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Metric system

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The metric system is a system of units for measurement that are all interrelated in a mathematically convenient way. For example, a force of one newton applied to an area of one square metre is exactly one pascal of pressure, and one newton applied over a distance of one meter is one joule of energy. As another example, one liter is one cubic decimeter[note 1]. One liter of water has a mass of one kilogram and requires 4,184 joules (or one kilocalorie) to raise the temperature by one kelvin, assuming no phase transitions.[note 2]

Such systems are called coherentWikipedia and are used in a decimal fashion for smaller and larger measurements, using a system of prefixes to indicate orders of magnitude. This makes the system incredibly easy to work in. It has been almost universally adopted for use around the world, and is commonly used in scientific work. Nowadays, it is standard for undergraduate students in science and engineering to be taught using only SI units, although different systems of units are used at the graduate level and in the literature. For example, books and research papers in electromagnetism and quantum mechanics tend to use Gaussian units while those in particle physics Lorentz-Heaviside units.[1][2][note 3]

The SI[edit]

The metric system had been discussed as early as the 16th and 17th centuries. Its first implementation came in 1799 during the French Revolution. The modern version of the metric system, first announced in 1960, is the Système International (International System), abbreviated "SI", which defines the specific units used in science. The SI follows strict mathematical principles such as coherency: each physical dimension (such as length, mass, or energy) has a single unit associated to it, and these units are interrelated by dimensional analysis, always using a factor of one. This means that the mathematical relationship between any two physical dimensions is identical to the relationship between the units that measure them; in modern physics and engineering, equations are almost always written in SI units for this reason.

For example, since Newton's Second Law defines force as the product of mass and acceleration, it follows that the SI unit of force, the newton, must be equivalent to the product of the SI units of mass (the kilogram) and acceleration (the metre per second squared). Thus 1 N = 1 kg·m·s-2, in terms of the SI base units.

Some common metric units are not SI units, but relate directly to them. For instance, the SI considers the litre (l or L) to be a special name for the cubic decimetre (dm3); the SI unit of volume, following dimensional analysis (i.e., volume is the cube of length), is the cubic metre.

One of the great strengths of the SI in terms of promoting science literacy is that it emphasises the connections between different kinds of physical dimension: the watt (power unit) is one joule (energy unit) per second (time unit). Pre-metric units of power and energy, such as horsepower and British Thermal Units (BTU) lack this transparent relationship, and thus their relationships to other units are obscure and extremely difficult to understand. In practice, when using the older units, it is common to "cheat" and convert the inputs to SI units, calculate a result in SI units, and then apply conversion factors to get a result in the desired unit.

Countries that have not completely adopted the system[edit]

In spite of the obvious and well-established practical and mathematical advantages of the metric system, the following few countries remain outside of the pack.

In the United States[edit]

Despite the utter sense that the metric system makes, and the ease of use, in the United States there has been tremendous resistance to its full adoption for two reasons:

  1. Resistance to change
  2. All those awful complicated headachy conversion thingies. In spite of this, everyone in the U.S. is quite comfortable with two-liter bottles of carbonated sweetened beverages, 9 mm bullets, and nutritional information and medicine measured in grams and milligrams (example: a fat-free product saying it has 0 g of fat).[3] And every alcoholic knows perfectly well that 750 mL is close enough to a "fifth" (1/5 US gal) that it doesn't really matter.)
Extreme crackpot right-wing responses to the metric system are not unheard of. For example, Dean Krakel, Director of the National Cowboy Hall of Fame:

Metric is definitely communist. One monetary system, one language, one weight and measurement system, one world — all communist! We know the West was won by the inch, foot, yard, and mile.[4]

Never mind that that was before communism was really a thing, and that time the commies were beaten,Wikipedia it was done by the kilometre.

and Dave Barry (who - it should be noted - is a humorist):

"[…] my belief, as an American, is that if I have to start understanding the metric system, then the terrorists have won."[5]

The metric system has, however, found wide use among entrepreneurs, scientists, and hospitals, the last of which tend to have scales that measure in kilograms for the hospital's information on the patient and can switch to pounds for laypeople who aren't completely familiar with the system (and they assume every patient is not). In addition, hospitals often use 24-hour time like mainland Europe.

In the United Kingdom[edit]

In the UK, by comparison, there is less outright hostility (well, with the exception of Daily Mail readers, who probably think centimetres cause cancer) to the system and more tedious bloody-mindedness to just stick with the traditional system.[6] Despite EU regulations that say food products must be sold in metric kilograms (a form of standardisation across Europe), some traders insist quite forcefully in using old Imperial units. Because this is illegal and against Trading Standards laws, it leads to the so-called "Metric Martyr" cases. Originally just a tabloid euphemism for traders prosecuted for dealing in Imperial units, the term is now used for those fighting against the original prosecutions, and expanded to outright opposing Europe in general.[7] It's not yet known whether Brexit will enable the UK to finally go back to furlongs and firkins.

A couple of extremely marginal crackpot organisations, namely the British Weights and Measures Association and Active Resistance to Metrication, serve as rallying points for charlatans and luddites of every persuasion to unite in their opposition to modern, scientific units of measure. The latter group of anti-metric extremists delights in their obnoxious and antisocial habits of vandalism, altering metric distances on signs (even privately owned ones) to – often less precise – values in obsolete units, and even posting pictures of their crimes to social media. Notably, their leader has a standing conviction for criminal damage. Their former website was a treasure-trove of lunatic advocacy for far-right causes, such as protesting the "Islamification" of Britain and the "redefinition of marriage", on which the organisation's zealot members went by bizarre pseudonyms such as "Wun Tun" and "Hundred Weight".

And, as everyone knows from watching Top Gear, British automobiles still measure their speeds in miles per hour, and their fuel efficiency in miles per (imperial) gallon. However, the metrication of transport in the UK is underway, even if it is plodding along at a top speed of 1 mph. The bizarre hybrid of measurements used in the UK is such that buses measure their speeds in miles per hour, whereas trams use kilometres per hour. Although road speeds are typically measured in miles per hour, speed limiters are commonly set to speeds in kilometres per hour, thus you can see bizarre signs on vans and trucks such as "Limited to 68 mph" (i.e. 110 km/h). Trains are transitioning slowly from the Ye Olden miles and chains to kilometres.

In Ireland[edit]

The real sign to show that you are in the Republic instead of the North

Ireland started switching from imperial measures to metric at roughly the same time as the United Kingdom from the early 1970s with very little hostility, as the imperial system was seen as a legacy of British rule. In the 1980s when the country modernised and updated its traffic signage, it also changed the measurements from miles and yards to kilometres and metres. However, in a very surreal fashion, it still kept speed limits in miles per hour until 2005! To persuade drivers a little, they did raise the speed limit on motorways from 70 mph (112.7 km/h) to 120 km/h (74.6 mph). Compared to the UK, it completed its metrication in 2000.

Nevertheless, there is still one exception to the rule on metrication in Ireland. When you buy your Guinness, Smithwick's or Bulmer’s from a pub, it still comes in an imperial pint of 568 millilitres. Only if you buy from an off-licence does it comes in half-litre cans.

Arguments against metrication[edit]

The logical, simple and obviously superior English units compared to the Satanic Metric units
The metric system is the tool of the devil! My car gets forty rods to the hogshead, and that's the way I likes it!
—Fuel efficiency lover Abraham Simpson[8]
Divisions into tenths are awkward to work with on a practical basis!
The division of a foot into 12 equal pieces, for example, allows you to easily divide lengths in feet by 3 or 4, which apparently crops up all the time in construction or baking or some such. In practice, this is not a problem when working with metric units, since there is nothing to prevent you from using 300 mm intervals divided into twelfths of 25 mm. Indeed, the case could be made that the small size of the millimeter makes it a far more practical unit than the inch, since it is rarely necessary to work with fractions (17/64", anyone?), and it is easy to work in intervals that can be subdivided in many ways (e.g. 360 mm) if so desired. In practice, the users of the obsolete units often nod to the greater utility of base-ten arithmetic by decimalising inches etc. Of course, this is not done consistently, so there is often need to consult a fraction-decimal conversion chart.[9] Anyway, what is a third of 11 inches? What is a third of a pint? The fact that the olden units don't use a consistent base at all makes this argument void.
Fahrenheit degrees are smaller, so they offer greater precision than Celsius!
If we are to accept this reasoning, we also have to look at measures of distance and volume. Kilometers and centimeters offer greater precision than miles and inches, and liters offer more precision than gallons. Also metric units are simple to scale down for greater precision: millimeters and milliliters, for instance. In practice, using a decimal point where appropriate solves all these apparent problems, so this is really a non-issue.
Fahrenheit is more practical for everyday use than Celsius! 100 °F gives a nice cutoff for really hot weather, and 0 °F for very cold weather!
That's not much of an argument for avoiding an entire system of weights and measures. One gets used to thinking in Celsius, just as one did for Fahrenheit.[note 4] The Celsius scale also integrates neatly with the kelvin, the unit of absolute temperature as used in many science and engineering applications. a Celsius temperature is simply the difference (in kelvins) from the freezing point of water (273.15 K), a quantity that can be ignored when talking about differences in temperatures. In other words, one degree Celsius has the same size as one kelvin. The equivalent to the Kelvin scale for Fahrenheit (the Rankine scaleWikipedia) is now of historical interest only.
It's too hard (for old people) to learn a new system!
This argument is needlessly patronizing towards those of older generations, who are in general quite capable of learning and using SI if they choose to. It is a completely unproven claim that old people couldn't cope with the switch to a simpler system, and besides, since there will perpetually be a demographic of old people in the population of society, this claim seems to imply that progress in society will have to be postponed indefinitely.
What about kitchen measurements? Replacing cups and spoonfuls with, say, 75 milliliters? That doesn't have the right feel to it at all!
In reality, it is entirely practical to measure everything in the kitchen in grams and milliliters as appropriate. Even in metric countries, spoonfuls are used for small quantities. One teaspoonful equals 5 milliliters, making conversion easy. One tablespoonful equals 15 ml. A cup equals 0.2 liters, which means one liter makes five cups. Plus, why are you measuring butter in cups anyhow? As a further aside, the First Amendment totally allows you to write a cooking book with cups and furlongs and eggshells as measurements all you like. But don't try to force pound force on NASA. Incidentally, how many times have you cursed your measuring cups when you needed to halve a recipe that called for a tablespoon or 1/3 cup of something? But if you really are into molecular gastronomy, one drop equals quite exactly 0.05 milliliters (or cubic centimeters), making exact measurements even easier - even in the kitchen! Also, some recipe books list their measures in metrics on introduction page, thus allowing for easy two-way conversion on the fly.
Changing everything in the country would be too expensive!
In practice, this wasn't a serious problem in countries like Australia, which just got on with it and changed everything over to the new system in a few years. Metrication is a one-off cost, whereas unit conversions and the associated confusions, problems and incompatibilities are recurring. Speaking of "too expensive", see our below non-comprehensive list of costs incurred solely by the failure of the US to adopt the metric system like the rest of the world.
Important to know.
Drugs are measured in metric, especially cocaine and other "hard drugs"!
Besides the fact that this claim is untrue (as ounces are a typical measurement for drugs as well), it's simple poisoning the well. If anything, it's probably a sign of both the precision and the ease-of-use for any measurement system that gets picked up by street hustlers and drug cartels that know violence may erupt in response to measurement error.
Metric is better for scientific use but English units are better "calibrated" for common use! For example, the gallon has the size it does because that is a good size for laypeople to measure volumes with, and a foot has roughly the size of a human foot. A meter is defined to be some fraction of the distance traveled by light in a second, which may be great for some Communist scientist in a laboratory, but not for a farmer!
This argument is common in the USA, yet everywhere else where metric units are used, laypeople have absolutely no problem using metric units in everyday situations. In fact, they generally become lost when told to use the supposedly "better calibrated" imperial units. Imperial units have a huge number of distinctly named, arbitrarily sized units and because of the unsystematic definition of the units, conversion between units is nearly impossible without memorizing them all and the chaotic plethora of conversion factors between them. Everyone who regularly uses metric agrees that metric units are much easier for common usage, including farmers all over the world. Additionally, even with the metric system, the expression "foot" is still used as an everyday layperson measurement. This is because people in countries that use the metric system still have feet, and thus, still have a general idea of what size range you mean when you compare something to "the size/length/volume" of a human foot. Also, it's easy to remember some of your personal measurements in metric, and unless you cannot get used to extremely basic multiplication, whole complaint easily becomes moot. The loss of the ability to compare things and measurements to human feet within the metric system is, in other words, an unfounded fear. The Quarterpounder is still sold outside the US and Dutch people all know that an ons is exactly 100 grams.
Metric Units are a communist atheist plot cooked up by some proto-communist during the French Revolution, just like the Guillotine and decimal timeWikipedia. We prefer American units
While it is true that the Metric system originates in the French Revolution, so does the declaration of the rights of man and the citizen, so this guilt by association is a bit stupid. Also, the imperial measurements are the same King George III and his goons left behind when you threw them out. Furthermore, the guillotine was in use well before the French Revolution and the people involved in it (including its most radical leaders like RobespierreWikipedia) were not atheistsWikipedia. On another note, is that how you thank the Marquis de La FayetteWikipedia for his service?

Metric time[edit]

When the French revolutionaries brought in the new metric system, they also brought in the French Republican Calendar, which decimalized time with uniformly thirty-day months (five or six days being added at the end of each year to keep the seasons in step), ten-day weeks, ten-hour days,[10] 100-minute hours and 100-second minutes. And catchy names like Brumaire and Thermidor, which we can only hope made some sense in French. This did not prove terribly popular and was abolished less than 15 years after it was brought in.

Nearly two centuries later, Saturday Night Live parodied it in their "Metric day" sketch.

Ironically, using a decimal system for the "arbitrary" increments of the day (as noted above), the "new second" would be within 20% of the "old second." So counting off would translate to "one nine hundred, two nine hundred, three nine hundred..." See how easy this would be? It's effectively just a way of stating as a decimal fraction the proportion of the day that has elapsed.

There are apps such as LogiClock which can display decimal time.

Strictly speaking, SI time is already a decimal standard: like any other SI unit, the second can be used with decimal prefixes. Whereas this is common with the reducing prefixes (milli-, micro-, nano-, etc), the magnifying prefixes (kilo-, mega-, giga-, etc) are not widely used in this way, because they don't align neatly with days, weeks, months and years.[11] Given that the way humans typically experience time is cyclical (unlike any other physical dimension, such as length, mass or temperature), time is a rather unusual dimension. Moreover, any system of timekeeping that was decimalised on Earth would make no practical sense to humans living in deep-space habitats, or on colonies on other planets, which would have very different time cycles. So there is relatively little reason to adjust the SI – all units derived from the second, such as the joule, newton and pascal – such that there are 100 000 seconds in a day.

Problems caused by having two systems[edit]

If kilometers are shorter than miles, could I save gas by taking my next road trip in kilometers?

It is often claimed that, while the metric system offers important advantages in science, there is no real harm to retaining the old units and using them in parallel with SI. However, there are many ways in which this "dual-units" approach can cause problems which are just as severe as those caused by the lack of metrication, leading some metric advocates to adopt a position of "don't duel with dual"[13]:

  • The Gimli GliderWikipedia incident of 1983 was the result of improper conversions that left a plane with less than half of its needed fuel for a trip. Incredible piloting prevented any deaths.
  • In 1999, NASA's Mars Climate OrbiterWikipedia was lost due to unit mismatch in software: the output of the program that kept track of small thruster firings while the probe was en route reported these impulses in pound-force-seconds, but the program that used this data to update the spacecraft's known position expected the numbers to be in newton-seconds. A pound-force is more than 4 N, so the probe ended up being far closer to the Martian surface on its first orbit than it was supposed to, slicing into the upper Martian atmosphere extremely fast and burning up.
  • There are frequent problems when doses of medicine are measured in non-metric units such as drams or teaspoons (the latter of which is readily confused with the tablespoon, a factor of three or four larger). Such confusions have repeatedly led to fatal overdoses, meaning that medicine has increasingly standardized on metric units, requiring all devices for measuring liquid medicines to display millilitres only, and asking parents to dispense medicines to their children using millilitres only.[14][15][16]
  • Dose errors can also be caused by confusion regarding patient weight, since medicines are commonly prescribed in a quantity which is proportional to the body mass of the patient (e.g. milligrams of drug per kilogram of patient body mass); notably, no medication is commonly prescribed or described in terms of imperial units. In the US, confusion between pounds and kilograms could cause a dose to be wrong by a factor of 2.2, and in the UK, incorrect dosage due to imperial weighing in the past (e.g. a patient weight recorded as 13 stone 7 pounds and misread as 137 kg, which is about 60 % more) has forced standardization on metric measures for weighing patients, with imperial measurements being explicitly forbidden.[17] This practice also allows ready calculation of the patient body mass index, which is the patient's body mass (kg) divided by the square of their height (m2).
  • In the UK, the confusing situation of fuel being sold exclusively by the litre (which is a legal requirement) but driving distances typically still being measured in miles (due to inaction by the Department for Transport), there is no truly useful measurement of fuel economy. Neither miles per imperial gallon (since fuel has not been sold by gallons for decades) nor litres per 100 kilometres (since road signs and associated measurements are in miles and yards) is compatible with these conflicting units for fuel volume and road distance.
  • Incompatibility between US Customary and metric units might have contributed to the failure of the US company Target's attempt to expand into Canada.[18] It has also been suggested that similar incompatibilities have caused problems for Boeing when outsourcing work to other countries; their competitors (such as Airbus) have not faced such problems.[19][note 5] This point relates to the main reason for the push for metrication in the 1970s: the economic benefit to everyone of the world sharing a single unambiguous language of measurement.
  • The education of children is hampered by their having to use two incompatible sets of units in their studies (as in the USA) or the conflict they observe between the units they use exclusively in school, and the older units that are still retained in the outside world (as in the UK). One of the main motivations for metrication was to prevent children from having to spend the enormous amounts of classroom time required to learn the extensive conversion factors necessary to use imperial and US customary units correctly, but until metrication is complete this cannot truly happen, nor can children be free from the need to learn the clumsy conversion factors between imperial and metric units.
  • Even the most trivial calculations are made unnecessarily difficult by imperial units, impeding people who use imperial from gaining an intuitive understanding of many measurements, e.g. how they scale up. The smooth and intuitive scaling of metric units does not pose such problems: if one knows what a drive down a 500-metre section of highway feels like, then one can easily reason that a 60-kilometre drive comprises 120 such sections; the same comparison between 500 yards and 60 miles is not so easily made. Likewise with innumerable scalings and comparisons of everyday measurements – if a steak is weighed in ounces, a bicycle in pounds, a man in stones, and a car in long tons and hundredweights, how does one get an intuitive feel of the ratios of their weights? To speak in an aphorism, one might say that the essence of stupidity is to make trivial things difficult, while the essence of intellect is to make difficult things trivial.
  • Refusing to convert to the metric system makes travel more difficult for Americans. Americans unfamiliar with the metric system traveling outside of their country have to convert all distances, weights, measures, and temperatures to their system to get a feel for what the local figures mean. So it is a good idea for Americans learn the metric system, even if they have no intentions of using it at home.[note 6]

Specific impulse[edit]

In SI, impulse (the integral of a force of a given magnitude applied over a given time, equivalent to the change in momentum due to the force) is measured in newton-seconds. An important measure of the power of a rocket fuel is its specific impulse — meaning the amount of impulse the fuel delivers per unit mass, or newton-seconds per kilogram.

In the imperial system this measure becomes confused because the same word pound is used to describe both force and mass. So specific impulse, in that system, is "pound-seconds per pound" and is quoted as simply "seconds." This measure is so ingrained in rocketry that specific impulse is still quoted in seconds even though nobody in the rocketry field now uses imperial measurement.

The dimensions of specific impulse are, of course, not simply T but LT-1, same as velocity.

How the metric system is flawed[edit]

Despite its simplicity, in the real world, the common implementation of the metric system can be problematic. Nature is of course indifferent to human conventions.

  • Common use of non-decimal minutes, hours and days for measuring time (but at least the hours are counted to 24, avoiding the AM/PM disaster).
    • Related, the common use of km/h for measuring speed, which must be divided by 3.6 to get the SI speed in m/s.
    • Electricity usage is usually billed in kilowatt-hours instead of joules (1 kWh=3.6 MJ).
    • Battery capacity (especially in mobile phones) is measured in milliampere-hours instead of the SI unit of electric charge coulombs (1 mAh=3.6 C).
  • Fairly common use of "metric horsepower" or pferdestärke (instead of kilowatts) for measuring power of automotive engines.
  • While a proper metric system for shoe size exists, Mondopoint, it is really only used for ski boots and in NATO. The base unit for the most common shoe size system in Europe is the Paris point (two thirds of a centimetre), no less. Still way better than imperial shoe sizes, which are based on the barleycorn, with different offsets for male/female/child/UK/US shoes to make it more interesting.
  • Clothes sizes cause problems to both metric and imperial, with most male sizes letter based and most female sizes two or three numbers smaller for the same actual size than a decade or two ago. This is why — naturally — online clothes retailers ask you to measure yourself and give the centimetre value behind sizes used by certain brands.
  • Distances at sea and air are still measured as nautical miles (= 1852 m exactly) and speeds as knots (nautical miles per hour). At inland waterways the CEVNI rules use kilometres and km/h, though. For conversion purposes, 1 m/s is very nearly 2 kn.
  • Angles are likewise measured in degrees, while the absolute unit of angle, radian, has very few practical applications. (Milliradian, its subdivision, is extremely handy on measuring skinny triangles, such as in surveying or acting as a sniper. All non-American scope sights are equipped with milliradian scales.)

Common phrases[edit]

1+1=\ ? This article/section deals with mathematical concepts appropriate for notedscholar.

As these examples show, the metric system makes expressing simple statements complicated.

  • I'd walk 1.609 km for a Camel.
  • (Sings) "2.54 centimetre worm, 2.54 centimetre worm, measuring the marigold..."
    • "I'd walk 1,609,344 km/For one of your smiles..."
    • "I would walk 804.674 km/And I would walk 804.674 more/Just to be the man who walked 1609.348 km to fall down at your door."
  • 28.35 g of prevention is worth 0.453 kg of cure – except if you're talking Troy weights, in which case 31.1 g of prevention is worth 0.373 kg of cure
  • 0.473 L is 0.454 kg the world around (Er, well actually only in the USA)
  • Give them 2.54 cm and they'll take 1609.344 metres!
  • 96,561 Kilometres Under the Sea by Jules Verne[20]
  • How many teaspoons in a cup, again? (50) (48 in the U.S.)
  • "But I have promises to keep, and multiples of 1.609 km to go before I sleep" - Robert Frost, "Stopping by Woods on a Snowy Evening"
  • The longest word in the English language is "s1.609kms," because there are 1.609 km between the first and last letters
  • Texans can now wear 37.8-litre hats!
  • 1.609 km high cityWikipedia
  • "The 453.592 grams of flesh, which I demand of him..." - Shakespeare, The Merchant of Venice

External links[edit]


  1. 1dm3 =.1m x .1m x .1m = 0.001m3
  2. One degree Celsius also works in this case, because the size of one kelvin is equal to the size of one degree Celsius.
  3. Readers who have studied elementary chemistry have no doubt encountered yet another non-SI unit, the atomic mass unit, used in the periodic table of the elements.
  4. This line of reasoning can also be turned around to argue against metrication.
  5. However, the Boeing 787 Dreamliner has had more orders and deliveries than the Airbus 380 super jumbo jet. Furthermore, outsourcing currently faces broad popular opposition in the U.S. as many Americans lose their jobs to foreigners.
  6. But it goes both ways. Non-Americans traveling to the U.S. should have a basic grasp of U.S. customary system to avoid a culture shock.


  1. Jackson, John David. Classical Electrodynamics. 3rd ed., Wiley, 1999. Preface.
  2. Griffiths, David J. Introduction to Electrodynamics. 4th ed,. Pearson, 2013. Advertisement.
  3. Some businesses manage to sell beverages in 2-quart (1.89 L) bottles/cartons which make them slightly more profitable. (N.B.: An Imperial quart is 1.16 US quarts, and is in fact larger than a litre at about 1140 mL.
  6. See, for example, the British Weights and Measures Association
  7. — and just to show that the US doesn't have the monopoly on conservative paranoia, they decided to post a (dead) link to "20,000 road signs in kilometers [sic] – an evil EU plot?"
  9. See this video on real-world instances where feet, inches, pounds, gallons, etc. get divided into tenths.
  10. Working eight hours a day all of a sudden sounds a lot longer!
  11. A typical human lifespan, for example, is 2-3 Gs
  20. Note that the original French name was Vingt mil lieues sous les mers: French lieue is exactly 4 km, making the original journey 80,000 km; twice the circumference of Earth.