Frequently Misused Units of Energy and Work
A frequent instance of Unit Confusion is when "watts" is used with a unit of time, as in "watts per second". "Watts" already incorporates a rate (one watt = one joule per second) so "watts per second" only makes sense if referring to a power source that is changing in intensity. A similar mistake is the use of "watts" when it is really a quantity of energy that is meant, as in "this battery can store up to 200 megawatts of power", when the accurate thing would be to measure the stored energy in joules (watt-seconds), watt-hours (1 Wh = 3600 J), or as technicians usually do, in ampere-hours (which when multiplied by the battery's voltage give watt-hours).
Another issue that some may face is the fact that energy is energy. It doesn't matter where it comes from. That is, a watt is a watt, regardless if it's an electrical watt or a thermal watt. For example, computer hardware that requires cooling often has a "thermal design power" specification attached. While on a technical level this specifies the minimum amount of cooling required for a cooling system to dissipate, it's also useful for roughly how much electrical energy the part will consume when working at full bore.
But this also leads to yet another bit of confusion. Most energy delivery systems have two notable values: how much energy they can handle at once and how much energy they can handle over time. For example, some people may think that a 1500 W-Hr battery backup system for homes can't handle something like hair dryer, which typically consumes about 1500-1800W. Usually they can, since that's the typical capacity of a home electric circuit (though double check the specs). They can only do it for about less than an hour. In a related note, some people may see headlines about a super powerful laser being used in science experiments with power outputs of around 30 terawatts or higher. For comparison, as of 2022, the US consumed about 4050 terawatt-hours of electricity. So one might think that these super powerful lasers are eating up around 1% of the total energy consumption. Except these lasers only activate for milliseconds at a time, so their actual power consumption is more like in the kilowatt-hour range when averaged out over time. These articles are likely scaling the instantaneous power consumption over a full second to make it sound more impressive.
Conversely, with computer hardware, people have been confused as to why processors can consume much more power than its rated TDP would suggest. For instance, one would expect a 65W TDP CPU to consume only up to 65W of power, but it can, briefly, consume twice that in short periods before dropping down to a lower power consumption such that over basically infinity, the average power dissipated is 65W.
Frequently Misused Units of Time and Astronomical Distance
A mistake that seems to be getting less common (but it still showed up in, eg., Earth 2): Like parsecs, light-years are a unit of distance (the distance light travels in a year), not time. Whether or not the phrase "light-years more advanced" is a mistake or just an analogy (as in "miles ahead") is debatable, and probably varies from case to case.
People mistook "light-years" to be a construction along the lines of "Space Miles" or "Earth Minutes" - sciencey word + unit of measure = sci-fi unit of measure. Of course due to the effects of time dilation
light does not feel the passage of time so in the incorrect interpretation a light-year is no time at all.
To increase the confusion a bit more, the second in parsec (parallax second) is a unit of angle (an arcsecond), while the year in light-year is indeed a unit of time.
Frequently Misused Units of Temperature
One obscure enough that it comes up all the time: Since 1968, the standard unit of absolute temperature is "kelvins", not "degrees Kelvin". The older usage dates to before the 13th General Conference on Weights and Measures (CGPM).
On a related note, some works make reference to a temperature which is lower than absolute zero. Absolute zero occurs in the total absence of heat or energy of any kind. You can't get colder than that. (Technically, negative absolute temperatures do exist, but these are only mathematical abstractions describing a very particular states of matter, such as the excited electrons in the laser's working medium, and they don't refer any actual temperature. What's more, negative temperatures are actually considered hotter than positive temperatures.)
Another related fallacy is the assumption that, for example, 40°C is twice as hot as 20°C. This is not true because 20°C is equal to 293.15K; twice as hot as this would be a lot more than 313.15°C (though not as much more as you might think; the relationship between heat and temperature is exponential rather than linear).
Numbering the Years and Days
Perhaps not, strictly speaking, a unit, but "AD", unlike "BC" and "CE", is supposed to come before the year, so "2005 AD" is incorrect. This particular error is so near-universal both in and out of television that it's even accepted (and used) by professional historians.
Another frequent confusion with casual users of A.D. comes from the (incorrect) notion that it stands for "After Death." Their thinking is that years B.C. were years before Christ was born, and years A.D. were years after Christ died, with 30-some-odd years passing in between that weren't numbered. In reality, A.D. stands for Anno Domini ("in the year of our Lord") and was supposed to mark the year that Christ was born, so the day after 31-December-1 B.C. was 1-January-A.D. 1. Note that there is no year 0, and due to old calculation errors, historians now believe that Jesus was born in the single digits B.C. (but it's easier to change one date and live with the oddness than to change all of them to recalibrate the timeline).
Some astronomers use a year zero to facilitate calculations between years (namely, subtraction). This is also why you'll see years given as negative numbers. It's much easier to do math by hand or by programming if you don't have to make strange exceptions for how numbers work at any given point, and then just convert (say) -752 to 753 B.C. Other astronomers use a Julian Day Number to describe dates, and that has no "year" component at all. It's expressed as the (usually large) number of days since the start of the epoch, with the time of day indicated by a decimal, and is a probable inspiration for the "stardates" in Star Trek.
Frequently Confused Units of Volume and Weight
Imperial and American Customary measurements share the names of measurements, and lengths are the same value in both, but not volumes - pints and gallons for example. (An Imperial pint is 20 Imperial fluid ounces; a U.S. liquid pint is 16 U.S. fluid ounces. Similarly, a U.S. ton or "short ton" is exactly 2000 pounds, but an Imperial ton or "long ton" is 2240 pounds — because it's exactly 160 stone.)
Occasionally, confusion between normal ("avoirdupois") ounces and Troy ounces can occur. Gold, silver, and other precious metals are still traded in units of Troy ounces; a bullion ingot of exactly 1 Troy ounce would weigh 1.07 ounces on a postal scale.
Carats and karats should not be confused; one is a unit of mass and the other is a unit of purity, respectively. Gems are measured in carats, with 1 carat = 0.2 grams. Gold is measured in karats, on a scale of up to 24. Just to make things more confusing, karat can also be spelled as carat!
Confusion Regarding Storage Space
To a computer, a kilobyte is 1024 bytes, a megabyte is 1024 kilobytes, a gigabyte is 1024 megabytes and so on. However, to hard drive manufacturers, a kilobyte is 1000 bytes, a megabyte is 1000 kilobytes, etc. To avoid confusion in recent times, the binary prefix system was invented. So a kibibyte is 1024 bytes and a kilobyte is 1000 bytes. Still, the old way is interchangeable.
- Mac OS X Snow Leopard and recent versions of Ubuntu report space with each order of magnitude increasing every 1000.
- The old High Density 3.5-inch floppy disks were marketed as being "1.44 MB". Their actual storage capacity (before formatting) was neither 1.44 x 1000 x 1000 bytes, nor 1.44 x 1024 x 1024. It was 1.44 x 1000 x 1024 bytes, or 1440 Kilobytes.
- Hard drive manufacturers most often use the convention of one billion bytes to the gigabyte to make their products' capacities sound bigger. Even flash memory chips, which are manufactured in powers of 2, report their size in powers of 10 so that they can use the extra 5% to 7% as spares in case sectors of the chip wear out.
- "Kilo" and "Mega" are exactly 1000 and one million, respectively, when describing data transfer rates in bits per second; e.g. a 56 kbps analog modem transfers data at 56,000 bits per second, not 57,344 (56 x 1024) bits per second. However, the number of kilobytes transferred per second is in increments of 1024 bytes, to match the numbers reported by the file system.
Frequently Misused Units of Distance and Area
You cannot have "a one square mile radius." It's describing an area, yes, but it's still a "one mile radius", and also an area a fair bit bigger than one square mile.
The hectare is not a unit of distance, but a unit of area equal to that of a square whose sides are 100 meters long, i.e. 10,000 square meters.
What Measure is a Billion?
Even unitless numbers can suffer from similar problems. In the US (and since a lot of other countries around the world have adopted the convention) a million is 10^6, a billion is 10^9, a trillion is 10^12, and so on. So the prefix n (Latin for one, two, three etc) the "short scale" is used determines the number by 10^(3n+3). However in other countries that still use the old British/European "long scale" (no longer used in Britain since 1974), a million is 10^6, a billion is 10^12, a trillion is 10^18, and so on (using the formula 10^6n), while 10^9 is a milliard. This is why scientist forgo using words and write large numbers in scientific notation instead.
Also, since all countries at least agree that a million is 10^6, sometimes larger numbers will go unused in favour of stating in millions. 10 thousand million million million is unambiguous, for instance, whereas while in the US and elsewhere it would be typically referred to as 10 sextillion, but some people in Britain and Europe would call that 10 thousand trillion (or in French possibly, 10 trilliard).
The Chinese used to have the same problem with their own words for big numbers. Although nowadays most people never use any number above 亿 (10^8), there are at least four different ways to interpret the higher numbers like 兆, 京, and 垓. Today, everybody agrees that 亿 is 10^8, which means method 1 is no longer used. The structure of methods 2 and 3 are reminiscent of the short and long scale in European numbers (modern Chinese people always use method 2 if they use the larger numbers at all), while method 4 is the basis for Donald Knuth's -yllions system.
