Common units in the U.S. Customary System of Weights
and Measures, for students of FDMath 108
Bro. David E. Brown, BYU–Idaho Dept. of Mathematics
Version 0.11, of April 24, 2013
Introduction
Units of measure are used to indicate the nature of the thing being measured. Measurable natures include
distance, area, volume, and capacity; time; weight and mass; temperature; and so on. There are many
systems of units of measure. This document focuses on the U.S. Customary System of measurements.
Note that when abbreviating units of measure, the period is no longer used (except at the ends of
sentences). Example: “ft” and not “ft.” is the current custom. Also, abbreviations of units never include
the “s” that indicates the plural. Example: “in” and not “ins” for “inches.” Finally, the hyphen (-) has been
used in the past to indicate multiplication of units, as in “ft-lbs.” To avoid confusion with the subtraction
symbol, the hyphen is to replaced by a centered dot, as in “ft · lbs,” or by nothing, as in “ft lbs.”
The great, grand key to working with units of measure is that you treat them just like the
symbols x and y that you’ve used in your algebra classes. That is, combine like terms1 (as in 3ft +
2ft = 5ft), and multiply and divide just as you would do with x and y, even to the point of using exponents
(ft · ft = ft2 ) and canceling (ft3 /ft = ft2 ).
Quick reference
These are the units conversions from the U.S. Customary System that you really ought to have memorized.
Some information about them, as well as some additional units, are given in the following sections.
1ft = 12in
1yd = 3ft
1mi = 5280ft
1C = 8fl oz
1pt = 2C
1qt = 2pt
1gal = 4qt
1 day = 24hr
1 week = 7 days
1lb = 16oz
1 ton = 2000lb
1min = 60s
1yr = 365 days
1 decade = 10yr
1hr = 60min
1 leap year = 366 days
1 score of years = 20yr
1 century = 100yr
1 millennium = 1000yr
Distance and area
In order from smallest to largest, common U.S. Customary System units of distance are the inch (in), foot
(ft), yard (yd), and mile (mi).
1ft = 12in
1yd = 3ft
1mi = 5280ft
In
to largest, common
U.S. Customary System units of area are the square
inch
order from smallest
in2 , square foot in2 , square yard in2 , acre (no standard abbreviation) and square mile in2 . Don’t
1 “Like”
means “having the same units of measure”
1
memorize how many square inches are in a square foot, or whatever. Your brain is too important to waste
on that. Instead, use the great, grand key:
1ft2 = 1ft × 1ft = 12in × 12in = 144in × in = 144in2 .
Exercise: How many square feet are there in a square mile?2
The acre is 43,560ft2 , and there are 640 acres in a square mile, but you don’t need to memorize these
facts.
Volume and capacity
Volume and capacity are almost the same thing. The difference is that capacity is the amount of space inside
a container and volume is the amount of space taken up by something.3 In order from smallest to largest,
common U.S. Customary System units of volume are the cubic inch (in3 ), cubic foot (ft3 ), and cubic yard
(yd3 ). These units suffice for use around the home. In discussions of things like climate change that happen
on a larger scale, the cubic mile (mi3 ) is sometimes used.
Don’t memorize how many cubic inches there are in a cubic foot, or whatever. Your brain is too precious
to waste on that. Instead, use the great, grand key:
1ft3 = 1ft × 1ft × 1ft = 12in × 12in × 12in = 1728in × in × in = 1728in3 .
Exercise: How many cubic feet are there in a cubic yard?4
“Wet” or “liquid capacity”
Units of measure for “wet” or “liquid” capacity are a little different than for “dry” capacity, as explained
below.
In order from smallest to largest, common U.S. Customary System units of wet or liquid capacity are the
teaspoon (tsp5 ), tablespoon (Tbsp6 ), fluid ounce (fl oz or just oz), cup (C), pint (pt7 or not abbreviated),
quart (qt), and gallon (gal). These units suffice for use around the home. As with volume, when larger units
of measure are needed, the cubic mile (mi3 ) is sometimes used.
1Tbsp = 3tsp
1C = 8fl oz
1C = 16Tbsp
1pt = 2C
1fl oz = 2Tbsp
1qt = 2pt
1gal = 4qt
“Dry capacity”
In order from smallest to largest, common U.S. Customary System units of dry capacity are the dry ounce
(oz), pint, quart (qt), peck (no standard abbreviation), bushel (bu), and cubic yard (yd3 ). These units suffice
for use around the home. When larger units are needed, the cubic mile (mi3 ) can be used.
1qt (dry) = 2pt (dry)
1 peck = 8qt (dry)
1bu = 2 pecks
The cubic yard and cubic mile are the same as they are for volume.
The dry quart is 1.164 fluid quarts (approximately).
2 Answer:
27878400.
like to think of capacity as potential and volume as actual. A gallon jug could potentially hold a gallon of liquid, so its
capacity is 1 gallon. But if it’s half full of water, the volume of the water is not 1 gallon; it’s actually half a gallon.
4 Answer: 27.
5 The letter t is often used, but it’s only safe to do so if only cooking is being discussed
6 The letter T is often used, but it’s only safe to do so if only cooking is being discussed. The abbreviation Tsp is also used,
but should be avoided to prevent confusion with the abbreviation tsp.
7 The symbol pt is also used as th abbreviation for the word “point,” a unit of distance used in typing, word processing, and
typesetting. Context will usually tell you whether points or pints are meant.
3I
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Weight and mass
Weight and mass are different, but related. Mass directly measures the amount of matter in a thing, in a
sense having to do with how much “effort” is required to move the thing. Weight actually measures how
hard the Earth’s gravity pulls on the thing.8 The U.S. Customary System focuses on weight. By contrast,
the metric system focuses on mass. If you’re talking about everyday things in everyday situations, it’s safe
to ignore the distinction. However, when solving problems in science and engineering, it is not safe to ignore
the distinction.9
Weight
In order from smallest to largest, common U.S. Customary System units of weight are the ounce (oz), the
pound (lb) and the ton (no standard abbreviation).
1lb = 16oz
1 ton = 2000lb
Mass
The unit of mass in the US Customary System is the slug (no standard abbreviation, though “sl” and “sg”
have been used). One pound of anything, when at rest near the earth’s surface, has a mass of 32 slugs.10
THIS DOES NOT MEAN THERE ARE TWO SLUGS IN AN OUNCE. Ounces and slugs measure different
things. Now, if you’re not studying science or engineering, you don’t need to memorize the slug or its
equivalent in pounds.
Time
From smallest to largest, common U.S. Customary System units of time are the second (s), minute (min),
hour (hr), day (no standard abbreviation), week (no standard abbreviation, though “wk” is sometimes
used), month (mo), year (yr), leap year (no standard abbreviation), decade (no standard abbreviation),
score of years (no standard abbreviation), century (no standard abbreviation), and millennium (no standard
abbreviation).11
1min = 60s
1hr = 60min
1yr = 365 days
1 decade = 10yr
1 score of years = 20yr
1 day = 24hr
1 week = 7 days
1 leap year = 366 days
1 century = 100yr
1 millennium = 1000yr
Concerning the year: First, there is a “business year,” of 360 days, which is not part of the U.S.
Customary System, but which can show up in finance problems solved by FDMath 108 students. Second,
the rules for leap years are. . .
1. If the number of the year (in the Western calendar) is divisible by 4, the year is a leap year, except. . .
2. if the number of the year is divisible by 100, the year is not a leap year, except. . .
3. if the number of the year is divisible by 400, the year is a leap year.
There are additional rules, but these will see you through any FDMath 108 problem, and maybe much of
your family history!
8 The
truth is quite a bit more complicated than this, but this will do for FDMath 108.
to those of you for whom science or engineering problems are “everyday things.” You know what I mean.
10 Rounded to the nearest whole number. The actual conversion factor depends on the local value of acceleration due to
gravity. If you don’t know what this is, you can safely ignore this footnote.
11 There are several different definitions of the day and year, each definition having a different, specific use. With the exception
of the business year, all definitions given here are for the U.S. Customary System.
9 Apologies
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Temperature
The U.S. Customary unit of temperature is the degree Fahrenheit (◦ F). The definition of the degree Fahrenheit is complicated and arbitrary, and so will not be given here. (Since there’s no other unit in the U.S.
Customary System for temperature, no conversions are necessary or possible.)
Miscellaneous “units”
Here are some “units” that aren’t necessarily part of the U.S. Customary System, but which you should
have memorized.
1 dozen = 12
1 score = 20
1gross = 144
Example: “Four score and seven years ago. . . ” means 4 score years + 7 years = (4 × 20 + 7)yr = 87 years
ago.
Metric conversions
For reference, the basic units in the metric system for everyday use are the meter or metre (m) for distance,
the gram (g) for mass, the second (s) for time, and the degree centigrade (◦ C) for temperature.12 The meter
is defined in terms of how far light travels in a certain fraction of a second. The kilogram is defined to be
the mass of a particular bar of platinum and iridium stored and maintained by the International Bureau
of Weights and Measures, in Paris, France. The degree centigrade is defined to be 1/100th of the difference
between the boiling temperature of pure water and the freezing temperature of pure water (at sea level).
Units of time are the same in the metric system as in the U.S. Customary system.13
(Technical detail: When converting weights in the U.S. customary system to the metric system, you’re
actually converting weights into masses. There are complicated rules for being precise about this. However,
the above works fine, for everyday use.)
U.S. Customary to metric conversions All of the following conversions are approximate. I do not
require my FDMath 108 students to memorize them. However, if you live in the States near Canada or
Mexico, or if you’re from another country, you may find it handy to memorize them.
1in = 2.54cm
1oz (weight) = 28.3g
1ft = 30.48cm
1lb = 453g
1yd = 91.44cm = 0.9144m
1mi = 1.609km
1 ton = 907kg
1gal = 3.79L
Metric to U.S. Customary conversions All of the following conversions are approximate. I do not
require my FDMath 108 students to memorize them. However, if you live in the States near Canada or
Mexico, or if you’re from another country, you may find it handy to memorize them.
1cm = 0.394in
1g = 0.0353oz (weight)
1m = 1.094yd = 3.281ft
1km = 0.621mi
1kg = 2.205lb
12 The official unit of temperature is actually the Kelvin (K). One Kelvin is the same as one degree centigrade. The difference
is that the zero of the centigrade scale is at the freezing temperature of water, while the zero of the Kelvin scale is “absolute
zero,” a temperature so cold that atoms and molecules don’t wiggle. The degree centigrade is very widely used for everyday
temperatures. It’s more convenient, and has had more advertising.
13 Some organizations, such as the Soviet Union, have tried ten-day weeks. It turns out that ten days is too long between
weekends for humans to cope with. A ten-month year makes no sense, unless months are 36.5 days long (too weird!). I think
these calendrical conundrums are one of God’s ways of reminding us who’s in charge.
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TEMPERATURES DO NOT CONVERT IN THE SAME WAY AS OTHER UNITS.14 Here
are formulas for converting temperatures:
Temperature in ◦ F =
9
temperature in ◦ C + 32
5
Temperature in ◦ C =
5
temperature in ◦ F − 32
9
References:
Herbert L. Anderson, editor-in-chief, A Physicist’s Desk Reference, 1st ed.
Chemical Rubber Co., Handbook of Chemistry and Physics, 37th ed.
James & James, Dictionary of Mathematics, 5th ed.
And my own memory
14 This has to do with the fact that conversion factors are ratios, which require the “zero point” of the measure to be an
absence of something. For example, 0ft is an absence of distance. The zero of the Kelvin scale represents an absence of heat. The
zero of the Fahrenheit scale and the zero of the centigrade scale do not represent an absence of anything (not of temperature,
for example, nor of heat). Therefore, ratios cannot be used to convert from one to the other.
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