800.334.5551 Live Chat (offline)

# The Metric System

Kim Mace, PhD, MBA
Product Manager - Physics and Physical Science

May 2017

In the United States, measurements are generally provided in English units. For example, when driving to a nearby town to see a friend or family member, we may say “it’s 20 miles from here.” In many parts of the world, a person referring to the same distance may say “it’s 32 kilometers from here.” People who use the term “kilometer” to describe distance are employing the metric system.

The metric system, or more accurately the International System of Units (SI), is an international system of measurement and the unit system most often used in STEM (science, technology, engineering, and math). Scientists around the world use and understand the SI. (In writing, “S” appears before “I” because in French the “International System of Units” is written “Systѐme International d’Unités” [Bryant 1976]).

Unlike the English system of units that uses different names and unit sizes for volumes (e.g., gallons, pints, quarts), weights (e.g., pounds, stones, tons, short tons, long tons), and distances (e.g., feet, yards, miles), the SI uses the same base units and the same prefixes for all types of measurements.

Prefixes are provided in scales that function around 7 units known as metric system (or SI) base units. As shown in Table 1, base units include the meter (m), the kilogram (kg), the Kelvin (K), the second (s), the ampere (A), the candela (cd), and the mole (mol).

Table 1  Metric base units, abbreviations, and reference standards (Helmenstine n.d.).

 SI/METRIC BASE UNITS SI Term What It Measures Abbreviation Reference Standard meter length m The length a path of light travels in a vacuum in 1/299,792,458 seconds (speed of light (c) = 299,792,458 m/s). kilogram mass kg A platinum/iridium 1-kg mass located at the International Bureau of Weights and Measures near Paris, France. Kelvin temperature K The fraction 1/273.16 of the thermodynamic temperature of the triple point of water (273.16 K = 0.01° C). second time s The duration of 9,192,631,770 periods of radiation, which is the difference in the transition between the levels of the cesium-133 atomic ground state. ampere current A A constant current maintained in 2 straight, parallel, non-negligible conductors of infinite length placed 1 meter apart in a vacuum that produces a force between them of 2 x 10–7 newtons (N) per meter (1 N = 1 kg x m2 x s–2). candela luminous intensity cd A source emitting monochromatic radiation of frequency 540 x 1012 hertz with a radiant intensity in the same direction of 1/683 watt per steradian. mole amount of substance mol The number of atoms in 0.012 kilograms of carbon-12.

Since this list of 7 units is rather simple for all of the things scientists interact with in their work, they often adopt derived units (units that originate from the base units) when describing data. Some of the most common non-SI units found in scientific texts and documents, as well as commonly used equivalents, are provided in Table 2.

Table 2  Commonly used non-SI units (National Institute of Standards and Technology n.d.;
K. Mace, personal knowledge; conversions from OnlineConversion.com n.d.).

 COMMONLY USED NON-SI UNITS Unit Symbol Commonly Used Equivalents Common Uses Time minute min 1 min = 60 s Calculations involving time hour h 1 h = 60 min = 3,600 s Calculations involving time day d 1 d = 24 h = 1,440 min = 86,400 s Calculations involving time Navigation degree (angle) ° 1° = (π/180) radians Longitude, latitude minute (angle) ' 1' = (1/60)° = (π/10,800) radians Longitude, latitude second (angle) " 1" = (1/60)' = (π/648,000) radians Longitude, latitude Volume liter L 1 L = 1 dm3 = 0.001 m3 = 1000 cm3 Calculating volumes smaller than ocean-sized centimeter cubed cc 1 cc = 1 mL Medical applications, small volume calculations Sverdrup Sv 1 Sv = 1 million cubic meters per second Calculating volumes of water in the world oceans Mass pound lb 1 lb = 0.4536 kg = 16 oz Masses of food, people, animals, etc., in the US ounce oz 16 oz = 1 lb Masses of food, people, animals, etc., in the US ton ton 1 ton = 2,000 lb = 1.016 t = 1,016.05 kg Shipping, manufacturing, etc., in the US tonne t 1 t = 1,000 kg Shipping, manufacturing, etc., in the US and globally metric ton t 1 t = 1,000 kg Shipping, manufacturing, etc., in the US and globally unified atomic mass unit u (Da) 1 u = 1.6605 x 10–27 kg Measuring the size of atoms Energy electronvolt eV 1 eV = 1.602176 x 10–19 J Calculating the energy of particles streaming to Earth from the Sun, high-energy physics/particle physics, etc. joule J 1 J = 1 kg x m2 x s–2 = 2.78 x 10–7 kWh Scientific publications, oil and gas industry British thermal unit BTU 1 BTU = 1,055.06 J = 252.16 Cal Electric utilities, oil and gas industry, machinery calorie cal 1 calorie = 4.184 J Chemistry and physics measurements Calorie Cal 1 Cal = 1,000 calories Food and drink packaging Newton N 1 N = 1 kg x m x s–2 Force calculations, anchors, fasteners, thrust of rockets, etc. Power watt W 1 W = 1 J x s–1 = 1 N x m x s–1 = 1 kg x m2 x s–3 Electric power generation and delivery, radio transmission horsepower HP 1 HP = 745.7 watts Automobile, truck, and machine engine ratings Distance nautical mile nm, NM, M 1 nautical mile (NM) = 1,852 m Shipping, sea navigation, ocean mapping, military operations knot kn 1 knot = 1 nautical mile (NM)/hour = 1.151 miles/hour Shipping, sea navigation, military operations mile m 1 m = 5,290 ft = 1.609 km Highway signs, navigation, etc., in the US foot ft 1 ft = 0.3048 m Construction, textiles, assembly, etc., in the US yard yd 1 yd = 3 ft = 0.9144 m Construction, textiles, assembly, etc., in the US Area hectare ha 1 ha = 2.47 acres = 10,000 m2 Scientific publications in ecology, international land development, etc. acre a 1 acre = 43,560 square feet = 4,047 m2 Real estate, English language documents describing areas Pressure pascal Pa 1 Pa = 1 N/m2 = 1 kg x m x s–2 = 1 J x m–3 Official scientific publications (shown as hectopascal [hPa]), weather forecasting, oceanography, military applications, etc. atmosphere atm 1 atm = 10,1325 Pa = 760 mmHg = 1,013 mbar = 760 torr Weather forecasting, military applications, scientific publications, etc. millibar mbar 1 mbar = 100 Pa = 0.000987 atm Weather forecasting, military applications, etc. millimeter of mercury mmHg 1 mmHg = 1.33 mbar = 133.32 Pa Scientific publications, weather forecasting torr torr 1 torr = 133 Pa = 0.0013 atm Scientific publications Temperature Fahrenheit °F °F = °C x (9/5) + 32 K = (5/9) (°F – 32) + 273.15 Scientific documents, US weather forecasts, appliances, machinery, and food packaging in the US, etc. Celsius °C °C = K – 273.15 Scientific documents; European, Middle Eastern, and Asian weather forecasts; appliances; machinery; food packaging outside the US; etc.

When you report data in metric (SI) or non-metric (non-SI) units, it is often necessary to use a prefix so numbers are not extremely large or extremely small when written. As examples of how scientists use units in their work, consider the following:

1. Most bacteria are 0.0000002 to 0.00001 meters in length (Carter n.d.). Instead of expressing the length as 0.0000002 meters, we could write 2 x 10–7 meters (in scientific notation) or 0.2 µm (pronounced “micrometers”). Note: Although “micron,” which denoted the micrometer, was part of the scientific vernacular for many years, the term is no longer accepted in academic science circles. The mathematical transition is, as follows, based on the SI prefixes provided in Table 3:

0.0000002 meters (m) x 106 micrometers (µm)  =  0.2 µm
1 meter (m)

1. NASA (National Aeronautics and Space Administration) and NOAA (National Oceanic and Atmospheric Administration) often report the units of carbon flowing into and out of the atmosphere, the terrestrial biosphere, and the oceans, and carbon stocks in units of gigatons (a non-SI unit with a metric prefix) (Riebeek 2011). In NASA’s and NOAA’s carbon maps, the largest carbon reservoir on Earth is located in the deep ocean (below the level of photosynthesis and respiration). NASA and NOAA assign a value of 37,000 gigatons to this carbon reservoir. In tons this is:

37,000 gigatons x 1 ton                 =  37,000,000,000,000 tons or 3.7 x 1013 tons
10–9 gigatons

Note that this is an example of a non-metric (or non-SI) unit used with the metric prefixes shown in Table 3. Many of the non-SI units shown in Table 2 are often used in this way—especially in earth science, physical science, and engineering.

Table 3  Metric (SI) prefixes.

 METRIC (SI) PREFIXES Prefix (Symbol) Formation Number Often Stated as… yotta (Y) yotta + BASE UNIT 1024 1 septillion zetta (Z) zeta + BASE UNIT 1021 1 sextillion exa (E) exa + BASE UNIT 1018 1 quintillion peta (P) peta + BASE UNIT 1015 1 quadrillion tera (T) tera + BASE UNIT 1012 1 trillion giga (G) giga + BASE UNIT 109 1 billion mega (M) mega + BASE UNIT 106 1 million kilo (K) kilo + BASE UNIT 103 1 thousand hecto (h) hecto + BASE UNIT 102 1 hundred deka (da) deka + BASE UNIT 101 1 ten BASE BASE UNIT 100 BASE UNIT deci (d) deci + BASE UNIT 10–1 1 tenth centi (c) centi + BASE UNIT 10–2 1 hundredth milli (m) milli + BASE UNIT 10–3 1 thousandth micro (µ) micro + BASE UNIT 10–6 1 millionth nano (n) nano + BASE UNIT 10–9 1 billionth pico (p) pico + BASE UNIT 10–12 1 trillionth femto (f) femto + BASE UNIT 10–15 1 quadrillionth atto (a) atto + BASE UNIT 10–18 1 quintillionth zepto (z) zepto + BASE UNIT 10–21 1 sextillionth yocto (y) yocto + BASE UNIT 10–24 1 septillionth

### References

Bryant, S. 1976. Système international d’unités. The Australian and New Zealand Journal of Surgery 46(3): 266–8. https://www.ncbi.nlm.nih.gov/pubmed/1070306 (accessed March 13, 2017).

Carter, P. n.d. Functional anatomy of prokaryotic and eukaryotic cells. http://classes.midlandstech.edu/carterp/courses/bio225/chap04/lecture2.htm (accessed February 28, 2017, and March 13, 2017).

Helmenstine, A.M. 2017. Metric units—base units: Seven basic metric measurements. https://www.thoughtco.com/metric-units-base-units-604140 (accessed February 28, 2017, and March 13, 2017).

NIST (National Institute of Standards and Technology). n.d. International System of Units (SI): Units outside the SI. http://physics.nist.gov/cuu/Units/outside.html (accessed February 28, 2017, and March 13, 2017).

OnlineConversion.com. n.d. Welcome to OnlineConversion.com. http://www.onlineconversion.com/ (accessed February 28, 2017; March 6, 2017; and March 13, 2017).

Riebeek, H. 2011. The carbon cycle. https://earthobservatory.nasa.gov/Features/CarbonCycle/ (accessed February 29, 2017, and March 13, 2017).