Common mistakes when using the metric system

Mandatory rules

The International System of Units (SI), commonly known as the metric system, is a logical, universal, and precise way to express physical quantities. But sloppy usage and unawareness of SI rules threaten to cause confusion and destroy the uniformity of the system.

Here is a list of common mistakes in using the metric system, with examples of incorrect usage and how to make them correct. Each subtopic on the left column is a link to a longer explanation at the bottom of the page.

Suggested rules

In addition to the mandatory rules above, the following table contains common usages that are not ideal. They may be popular enough to resist change or they are only minor deviations, but should be improved on when there is an opportunity to do so.

Explanation of rules

Ad hoc abbreviations (mandatory)

Don’t make up your own abbreviations for units. Metric already defines short, reasonable abbreviations, and introducing non-standard ones brings unnecessary confusion. The most common violation is sec for second, which should be s. Also, never put a period after a metric symbol unless it comes at the end of a sentence.

Plural of symbols (mandatory)

For a unit symbol (abbreviation), never add an s to the end of it. Unit symbols do not change spelling to indicate plural. Furthermore, s already means second, and juxtaposition means multiplication (for example, N s means newton times second). However, full unit names have their own set of rules for pluralization (e.g. metre vs. metres).

Capitalization of symbols (mandatory)

Metric notation is case-sensitive. For example, the prefix M means mega (10⁶) and the prefix m means milli- (10⁻³); the prefix k means kilo- and the unit K means kelvin; the unit s means second and the unit S means siemens. Forsaking the capitalization destroys useful distinctions in the metric system.

Capitalization of unit names (mandatory)

When spelled out in full, all prefix names and all unit names are in lowercase (e.g. millivolt, kiloohm, megapascal), except that degree-person must capitalize the person’s name (e.g. degree Celsius, degrees Fahrenheit). This point is a matter of convention; it won’t cause ambiguity if disobeyed.

Degree sign/word (mandatory)

The units of degree Celsius, degree Fahrenheit, and degree Rankine always contain the word degree(s) (but dropped in informal contexts). The unit kelvin must not be written with the word degree (although it did in the past). Regarding plain unit symbols without °, C means coulomb and F means farad – hence including the degree sign is critical to indicate degrees Celsius.

Multiplication/division confusion (mandatory)

The difference between multiplying and dividing units is critical when working with any physical quantities. If an object moves 100 km in 2 hours, its average speed is (100 km) / (2 h) = (50 km) / (1 h) = 50 km/h. Writing 50 kmh conveys an entirely different physical quantity, one that is almost certainly meaningless as there are no conventional formulas that multiply length by time.

In the case of the kilowatt-hour (kW⋅h), a unit of power is multiplied by a unit of time, yielding a unit of energy. Conversely, a unit of energy divided by a unit of time gives a unit of power; the joule (J) divided by the second (s) is the watt (W). So, a kilowatt-per-hour (kW/h) would be a change in the rate of power delivery over time, like a power plant slowing down from 1000 kW to 900 kW over a span of time.

p standing for per (mandatory)

Unlike the imperial system which uses p to denote per (e.g. mph, mpg, APM), p stands for the pico- prefix in SI, and the role of per is covered by division and negative powers. For example, kilograms per litre can be expressed as kg/L or kg L⁻¹.

Power-of-1024 prefixes (mandatory)

SI prefixes always mean the same multiplier in every context. Kilo- is always 1000, even when applied to bytes. Treating kilo- as 1024 is an abuse of notation perpetuated by the computer industry, which ended up harming and confusing consumers everywhere (e.g. Why does my 1000 GB HDD show up as “909 GB” in Windows?). Always use SI prefixes to denote powers of 1000 (e.g. 1 MB = 1000000 bytes), and instead use IEC binary prefixes to denote powers of 1024 (e.g. 1 MiB = 1048576 bytes).

A naive idea is to make prefixes context-dependent so that they are powers of 1024 when applied to bytes, but powers of 1000 on anything else. Even prefixes applied to bits already pervasively use powers of 1000, such as 100 Mb/s Ethernet (but not 64 “kilobit” RAM chips). Why this idea is wrong is that it creates problems at interfaces. For example, we know 1 B = 8 b (1 byte equals 8 bits), but then 1 “kB” ≠ 8 kb (left side would implicitly mean 1024 bytes, but right side means 8000 bits). Another example is if a data bus transfers 1 byte per second per hertz, then a 100 MHz bus can transfer 100 MB/s, not 100 MiB/s.

Multiple prefixes (mandatory)

Never use multiple prefixes for metric quantities. Either write out the full number, or adjust the single prefix to equal the product of multiple prefixes.

Bare prefix (mandatory)

Never write a quantity with a prefix but no unit. It is unacceptable to imply a unit (e.g. She drove 30 k vs. She drove 30 km).

Wrong unit (mandatory)

Units that have multiple parts cannot be abbreviated. A kilometre is a unit of distance, while a kilometre per hour is a unit of speed; it is wrong to write “kilometre” (or its symbol) to imply “kilometre per hour”. A kilowatt is a unit of power, while a kilowatt-hour is a unit of energy; these units are incompatible and measure different quantities.

Mass/weight distinction (mandatory)

Grams (g) and prefixes thereof are measures of mass, not weight or force. Newtons (N) measure weight and force. This distinction is made clear when you consider that if you take a trip up to the International Space Station, your body mass in kilograms will stay the same, but your weight in newtons will be zero (weightlessness in orbit).

Deprecated units (mandatory)

The standard symbol for cubic centimetre is cm³, not the commonly used cc. Moreover, a millilitre (mL) is exactly equal to a cubic centimetre and is more appropriate for indicating volumes. Micron (μ) is the old way of expressing micrometre (μm). The unit’s name and symbol both break the spelling pattern and is an unwanted wart. An ångström equals 0.1 nanometre, and is needless field-specific jargon (particularly in optical physics) that can be easily converted to nanometres by dividing 10. Don’t use units like these.

Substitutions for Greek mu (mandatory)

Almost all SI prefixes, SI units, and non-SI units are written in Latin letters, with the exception of the prefix micro (μ), the unit ohm (Ω), and the unit ångström (Å). Typing and transmitting non-Latin characters can pose technical difficulties, and sometimes writers work around this in haste by substituting μ with u or mc. This can be okay for informal private communications, but is unacceptable for published works with wide dissemination.

Spurious conversion precision (mandatory)

Unit conversions, such as from imperial to metric, should follow the rules for significant figures. Just because the definition of a unit has numerous digits doesn’t mean you need to keep that many digits after a calculation. Having too many significant figures in metric numbers makes them harder to understand and reduces their chances for wide acceptance. For example, a road speed limit posted as 40 mph is equal to exactly 64.37376 km/h by definition, but should be written as 65 km/h because the precision is superfluous in such a context. The long number makes the metric system look arbitrary and incomprehensible.

Additive mixed units (mandatory)

In other systems it is customary to express quantities in mixed units, for example “4 foot 9 ³/₈ inches” or “11 stone, 2 lb, and 5 oz”. However, the metric system is decimal-based and does not need this kind of phrasing. Splitting the units makes no improvement to clarity, but adds needless work when handling numbers in calculations.

Multiple quantities (mandatory)

When more than one physical quantity participates in a calculation (e.g. addition, multiplication), every quantity must have its own units, or appropriate parentheses must be used. If we say that a film frame has the dimensions “36 × 24 mm”, this arithmetic expression evaluates to 864 mm, a quantity of length which makes no sense in this context. Instead, we say that it has dimensions “36 mm × 24 mm”, which correctly evaluates to its area of 864 mm².

Space between number and unit (suggested)

For readability, there should be a space between the number and the unit(s). This is especially important for numbers with decimal places and compound units, e.g. 4.567 N⋅m²⋅s⁻². Also, the space should be non-breaking (U+A0), to avoid splitting the number and units on different lines. However, there is no space before the angle units of degrees, minutes, and seconds (e.g. 12° 34′ 56″).

Capital L for litre (suggested)

The lowercase letter l looks like the number 1 in many fonts. As such, the unit symbol for litre should be written with an uppercase L. There are other writers and manufacturers who use script lowercase ℓ, but it seems to be non-standard.

Pronunciation of kilometre (suggested)

The English word kilometre should be pronounced with stress on the first syllable, not the popular way where stress is on the second syllable. The former style matches the pattern of how kilo- is pronounced in front of every other unit, and also respects the fact that every other prefix in front of metre is also pronounced with stress on the first syllable. The latter style is self-inconsistent – why not extend it to pronounce centimetre as [sɛn.ˈtɪ.mɪ.tɚ], millimetre as [mə.ˈlɪ.mɪ.tɚ], et cetera? One danger of the extension is that the word micrometre means the unit when stress is on the first syllable, and the measurement device when stress is on the second syllable. Hence, other than popularity, it makes no sense whatsoever to pronounce kilometre with stress on the second syllable.

Avoid semi-SI units (suggested)

Just putting a prefix like kilo- or milli- in front of a non-SI unit doesn’t make it compatible with SI. This gives the unit pseudo-legitimacy like SI units, but adds another unit for a quantity that can already be expressed by SI units. For example, a millimetre of mercury (mmHg) is a measure of pressure which is better expressed in pascals (Pa); a kiloparsec measures distance which should be expressed in metres (m) instead; a megaelectronvolt is a unit of energy that should be expressed in joules (J).

Avoid centi/deca/etc. (suggested)

Most SI prefixes are based on powers of 1000, except for centi-, deci-, deca-, hecto-, myria-, and dimi-. Out of these six oddball prefixes, centi- is by far the most popular, essentially only used in the unit centimetre. These prefixes, spaced apart by powers of 10 instead of 1000, are too near each other and can increase cognitive load by creating too many subunits. For example, in a typical supermarket you can buy various liquid goods that are between 1 to 10 millilitres, centilitres, decilitres, and litres. It is arguably easier to have a sharp divide between quantities expressed in millilitres and litres.

Avoid common non-SI units (suggested)

Some units like hour (3600 seconds) are not in SI but are commonly used anyway (e.g. km/h). For everyday purposes like driving, it is better to keep this customary usage. For serious science and engineering, SI units like metres per second should be used instead. Also, some non-SI units are related to SI units by some power of 10, for example 1 bar = 100000 pascals. These units create needless jargon for quantities that are already covered by SI units.

Short/long scale to prefixes (suggested)

In some languages and countries, big number words like billion and trillion can have unexpected or disputed meanings. SI prefixes like tera-, peta-, etc. always mean the same number everywhere. Leverage this fact to cut down on ambiguity and confusion. Moreover, SI prefixes are shorter – for example, 1.618 billion km is equal to 1.618 terametres (Tm).

Scientific temperatures in kelvins (suggested)

Measurements and calculations for scientific and engineering purposes should be expressed in kelvins. For example, working with cryogenic technology near absolute zero will yield small numbers on the kelvin scale, but ugly −200-something numbers on the Celsius scale. Conversely, when talking about high temperatures plasmas and stars above a few thousand kelvins, the fact that kelvin and Celsius are offset by 273.15 K makes no practical difference. The lack of negative kelvin temperatures removes a needless psychological distinction – for example, it’s not really special that nitrogen boils at 77 K (−196 °C) and gold boils at 3243 K (2970 °C); they are both temperatures on a uniform scale.

Everyday temperatures in °C (suggested)

There is no need to report everyday temperature measurements in kelvins. For outdoor weather, room temperature, body temperature, and cooking, it is customary to use degrees Celsius, with typical numbers from −50 °C to 250 °C. Using kelvins would be strange because ambient temperature is around 300 K, and the range of useful values would range from 250 K to 500 K.

Avoid unit-age words (suggested)

There are a couple of metric units where the suffix -age is appended to the name and that word has popular usage. For example, amperage means electric current, voltage means electric potential difference, wattage means electric power (even though non-electric phenomena such as human muscle output could be measured in watts too), and grammage refers to the area density of paper, and so on.

These unit-age words are problematic for several reasons. The first is that it linguistically links a unit to a type of quantity, even though many possible units could measure that quantity (e.g. volume can be measured in litres or cubic metres, a vehicle’s mileage (total distance traveled) could be expressed in miles or kilometres). The second reason is that it creates a temptation to omit the unit (e.g. “The voltage in this country is 120.”). Third, these words are not consistently applied (e.g. we don’t have the metreage (height) of a person, jouleage (energy) of food, newtonage (force) of pulling, daily kilowatt-hourage (energy) consumed, or hertzage (frequency) of a CPU).

More examples are found in non-metric units. For example, tonnage refers to the mass of cargo or a ship, mileage refers to distance, square footage refers to floor area, footage doesn’t mean length anymore but is instead a collective noun that refers to video clips, acreage means land area, and yardage refers to fabric sold in yards. Likewise, these -age words are not applied consistently to all measures. No one speaks of the gallonage (volume) of a car’s gas tank, the inchage (circumferential length) of a person’s waist, the Fahrenheitage (temperature) of an oven, the dollarage (monetary cost) of a purchase, or the knottage (speed) of an airplane.

Try unpopular prefixes (suggested)

For some reason, certain prefixes are not used in normal communication even though they are technically suitable. For example, car odometers report in kilometres (e.g. 12345.0 km), and car owners will colloquially mention that number rounded to thousands, like 10 thousand kilometres. This situation is undesirable because stacking prefixes is disallowed (e.g. 10 k km), and because using mega is both correct and more concise (e.g. 10 Mm). Similarly, large amounts of mass (e.g. commercial shipping, industrial mining) are reported in thousands or millions of tons instead of using large SI prefixes on gram, like gigagram (Gg) or teragram (Tg).

This situation is not symmetrical with small prefixes. Medicines are routinely labeled in milligrams and micrograms (not thousandths or millionths of a gram), transistors are measured in nanometres (not billionths of a metre), metal machining is specified to micrometres of accuracy, etc.

Moreover, the avoidance of large units like megametres, gigagrams, etc. is not explained by unfamiliarity with those prefixes, because words like megahertz and gigabytes are in common use.

One consequence of this suggestion is that respecting the case-sensitivity of metric notation is critical. Mm means megametre, while mm means millimetre, 9 orders of magnitude smaller. Gg means gigagram, while gg is a meaningless typo. kK means kilokelvin, KK could mean squared kelvin (but an intervening space or multiplication symbol is strongly recommended), kk is the illegal double-prefix kilokilo-, and Kk is meaningless.

More info

• NIST: Writing with SI (Metric System) Units
• NIST: Guide for the Use of the International System of Units (SI)
• Wikipedia: International System of Units - General rules
• UK Metric Association: Measurement units style guide
• Bureau International des Poids et Mesures: The International System of Units (SI)
• Wikipedia: International System of Units - Metric units that are not recognised by the SI