Understanding the Metric System

Long before global supply chains and trade agreements, convenience was paramount in measurements. With limited access to sophisticated tools, people often turned to body parts for convenience and consistency. For example, a man's thumb was approximately the length of an inch, with 'thumb' and 'inch' being interchangeable terms in many languages.

This rudimentary system worked well for centuries but started to unravel as small tribes expanded into nations. With growth came confusion, as different areas used varied measurement systems that interfered with trade. In France, by the time of the French Revolution in 1789, this chaos was particularly problematic. Different regions had different standards for length, volume, and mass. Some wanted Paris' system to be used nationwide, but resistance from guilds and the nobility made this difficult. With financial instability, King Louis XVI convened the Estates General to address the crisis. This assembly eventually led to the creation of the National Assembly and a new constitution, paving the way for a standardized system of measurement.

The French revolutionized the system by calling it 'métrique,' derived from 'mètre,' meaning meter—a fundamental length measurement defined as one ten-millionth of the Earth's meridian through Paris. The founders believed their invention would one day be universally adopted, and indeed, today the metric system is used worldwide, with the notable exception of the United States. While Americans remain skeptical about meters, liters, and kilograms, they have supported the metric system since the Civil War, and the inch-pound system is defined in terms of metric measurements.

Before diving into the details of the metric system, let's take a moment to explore the history behind the world's system of measurement and how it evolved into its current form, the Système International d'Unités, also known as the International System of Units or simply SI.

History of the Metric System: The Early Years

The modern metric system traces its origins back to Gabriel Mouton, the vicar at St. Paul's Church in Lyon, France, who was also a renowned astronomer and mathematician. In 1670, Mouton envisioned a system of measurement based on the length of one minute of longitude (remember, there are 60 minutes in each degree of longitude and latitude). He proposed that this unit of measurement should be based on decimal arithmetic, or powers of ten. Additionally, he suggested the use of prefixes to make the naming conventions more systematic.

While French scientists continued to refine Mouton's ideas, they were not officially formalized until the French Revolution. In 1790, the National Assembly tasked the French Academy of Sciences with creating a universal standard for all measures and weights. The academy then appointed a commission to devise the system, ensuring that it would be both simple and scientific. Drawing inspiration from Mouton, the commission established three fundamental principles.

The commission chose the name 'metre' (or 'meter' in the U.S.) for the unit of length, derived from the Greek word metron, meaning 'to measure.' The next challenge was determining the precise length of the meter. This task was undertaken by Pierre Mechain and Jean Delambre, who spent six years measuring the meridian distance from Barcelona, Spain, to Dunkirk, France. Their work resulted in the meter being defined as 'one ten-millionth of the meridional quadrant of the Earth.' Other units were based on this exact meter length. For instance, the gram was defined as the mass of one cubic centimeter of pure water at its maximum density, and the liter was the volume of a cube measuring 10 centimeters (4 inches) on each side.

This marked the first version of the metric system, officially adopted by France in 1795. Four years later, scientists created standards for the meter and kilogram using platinum. These standards were recognized by the French government and kept in a secure location so that copies could be produced when necessary.

Soon after, the metric system began to gain worldwide acceptance.

History of the Metric System: Meeting About Meters

Due to Napoleon's conquests across Europe in the early 19th century, various countries, some with reluctance, gradually adopted the metric system as their official system of measurement.

In 1875, a significant assembly took place in Paris, gathering representatives from 17 nations, including the U.S. During this meeting, they signed the Treaty of the Meter and established the International Bureau of Weights and Measures, an International Committee for Weights and Measures to manage the bureau, and the General Conference on Weights and Measures to review and approve any amendments. The treaty also mandated the establishment of a lab in Sèvres, near Paris, to house global metric standards and authorized the distribution of these standards to each participating country. In 1890, the U.S. received its copies of the International Prototype Metre and the International Prototype Kilogram.

In 1954, the 10th General Conference on Weights and Measures set the stage for a revamp of the metric system to better serve the scientific and technical communities. This overhaul introduced seven base units and clarified the definitions, symbols, and terminology of metric units. The revision continued through the 11th Conference, and by 1960, the new system was officially adopted and named the International System of Units, or SI for short.

The International System of Units is the modernized version of the metric system, though the terms are often used interchangeably. SI is the more precise and accurate term. Up next, we will explore the foundational components of SI — the seven base units.

Where Do SI Base Units and Their Standards Come From?

Before delving into the core SI units, it's important to first grasp the concept of measurement. To measure something, you use tools or devices that help quantify a physical property of an object. For instance, a ruler measures length, a scale gauges mass, and a thermometer checks temperature. Each of these tools is calibrated with standard units, ensuring consistency across different observers. In theory, each of these units has a direct connection to a prototype – the ideal example of that unit.

Earlier iterations of the metric system relied on tangible objects as prototypes, such as a specific meter bar or a kilogram reference weight. However, in 1960, the General Conference on Weights and Measures overhauled the system by moving away from physical objects and defining units based on the stable, inherent properties of the universe.

Now that we've set the stage, let's explore the seven SI base units. Below is a table listing each unit, the physical quantity it measures, and the corresponding standard on which it is based, as defined by the International Bureau of Weights and Measures.

If you don't fully understand the definition for each standard, don't worry. Instead of trying to picture two straight parallel conductors of infinite length or a cesium-133 atom vacillating between two hyperfine levels of its ground state, just remember this: The fundamental SI units are based on immutable properties of the universe, and they are mutually independent. All other units in the modern metric system come by multiplying or dividing these base units. We'll get into that more in the next section.

SI Derived Units: We Need More Than Plain, Old Meters

The fundamental SI units cover all of the basic measuring needs. There are times, however, when it's necessary to relate measurements mathematically. For example, let's say you measure the length of a soccer field and find it to be 120 meters (394 feet) long. Then you determine its width to be 90 meters (295 feet). If you wanted to find the area of the field, you would need to multiply its length by its width. But you don't just multiply the numbers in front of the units; you multiply the units, too. So, the math would look like this:

area = length × width = 120 m × 90 m = 10,800 m

Notice that the final unit is a meter times a meter, which results in what metrologists, or measuring experts, call a square meter.

Now let's say you have a cube measuring 1 meter on each side. If you wanted to find the volume of the cube, you would need to multiply three dimensions -- length, width and height. Here's the math:

volume = length × width × height = 1 m × 1 m × 1 m = 1 m = m

Notice again that the base unit gets multiplied along with the numerical factor. In this case, it's a meter times a meter times a meter, resulting in a cubic meter. Also observe that when the numerical factor is 1, you can drop the number and simply show the unit. Metrologists call this a coherent unit.

Area and volume are derived units because they are defined in terms of an SI base unit and a specific quantity equation. The table lists some of the most common derived units.

A few derived units are significant enough to have earned special SI names and symbols. Force serves as a great example. Isaac Newton defined force as the mass of an object times its acceleration. When you multiply these two quantities together, you get a derived unit of kilogram meter per second squared (kg-m/s). Because kg-m/s is a little cumbersome and because force is such an important quantity in physics, SI bigwigs decided to call the derived unit a newton, in honor of Sir Isaac. In all, there are 22 derived SI units with special names and symbols. Some of the most important ones appear in the accompanying table.

Finally, it's important to know that a few units are not officially part of the metric system but make frequent appearances. As such, the SI accepts these units for use with its family of measures. Some of the common time quantities -- the minute, hour and day -- fall into this category, as do the metric ton and astronomical unit. All of these units, however, can be defined according to SI base units. For example, a day is 86,400 seconds. And an astronomical unit (AU) -- a unit of length equal to the mean distance between the Earth and the sun -- is 1.495978 × 10 meters.

Of course, a base unit may be too large or too small to describe an object adequately. In the SI, making units larger and smaller requires nothing more than adding a prefix. We'll cover those on the next page.

SI Prefixes: Making Friends With Milli-

As we've emphasized throughout, each physical quantity – such as length, mass, volume – is measured by a specific SI unit. However, there are times when these base units don't provide a practical solution, especially for extremely small or large objects. For instance, measuring the length of an ant in meters gives us 0.003 meters. Now, consider trying to measure the width of a human hair or an atom in meters: the resulting numbers become increasingly small and impractical. The same issue arises with large measurements. For example, the distance between New York City and Los Angeles is 4,493,288 meters, a number that is cumbersome to work with.

To address this challenge, the General Conference on Weights and Measures introduced a set of prefix names and symbols to represent multiples and submultiples of SI units. By 1960, there were enough prefixes to cover multiples ranging from 10 to 10. Over time, new prefixes were added to account for even larger and smaller values. The table below lists several of these accepted prefix names and symbols.

Now, let's revisit our examples to see the benefit of using a prefix system based on powers of 10. An ant’s length of 0.003 meters is better expressed in millimeters. To convert meters to millimeters, simply multiply by 1,000, or move the decimal point three places to the right. This gives us a length of 3 millimeters (3 mm) for the ant. Similarly, for the New York City to Los Angeles trip, measuring in kilometers is far more convenient. Converting meters to kilometers requires dividing by 1,000, or moving the decimal three places to the left, which gives us 4,493 kilometers (4,493 km).

All prefixes work in a similar manner. However, there is one exception: the kilogram. It’s the only SI base unit whose name and symbol already include a prefix. While you might think to apply a prefix to kilogram (such as microkilogram), this would be incorrect. Instead, prefixes should be applied to the unit 'gram' to denote different scales of mass. For instance, 10 kilograms would be represented as 1 milligram (1 mg).

Now that you are familiar with SI units and their prefixes, you're ready to start using the metric system. It's been the standard for most of the globe for many years. In the next section, we will explore why the majority of countries have fully adopted the metric system and look into the consequences of a nation's reluctance to switch – we’re talking about you, America.

Metric System: Risks and Rewards

If the tour of SI units and prefixes hasn't fully convinced you of the metric system's advantages, try solving this exercise: convert 5 miles into inches. Do it mentally. Even if you recall the number of feet in a mile (5,280) and the number of inches in a foot (12), you’ll still face some complicated calculations. Here's the equation you'll need:

(5 miles)(5,280 feet/1 mile)(12 inches/1 foot) = 316,800 inches

The metric system simplifies things immensely. Take this similar conversion: determining how many centimeters are in 5 kilometers. A kilometer is 1,000 meters, and a centimeter is 1/100 of a meter. To convert, you simply move the decimal point five places to the right:

5 kilometers equals 5,000 meters, which is equivalent to 500,000 centimeters.

Now you see why SI units are so much easier, right?

The simplicity and efficiency of the International System of Units have made it a global standard. The United States stands alone among industrialized nations in continuing to rely on traditional measurements, leading to a confusing mix of unrelated units. Cost is a major factor behind the U.S.'s reluctance to adopt the metric system. For instance, NASA’s space shuttle program still uses the inch-pound system, and the cost to convert all the relevant materials to SI units was recently estimated at $370 million — a steep price, even for an agency that spends $760 million to launch a shuttle [source: Marks].

However, sticking with outdated units carries its own financial risks. NASA experienced a costly mistake in 1999 when the Mars Climate Orbiter mission failed due to a unit mismatch. The spacecraft's attitude-control system used imperial units, while its navigation software used SI units, causing the probe to veer too close to the planet, overheat, and malfunction. The result? A $125 million loss and a piece of space junk, all because of the U.S.'s delay in adopting SI units [source: Marks].

Many American companies have learned from such costly mistakes. Businesses like John Deere, Proctor & Gamble, Kodak, and Ingersoll-Rand have adopted SI units in at least some of their operations. This move allows their domestic and overseas factories to use the same system and the same parts, resulting in significant savings. The benefits come from two key factors: greater productivity due to the simplicity of a decimal-based system and a stronger competitive position in the global market.

One day, the United States will likely require its citizens to adopt the metric system. When that shift happens, road signs, gas pumps, and food labels will all reflect the change. However, some iconic American phrases will remain unchanged. Why? Because expressions like a country kilometer or a 30-centimeter hotdog just don't capture the essence of the American experience.