Project Nayuki

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.

Type of error Incorrect example Correct example
Ad hoc abbreviations394 Mtr below sea level394 m below sea level
66 sqm downtown apartment66 m2 downtown apartment
29 gr. of sugar29 g of sugar
15 msec network latency15 ms network latency
Plural of symbolsDistance of 70 kmsDistance of 70 km
Mass of 86 kgsMass of 86 kg
Capitalization of symbols2.4 ghz wireless network2.4 GHz wireless network
15 mb picture file15 MB picture file
MM pen tipmm pen tip
Capitalization of unit names60-Watt light bulb60-watt light bulb
3 milliKelvins3 millikelvins
402 KiloHertz402 kilohertz
170 Degrees celsius170 degrees Celsius
Degree sign/word25 C weather is warm25 °C weather is warm
98 F is body temperature98 °F is body temperature
STP is defined as 273.15 °KSTP is defined as 273.15 K
Helium boils at four degrees KelvinHelium boils at four kelvins
p standing for perThe car went 100 kphThe car went 100 km/h
Fuel consumption of 9.4 LPKFuel consumption of 9.4 L / 100 km
Multiplication/division confusionMaximum speed 75 kmhMaxmimum speed 75 km/h
25 kW/h to boil a tank of water25 kW⋅h to boil a tank of water
Power-of-1024 prefixes1 KB = 1024 bytes1 KB = 1000 bytes
512 MB of RAM512 MiB of RAM
Multiple prefixesOdometer reading of 30 k kmOdometer reading of 30000 km
M kg of coal shippedGg of coal shipped
μF capacitorF capacitor
Bare prefix500 G hard disk drive500 GB hard disk drive
2 kilos of rice2 kilograms of rice
Mass/weight distinctionHe weighs 70 kgHis mass is 70 kg
She weighs 50 kgShe weighs 490 N on Earth
The bridge can hold up 3000 kgThe bridge can hold up 29 kN
Deprecated units30 cc of saline solution30 mL of saline solution
10 μ thick sheet of paper10 μm thick sheet of paper
6800 Å red laser680 nm red laser
50 cps (cycles per second)50 Hz (hertz)
Substitutions for Greek mu430 mcg of medicine430 μg of medicine
81 uL of catalyst81 μL of catalyst
Spurious conversion precisionAdd 1 ounce (28.349523125 g) of butterAdd 1 ounce (30 g) of butter
Additive mixed unitsThe tower is 630m 24cm 1mm tallThe tower is 630.241 m tall
Mass of 15 kilograms and 70 gramsMass of 15070 grams
Multiple quantitiesCardboard box with dimensions 100 × 300 × 200 mmCardboard box with dimensions 100 mm × 300 mm × 200 mm
Camera and battery have combined mass of 876 + 123 gCamera and battery have combined mass of (876 + 123) g

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.

Type of situation Bad example Good example
Space between number and unitMains voltage of 120VMains voltage of 120 V
700m racetrack700 m racetrack
Capital L for litrel plastic milk jugL plastic milk jug
355 ml soda drink355 mL soda drink
Pronunciation of kilometre40 kuh-LAW-mih-ter journey40 KIL-o-mee-ter journey
90 [kə.ˈlɑ.mɪ.tɚz] per hour90 [ˈkɪl.oʊ.mi.tɚz] per hour
Avoid semi-SI units120 mmHg systolic blood pressure16.0 kPa systolic blood pressure
938 MeV gamma ray150 pJ gamma ray
The Milky Way spans 50 kiloparsecsThe Milky Way spans 1.5 zettametres
Avoid centi/deca/etc.A4 paper is 21 cm × 29.7 cmA4 paper is 210 mm × 297 mm
Square field with 1 hm side lengthSquare field with 100 m side length
Shotglass containing 4 cL of vodkaShotglass containing 40 mL of vodka
Avoid common non-SI unitsAir pressure at 1020 mbarAir pressure at 102.0 kPa
Magnetic field of 38000 gaussMagnetic field of 3.8 teslas
6 tons of wheat6000 kg of wheat
Wind speed of 35 km/hWind speed of 9.7 m/s
280 kW⋅h monthly electrical energy consumption1008 MJ monthly electrical energy consumption
Short/long scale to prefixes1 billion (short scale) litres of oil1 gigalitres of oil
1 billion (long scale) litres of oil1 teralitres of oil
Scientific temperatures in kelvinsTank of liquid nitrogen at −196 °CTank of liquid nitrogen at 77 K
Copper melts at 1085 °CCopper melts at 1358 K
Color temperature of 5730 °CColor temperature of 6000 K
Everyday temperatures in °CRainy and 276 K outsideRainy and 3 °C outside
Set the oven to 450 KSet the oven to 175 °C
Try unpopular prefixes1000 kg is a metric tonne1 Mg (megagram) is a metric tonne
150 million km to reach the Sun150 Gm (gigametres) to reach the Sun
Compressed to 0.123 bits per symbolCompressed to 123 millibits (mb) per symbol
Frequency error of only 0.000045 HzFrequency error of only 45 μHz (microhertz)

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

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).

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).

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.

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).

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.

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