# List of Conversion Factors

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To change​
To​
Multiply by​
acres​
hectares​
.4047​
acres​
square feet​
43,560​
acres​
square miles​
.001562​
atmospheres​
cms. of mercury​
76​
Btu/hour​
horsepower​
.0003930​
Btu​
kilowatt-hour​
.0002931​
Btu/hour​
watts​
.2931​
bushels​
cubic inches​
2150.4​
bushels (U.S.)​
hectoliters​
.3524​
centimeters​
inches​
.3937​
centimeters​
feet​
.03281​
cubic feet​
cubic meters​
.0283​
cubic meters​
cubic feet​
35.3145​
cubic meters​
cubic yards​
1.3079​
cubic yards​
cubic meters​
.7646​
degrees​
.01745​
dynes​
grams​
.00102​
fathoms​
feet​
6.0​
feet​
meters​
.3048​
feet​
miles (nautical)​
.0001645​
feet​
miles (statute)​
.0001894​
feet/second​
miles/hour​
.6818​
furlongs​
feet​
660.0​
furlongs​
miles​
.125​
gallons (U.S.)​
liters​
3.7853​
grains​
grams​
.0648​
grams​
grains​
15.4324​
grams​
ounces (avdp)​
.0353​
grams​
pounds​
.002205​
hectares​
acres​
2.4710​
hectoliters​
bushels (U.S.)​
2.8378​
horsepower​
watts​
745.7​
horsepower​
Btu/hour​
2,547​
hours​
days​
.04167​
inches​
millimeters​
25.4000​
inches​
centimeters​
2.5400​
kilograms​
pounds (avdp or troy)​
2.2046​
kilometers​
miles​
.6214​
kilowatt-hour​
Btu​
3412​
knots​
nautical miles/hour​
1.0​
knots​
statute miles/hour​
1.151​
liters​
gallons (U.S.)​
.2642​
liters​
pecks​
.1135​
liters​
pints (dry)​
1.8162​
liters​
pints (liquid)​
2.1134​
liters​
quarts (dry)​
.9081​
liters​
quarts (liquid)​
1.0567​
meters​
feet​
3.2808​
meters​
miles​
.0006214​
meters​
yards​
1.0936​
metric tons​
tons (long)​
.9842​
metric tons​
tons (short)​
1.1023​
miles​
kilometers​
1.6093​
miles​
feet​
5280​
miles (nautical)​
miles (statute)​
1.1516​
miles (statute)​
miles (nautical)​
.8684​
miles/hour​
feet/minute​
88​
millimeters​
inches​
.0394​
ounces (avdp)​
grams​
28.3495​
ounces​
pounds​
.0625​
ounces (troy)​
ounces (avdp)​
1.09714​
pecks​
liters​
8.8096​
pints (dry)​
liters​
.5506​
pints (liquid)​
liters​
.4732​
pounds (ap or troy)​
kilograms​
.3732​
pounds (avdp)​
kilograms​
.4536​
pounds​
ounces​
16​
quarts (dry)​
liters​
1.1012​
quarts (liquid)​
liters​
.9463​
degrees​
57.30​
rods​
meters​
5.029​
rods​
feet​
16.5​
square feet​
square meters​
.0929​
square kilometers​
square miles​
.3861​
square meters​
square feet​
10.7639​
square meters​
square yards​
1.1960​
square miles​
square kilometers​
2.5900​
square yards​
square meters​
.8361​
tons (long)​
metric tons​
1.016​
tons (short)​
metric tons​
.9072​
tons (long)​
pounds​
2240​
tons (short)​
pounds​
2000​
watts​
Btu/hour​
3.4121​
watts​
horsepower​
.001341​
yards​
meters​
.9144​
yards​
miles​
.0005682​

Related Other Physics Topics News on Phys.org
BvU
Homework Helper
2019 Award
I sure wish Napoleon had conquered England and its colonies ....

dextercioby and anorlunda
robphy
Homework Helper
Gold Member
What this table really means:

Since
$$(1\rm\ acre)=(0.4047\rm\ hectares)$$
either take your quantity in acres
• and multiply it by 1 written as $1= \frac{(0.4047\rm\ hectares)}{(1\rm\ acre)}$
as in $$(5 \rm\ acres)=(5 \rm\ acres)\left(\frac{(0.4047\rm\ hectares)}{(1\rm\ acre)}\right) =5 (0.4047\rm\ hectares)$$
• or substitute $(0.4047\rm\ hectares)$ everywhere you see $(\rm acre)$
as in $$(5 \rm\ acres)=(5 \ (0.4047\rm\ hectares))=5 (0.4047\rm\ hectares)$$
which is "multiplying by 0.4047 AND replacing 'acres' with 'hectares' "

The parentheses are useful to avoid the common pitfall involving squaring or cubing units.
• $1\rm\ cm^3{ \color{red}{ {\bf\Huge\ \neq\ }}} 1 \times 10^{-2}\ m^3 =\frac{1}{100} m^3$

• $1\rm\ cm^3{ \color{blue}{ {\bf\Huge\ =\ }}} 1\rm\ (cm)^3\ =\ 1\rm\ \left(1 \times 10^{-2}\ m\right) ^3= 1 \times 10^{-6}\ m^3 =\frac{1}{1000000} m^3$
Note the unit is $\rm (cm)$, not $\rm (c)$.

my $0.02 ohwilleke, dextercioby and Greg Bernhardt mfb Mentor I'm so glad that degrees/radians is the only one I need from that list (although I use 180/pi, no need to remember or look up a number), not counting the occasional homework question that uses exotic units. I think it would make sense to sort the list by type of unit (e.g. all length conversions together). A conversion table can replace many individual entries. Greg Bernhardt sophiecentaur Science Advisor Gold Member A conversion that's really not trivial would be mm into and out of Fractions of an Inch. So many US metal workers and stock suppliers still use fractions a an inch ( interspersed with "thou" or thousandths of an inch, for 'good measure'). As someone who didn't need Napoleon to convince me that a metric measurement system had a lot going for it, I find the continuing US attitude difficult to understand. (I have found that many of them are actually nice chaps, aamof) ohwilleke Gold Member A conversion that's really not trivial would be mm into and out of Fractions of an Inch. So many US metal workers and stock suppliers still use fractions a an inch ( interspersed with "thou" or thousandths of an inch, for 'good measure'). Inches to mm isn't the bad because the inch is defined exactly as 25.4 mm. One "thou" is exactly .0254 mm. I normally do all length conversions starting from this definition and then figure out how many inches there are in a length unit, if I have a calculator on hand. Hundredths of an inch (which are 0.254 mm) are used quite frequently in U.S. land surveys. Likewise, I would never use the number in the table to convert acres to square miles when I know that there are exactly 640 acres in a square mile (a.k.a. a "section"), and 160 acres in a quarter section, etc., and a township is 36 square miles. (I almost never use the surveyors measures of rods (16.5 feet) and Gunter's chains (22 yards) (a Gunter's link is 1% of that, i.e. 7.92 inches), the engineer's chain (100 feet) (an engineer's link is 1% of that, i.e. 1 foot), or the naval cable (720 feet), however. A French foot is 12.79 U.S. inches (about 324.8 mm), and an arpent is 180 French feet in North America including Quebec (about 192 U.S. feet and 58.47 meters) and about 220 French feet in Paris (about 234 U.S. feet and 71.46 meters). Historically, in North America, 1 (square) arpent (arpent carré), also known as a French acre, was 180 French feet × 180 French feet = 32,400 French square feet = about 3419 square meters and about 0.845 acres. Certain U.S. states and countries have official definitions of the arpent which vary slightly. In Louisiana, Mississippi, Alabama and Florida the official conversion is 1 arpent = 0.84628 acres (3,424.8 square metres). In Arkansas and Missouri, the official conversion is 1 arpent = 0.8507 acres (3,443 square metres). In Paris, the square arpent was 220 French feet × 220 French feet = 48,400 French square feet, about 5,107 square metres or 1.262 acres. In Mauritius and Seychelles, an arpent was 200 French feet x 200 French feet, about 4220.87 square meters, 0.4221 hectares, 1.043 acres. In Japan, the traditional unit for measuring interior space in buildings which is still in common usage is the tatami mat, which has a a standard size of about 910 mm x 1820 mm (roughly two square yards which is roughly 18 square feet), with a half mat being 910 mm x 910 mm (roughly one square yard which is roughly 9 square feet) although there was historically regional variation in that standard. A lap on a U.S. running track is usually 440 yards (1/4 mile). A 5k race is very nearly 3 miles ad a 10k race is very nearly 6 miles. A marathon is 26.2 miles (derived from the length of the original course after which it is named from the battlefield in Marathon to the stadium in Athens) and a half marathon is 13.1 miles. A length (also sometimes called a lap although sometimes a lap refers to two lengths) in a U.S. swimming pool is usually 25 yards, 25 meters, or in an "Olympic sized" pool, 50 meters. I would never use a decimal to convert hours to days (24 hours in a day), minutes to hours (60 minutes in an hour), seconds to minutes (60 seconds in a minute), or seconds to days (86,400 seconds in a day). Why be inexact or avoid fractions that are more natural when you don't have to? Conversions from seconds to years are also useful (but tricky because you need to be clear if it is a 365 day year, a 366 day year, or an average year, which is best for long time period conversions to seconds and is roughly 365.24 days per year which is 31,556,736 seconds). Lawyers, of course, think in tenths of an hour (6 minutes each). A "shift" generically usually refers to 8 hours, although there are professions where ten or twelve hour shifts are customary (e.g. nursing) and where 24 hour shifts are customary (e.g. firefighters). A "watch" often used interchangeably with a "shift" refers to an eight hour period of which there are three canonical ones in a day. Usually, the first watch is 8 a.m. to 4 p.m., the second watch is 4 p.m. to midnight, and the third watch is midnight to 8 a.m., although sometimes 9-5, 5-1 and 1-9 are used instead. A "quarter" is three months, the first quarter is January-March, the second quarter is April to June, the third quarter is July to September, and the fourth quarter is October to December. A league is 3 miles on land (used in historical literary, military and naval terminology). A hand is 4 inches (which is 101.6 mm and is usually used to measure horse height). A stone is 14 pounds and quite commonly used for weights of people in British English speaking regions. A point (in a font) is exactly 0.013837 inches (about 1/72th of an inch) and a pica is 12 points (0.166044 inches which is about 1/6th of an inch). A cord is exactly 128 square feet (usually used to measure firewood). A barn (symbol: b) is a unit of area equal to 10^−28 m^2 (or 100 fm^2) used in nuclear physics. 1 mb is 2.56819 GeV^−2 in "natural units". A related units is the inverse femtobarn. This is typically used to measure the number of particle collision events per femtobarn of target cross-section, and is the conventional unit for time-integrated luminosity. Thus if a detector has accumulated 100 fb^−1 of integrated luminosity, one expects to find 100 events per femtobarn of cross-section within these data. A parsec is about 3.26 light years (and about the distance to the closest star to Earth although that is not how it is defined). An astronomical unit is exactly 149,597,870,700 meters (and is roughly the average distance from the Earth to the Sun). A light second is about 186,000 miles and about 300,000,000 meters (by definition it is actually exactly 299 792 458 meters, because the meter was defined with reference to a meter stick approximating one ten millionth of the distance from the north pole to the equator through Paris, when if Napoleon's advisors had known better they would have defined it as one/300,000,000th of the speed of light per second). The mass of the Sun is (1.98847±0.00007)×10^30 kg, but is commonly approximated when used as a unit in astronomy to describe things other than the Sun as 2×10^30 kg. The list also omits the conversion from ºC (celsius or centigrade with the former preferred in modern usage) to ºF ( Fahrenheit) which is (ºC *9/5)+32º equals ºF (exactly), the conversion from ºC to Kelvin (which is ºC + 273.16) and from ºF to Rankine (which is ºF + 459.67). It is also useful to know the conventional approximations of conversion of common oven temperatures such as 200º F, 325º F, 350º F, 375 ºF, 400º F, 425º F, and 450º F (about which there is not a total consensus even though it is trivial to make the exact conversion), and for room temperature (typically 68ºF or 20 ºC although 72 º F is also sometimes considered room temperature in U.S. units), human body temperature (98.6º F which is 37 ºC), in ºC and to know that the boiling temperature of water is 212º F, the 0º F is the freezing temperature of salt water, and that -40 ºF is the same as -40 ºC. At very high temperatures, ºC and Kelvin are approximately identical for most purposes. Temperatures are also sometimes described in electron volt units: each kelvin (1 K) corresponds to 8.6173324(78)×10^−5 eV; this factor is the ratio of the Boltzmann constant to the elementary charge. It also omits carats (a measure of gem weight equal to 0.2 grams) not to be confused with a karat (which is parts per 24 of gold in an alloy), caliber (which is hundreds of an inch of bullet width or bore diameter for small arms, but something different in the case of naval guns where it is the length of the barrel divided by its bore diameter), imperial gallons (equal to 1.2 U.S. gallons), barrels (usually of crude oil, for which one barrel equals 42 US gallons or 35 UK (imperial) gallons, or approximately 159 liters or 9,702 cubic inches (5.6 cubic feet); 6.29 barrels equal one cubic meter and (on average) 7.33 barrels weigh one metric ton (1000 kilograms), but barrels of other substances are not always the same). A long hundred weight is exactly 112 pounds. A cup is eight fluid ounces usually approximated in metric units in practice as 240 mL or 250 mL (even though it is actually 236.6 mL). And a fluid ounce is usually approximate as 30 mL (it is actually 29.5735 mL). A tablespoon (T.) is 3 teaspoons, and 1/2 of a fluid ounce (about 15 mL) and a teaspoon (t.) is 1/6th of a fluid ounce (about 5 mL). A quarter cup is about 60 mL (but sometimes approximated as 50 mL or 62.5 mL). A half-jigger is 3/4 fluid ounces (about 22.5 mL), a jigger is 1.5 fluid ounces (about 45 mL) and a shot is 1 to 1.5 fluid ounces (usually one or the other and sometimes instead 50 mL), and a pony is 1 fluid ounce, all of which are used regularly in mixing drinks. A fifth (of a gallon), a measurement usually used for distilled spirits, is 25.6 fluid ounces which is about 757 mL which is about the same size as a standard 750 mL wine bottle (which is about 25.4 fluid ounces). A magnum is 1.5 liters (twice the standard wine bottle). For champagne and brandy, a jeroboam is 2 magnums, and for champagne: a rehoboam is 3 magnum, a methuselah is 4 magnum, a salmanazar is 6 magnum, a bathazar is 8 magnum, and a nebuchadnezzar is 10 magnum. One cc (cubic centimeter) is equal to 1 mL. There there are joules and calories as well as Calories which are kilocalories and used in dieting (one small calorie is 4.1868 joules; a dieter's calorie is 4186.8 joules). A small calorie is the amount of energy needed to raise one mL of water by one ºC and the dieter's calorie is the amount of energy needed to raise one liter of water by one ºC making it somewhat analogous in definition to the British Thermal Unit which is the quantity of heat required to raise the temperature of one pound of liquid water by 1 degree Fahrenheit at the temperature that water has its greatest density (approximately 39 degrees Fahrenheit). A kilowatt hour is exactly 3,600,000 joules. A therm is 100,000 BTU and it is approximately the energy equivalent of burning 100 cubic feet – often referred to as 1 CCF – of natural gas. An electron volt is about 1.602×10^−19 joules. Another important conversion is between eV/c^2 and kilograms: 1eV/𝑐^2 is approximately equal to 1.78⋅10^−36 kg. One atomic mass unit (amu) is 1.66053906660(50)×10^−27 kg which is also 931.49410242(28) Mev/c^2 which is 1/12th of the mass of a carbon-12 atom. A Newton is 1 meter per second squared and is equal to 100,000 dynes. A pascal is 1 newton per square meter and an atmosphere is 101,325 pascals. An "each' is 1, a couple is 2 (but sometimes approximately 2), several is at least 3 and approximate, but not all that many more than 3, a half-dozen is 6, a dozen is 12, a baker's dozen is 13, a score is 20, and a gross is 144, a lakh a.k.a. lac is 100,000 in South Asian usage (although the commas are spaced differently), a crore is 10,000,000 in South Asian usage (although the commas are spaced differently), one arab is 1,000,000,000 in South Asian usage (although the commas are spaced differently). A C-spot is$100 and a grand a.k.a. "a G" a.k.a. "K" is \$1000. In finance, a "point" is a hundredth of a percent. A "mill" is a tenth of a percent. Some financial markets primarily deal in eights of a dollar. Two bits is 25 cents. A quire is 25 sheets of paper and a ream is 500 sheets of paper (in both cases of the same size and quality).

The term "gauge" as a measurement unit is particularly complicated because it has at least twelve different meanings in different contexts.

And, then there are cubits, generally taken as equal to 18 inches (457 mm), was based on the length of the arm from the elbow to the tip of the middle finger and was considered the equivalent of 6 palms or 2 spans. In some ancient cultures it was as long as 21 inches (531 mm), and a Roman cubit was sometimes as long as about 120 cm (about 4 U.S. feet). Other ancient measurements such as the shekel (14.1 grams), the Greek stadon (607.2 or 622 feet), the Roman stadium (606 feet), the Greek Drachma (about 4.3 grams), Mina (about 0.94 pounds) and the Talent (about 60 Mina) are also somewhat slippery.

Each of these are conversions that comes up now and then in my life.

As someone who didn't need Napoleon to convince me that a metric measurement system had a lot going for it, I find the continuing US attitude difficult to understand. (I have found that many of them are actually nice chaps, aamof)
One big issue, especially in land measurement, is back compatibility. If almost all of the the land in your country has had boundaries set for it that are convenient in their existing system, converting to metric doesn't make much sense. Indeed, back compatibility is such a big issue that in places where the pre-metric French were the colonial power when land boundaries were established, pre-metric French units are still used to describe that land. Old cook books likewise impose back compatibility pressure.

Another is that an ability to convert isn't good enough. To make a measurement system functional people need to have lots of mental calibration points for things that the measure frequently so that you don't have to do conversions and that means total immersion which requires imposing one system and pretty much forbidding another system on people which is hard in a country with a strong free speech tradition and a distrust of central authority. Congress authorized metric measurements to be used as the Constitution allowed it to do, centuries ago, but it never stuck.

You also need to convert a whole industry or group of people at a time. Measurement units are basically social conventions and almost everyone in the society needs for them to be converted for them to work. There are some areas (e.g. medicine and science and engineering and the military) where there has been substantial conversion, and there are other places where it has not. Many people who get medicines in milligrams and are quite used to that wouldn't know what to do with grams when cooking, for example.

Likewise, it isn't just measurements, adopting a measurement system also implicitly means, if it is going to work, that common manufactured goods, for example, are made in convenient, reasonably round units in the prevailing measurements system and people get attached to traditional sized goods. Americans use 8.5" x 11" paper while metric people use A4 sized paper. Americans care about being six feet tall, while metric people care about being 180 cm. British people want to drink pints, while metric people prefer half liters. Americans want to buy gallons of milk or filtered water, not four liter bottles.

Last edited:
BvU, gmax137 and Greg Bernhardt
sophiecentaur
Gold Member
It's a Tower of Babel.

One measurement unit that's still in use and which totally amazes me is the binary fractions of an inch, beloved by the US 'makers of things'. The hierarchy of sizes that has to be learned must be a nightmare to anyone who comes to it fresh but who hasn't ' reasonable arithmetic skills' for placing them on the number line. (Imo, it's only one stage better than Roman Numerals). Why does it persist? At the same time, they use the 'thou', which is not actually part of the binary fraction system at all. They all know what they mean and can communicate it ok but why??? I have a feeling it's a bit of an exclusive club.

Such an interesting post! I've learned several things here (inverse femtobarn!). A couple of comments if I may.

Inches to mm isn't the bad because the inch is defined exactly as 25.4 mm. One "thou" is exactly .0254 mm. I normally do all length conversions starting from this definition and then figure out how many inches there are in a length unit, if I have a calculator on hand. Hundredths of an inch (which are 2.54 mm) are used quite frequently in U.S. land surveys.

> A hundredth of an inch would be 0.254mm. Interestingly, the inch/cm (or mm) conversion was only defined in 1964! See the Wikipedia article on Inch.

A parsec is about 3.26 light years (and about the distance to the closest star to Earth although that is not how it is defined). An astronomical unit is exactly 149,597,870,700 meters (and is roughly the average distance from the Earth to the Sun).

> Slightly more than 8 minutes and 19 seconds.

The list also omits the conversion from ºC (celsius or centigrade with the former preferred in modern usage) to ºF ( Fahrenheit) which is (ºC *9/5)+32º equals ºF (exactly), the conversion from ºC to Kelvin (which is ºC + 273.16) and from ºF to Rankine (which is ºF + 459.67).

> "Absolute zero" being -273.16 °C or -459.67 °F.

Contact me to add more! Let's build a master list!

I've turned this into a spreadsheet for future use. Had to muck about with your table a bit to get it right (it didn't import faithfully). Thank you!

ohwilleke
Gold Member
A hundredth of an inch would be 0.254mm.
Fixed. All written utterances in excess of 20 words are prone to typos.

ohwilleke
Gold Member
It's a Tower of Babel.

One measurement unit that's still in use and which totally amazes me is the binary fractions of an inch, beloved by the US 'makers of things'. The hierarchy of sizes that has to be learned must be a nightmare to anyone who comes to it fresh but who hasn't ' reasonable arithmetic skills' for placing them on the number line. (Imo, it's only one stage better than Roman Numerals). Why does it persist? At the same time, they use the 'thou', which is not actually part of the binary fraction system at all. They all know what they mean and can communicate it ok but why??? I have a feeling it's a bit of an exclusive club.
I suspect, but do not know, that "binary fractions of an inch" became beloved because using them makes it possible to get great precision using simply analog methods with relatively low technology, compass and ruler style. And, once anything is done in a particular way for a long time it acquires lots of inertia and builds a base of resistance to change. In part, the inertia is due to economics, because barriers to entry of all kinds are good for people who are already part of the club.

ohwilleke
Gold Member
Contact me to add more! Let's build a master list!
Your list betrays your professional pedigree, I think. Physicists and engineers are not troubled in the least by formulas that are correct to three or four significant digits. People trained as mathematicians, like me, long for exact conversions whenever possible, even if it means using something other than a simple multiplicative factor. See https://xkcd.com/2205/ But, let's not talk about cosmologists (see the linked comic).

ohwilleke
Gold Member
Another obscure unit of measure: "a hecatomb is a sacrifice of 100 oxen" (usually and in the narrow sense).