The Metric System: How SI Units Work, How to Convert, and Where They Came From

The metric system rests on three ideas. Each kind of quantity has one unit. Bigger and smaller versions of that unit are made only by multiplying or dividing by powers of ten, and each power has a fixed prefix. The units themselves are defined by constants of nature that any well-equipped laboratory can reproduce. The modern, formally maintained version is called the International System of Units, abbreviated SI after its French name, and it is looked after by the International Bureau of Weights and Measures (BIPM) near Paris.

Everything below follows from those three ideas: the seven base units, the prefix ladder, the short list of exact factors that tie US customary units to the SI, and the two centuries of history that produced them.

Seven Base Units and Everything Built From Them

The SI has seven base units. Every other unit is a product or quotient of these, which is why the system is called coherent.

Quantity	Unit	Symbol	Fixed by
Time	second	s	a hyperfine transition frequency of the caesium atom
Length	meter	m	the speed of light in vacuum
Mass	kilogram	kg	the Planck constant
Electric current	ampere	A	the elementary charge
Temperature	kelvin	K	the Boltzmann constant
Amount of substance	mole	mol	the Avogadro constant
Luminous intensity	candela	cd	the luminous efficacy of a defined visible radiation

Derived units are assembled from these. Speed is meters per second. A newton is the force that accelerates one kilogram by one meter per second every second. A joule is a newton acting over a meter, and a watt is a joule per second. Nothing needs a separate conversion constant, so a physics formula that is correct in base units stays correct without any fudge factor.

Two everyday units sit slightly outside this neat picture. The kilogram is the only base unit whose name already contains a prefix, so a gram is a thousandth of the base unit rather than the base unit itself. The liter is not an SI unit at all but is accepted for use alongside it: one liter is exactly one cubic decimeter, a cube 10 cm on each side. The degree Celsius is the kelvin with its zero moved, so a change of one degree Celsius is identical to a change of one kelvin.

The Prefix Ladder

A prefix multiplies whatever unit it is attached to. The common ones step by a factor of a thousand: milli (10^-3), micro (10^-6), nano (10^-9) downward, and kilo (10³), mega (10⁶), giga (10⁹) upward. Between milli and kilo sit centi (one hundredth), deci (one tenth), deca (ten) and hecto (a hundred), which survive mostly in centimeters, deciliters and hectares. NIST lists 24 recognized prefixes running from quecto (10^-30) to quetta (10³⁰); the newest four, ronna, quetta, ronto and quecto, were added in 2022.

Converting within the system is therefore a matter of shifting the decimal point. A marathon of 42.195 km is 42,195 m, because kilo means a thousand. A 2 L bottle holds 2,000 mL, which is also 2 cubic decimeters. Prefix symbols are case-sensitive: lowercase m is milli, uppercase M is mega, and a misread case is a factor of a billion. Engineering notation writes numbers with exponents in steps of three so they line up with these prefixes, and the Scientific Notation Converter shows the matching prefix for any value you enter.

Converting Between Metric and US Customary Units

US customary units are not an independent system any more. Since a 1959 agreement described in NIST SP 811, the yard has been defined in meters, which makes the inch exactly 2.54 cm and the foot exactly 0.3048 m. The avoirdupois pound is exactly 0.45359237 kg, and US volume units follow from the inch, which puts the US gallon at about 3.785 L. Because these factors are exact, a conversion is only as approximate as the rounding you choose at the end.

Example 1: Will the sofa fit?

Dana measured an alcove in her living room with an American tape: 7 ft 10 in wide. The sofa she likes, from a European retailer, is listed at 240 cm.

1. Put the alcove in one unit: 7 ft × 12 + 10 in = 94 in.
2. Multiply by the exact factor: 94 × 2.54 = 238.76 cm.
3. Compare: the sofa is about 1.2 cm wider than the opening, so it will not fit.

The Length Converter does step 2 for any pair of units. Working in one unit before comparing avoids the classic error of treating 7 ft 10 in as 7.10 ft.

Example 2: An airline bag limit

Hiroshi is flying with an airline whose checked-bag limit is 23 kg. His bathroom scale, bought in Ohio, says the packed suitcase weighs 52 lb.

1. Convert pounds to kilograms: 52 × 0.45359237 = 23.5868 kg.
2. Convert the limit the other way for packing at home: 23 ÷ 0.45359237 = 50.7063 lb.
3. He is roughly 1.3 lb over and needs to move a pair of shoes into his carry-on.

The Weight Converter handles pounds, ounces, stone and metric tons as well as grams and kilograms.

Example 3: Volume and a thermometer reading

Mateo is comparing a 2 L soda bottle with American cans sold by the fluid ounce. Dividing 2 L by the exact US fluid ounce (29.5735295625 mL) gives 67.628 fl oz, or a little more than five and a half 12-ounce cans. The Volume Converter keeps US and UK gallons, pints and fluid ounces apart, which matters because the UK gallon is about 20 percent larger.

That evening his daughter's thermometer, set to Celsius, reads 38.6 °C. Temperature is the one common conversion that is not a single multiplication, because the scales have different zero points: multiply by 9/5 and then add 32. Here 38.6 × 9/5 = 69.48, plus 32 gives 101.48 °F. In kelvins it is 311.75 K, since the kelvin scale starts 273.15 degrees below the Celsius zero. The Temperature Converter applies the offsets for readings and, separately, drops them for temperature differences.

Before the Meter: Cubits, Feet and Royal Decrees

NIST's history of measurement notes that early Babylonian and Egyptian records describe length measured with the forearm, the hand and the finger. The ancient digit, palm, span and cubit gradually gave way to the inch, foot and yard, through a sequence of changes historians still do not fully understand. Rome contributed the habit of dividing the foot into twelve parts called unciae, the Latin word behind both "inch" and "ounce."

Rulers tried to impose order by decree. Clause 35 of Magna Carta in 1215 required "one measure of wine throughout our kingdom, and one measure of ale, and one measure of corn." In the 16th century Elizabeth I replaced the Roman mile of 5,000 feet with one of 5,280 feet so that a mile would be exactly eight furlongs. These fixes worked locally, but each country, and often each town, kept its own sizes.

The French Revolution and the Treaty of the Meter

In 1790 the French National Assembly asked the Academy of Sciences to deduce "an invariable standard for all the measures and all the weights." The answer was a decimal system tied to the Earth. The meter was to be one ten-millionth of the distance from the North Pole to the equator, along the meridian through Dunkirk and Barcelona. The gram was the mass of a cubic centimeter of water at its densest, and the cubic decimeter became the liter.

Starting in 1792, the astronomers Pierre Méchain and Jean-Baptiste Delambre surveyed the arc between Dunkirk and Barcelona. The work took about seven years, and the result was embodied in a platinum bar. Uptake was slow: France itself made the system compulsory only in 1840.

The United States made metric units lawful in contracts and trade in 1866. In 1875, 17 countries including the United States signed the Treaty of the Meter, also called the Metric Convention, which set up the BIPM at Sèvres as a permanent body to keep and improve the standards. Since 1893 the official US yard and pound have been defined from the metric standards, and by 1900 a total of 35 nations had officially accepted the metric system. In 1960 the General Conference on Weights and Measures gave the modernized system its current name, the International System of Units. A 1988 trade law, section 5164 of Public Law 100-418, designated metric as "the preferred system of weights and measures for United States trade and commerce," though everyday American use of customary units continued.

From Metal Artifacts to Constants of Nature

The weakness of a physical standard is that it can change. The meter moved away from a metal bar in stages and in 1983 was redefined as the distance light travels in vacuum in 1/299,792,458 of a second, which also fixed the speed of light at exactly 299,792,458 m/s.

The kilogram held out longer. For more than a century it was the mass of the International Prototype of the Kilogram, a small platinum-iridium cylinder cast in 1879 and kept in a triple-locked vault outside Paris. Repeated comparisons showed that the prototype and its official copies drifted slightly against one another over the decades. In November 2018 a group of 60 nations voted to redefine the kilogram through the Planck constant, and on May 20, 2019 the kilogram, kelvin, ampere and mole were redefined in terms of constants of nature. The second, meter and candela were already tied to such constants.

The practical effect is invisible at the grocery store: a kilogram of apples weighs what it always did. What changed is that the definition no longer depends on one object in one vault, so national laboratories can realize the kilogram independently, for example with a Kibble balance.

Habits That Prevent Conversion Errors

• Carry exact factors, round once. Use 2.54, 0.3048 and 0.45359237 in the arithmetic and round only the final answer. Rounding each intermediate step compounds the error.
• Write the unit with every number. A bare "23" on a packing list could be kilograms or pounds; the two differ by a factor of 2.2.
• Check the gallon, ounce and ton. US and UK gallons differ, the fluid ounce measures volume while the ounce measures mass, and the short ton (2,000 lb) is not the metric ton (1,000 kg).
• Treat temperature separately. A reading needs the offset; a difference, such as "the oven runs 10 degrees hot," does not.