tog. Audio and radio frequencies are universally stated in hertz. Most medical measurements are metric. For example, blood cholesterol load is given in millimoles per litre, though in this case the unit is often not stated. The Highway Code uses metres in describing driving behaviour. Athletic race distances are mostly metric. In rugby union the field dimensions are metric. 3. conclusion ============= This report has identified 51 distinct areas in which correct metric units are not being used. Clearly there is a long way to go before the country is fully metricated. The UK's metric conversion has been unnecessarily spun out over decades. Most countries underwent conversion much more rapidly, and without apparent ill effects. Only the US has followed a similarly slow route, and the US remains the only country that is less metricated than the UK. Experience in all countries shows that people rapidly grow accustomed to new units once they are introduced, despite popular anticipation of difficulty. This has occurred not only with switching to metric units of measurement, but also in the case of the logistically more difficult currency changes. The decimalisation of the pound sterling in 1971 stands as an example of how smoothly these changes go in practice [D-DAY]. Even this, though, pales in comparison to Sweden's change in 1967 from driving on the left side of the road to driving on the right, accomplished without a single fatality [DAGEN-H]. Even the most difficult changes of units of measurement do not present the logistical problems that were faced in Dagen H or Decimal Day. In most cases that are subject to regulation, little planning is required other than a legal mandate to use the metric unit. In cases where there is no legal impediment, all that is required is an act of initiative from individual users of units. Once metric units have become familiar in a particular situation, the tendency is for the less convenient non-metric units to gradually fall out of practical use. The process is much less painful than is popularly imagined. 4. references ============= [ANTIMETRIC] starship forty2, "Antimetric Sentiments", . [BIN-PREFIX] International Electrotechnical Commission, "Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics", IEC 60027-2, 2005-08-11. [BWMA] British Weights and Measures Association, "BWMA Online", . [D-DAY] Wikipedia, "Decimal Day", . [DAGEN-H] Wikipedia, "Dagen H", . [DESTRUCT] P. Brian, "Metrication - the wilful destruction of culture", 10th Sep. 2004, . [EN-13402] European Committee for Standardization, "Size designation of clothes. Terms, definitions and body measurement procedure", EN 13402-1, 2001. [SI-PREFIX] Bureau International des Poids et Mesures, "SI prefixes", . [VBM] Robin Paice (ed.), "A very British mess", 2004, ISBN 0750310146.