This entry uses the imperial system of measurement. For the metric system, click here.
When you want to describe the size of a line segment, you’re talking about length. An airplane is longer than a teddy bear, and a house is longer than a bicycle. You can try to imagine how many bicycles you need for them to be as long as a house if you add them all together. You can also try to imagine how many teddy bears you need to make a line of teddy bears that is as long as an airplane.
However, what if your teddy bear is really big, but your friend’s teddy bear is really small? Then your measurement and their measurement can be very different from each other. To solve these kinds of problems, scientists agreed upon specific length units. For the imperial system you use inch, foot, yard and mile for the measurement of length. As long as you know how long an inch, foot, yard and mile are, you can measure the length of an airplane, a teddy bear, a house or a bicycle and see which one is the longest.
In school, you’ll use a ruler to measure length.
Which unit you want to use when measuring the length depends on the object. For example, when measuring smaller object, we often use inches because the other units are too large, which will cause the number to be very small.
1 inch
is equal to $\frac{1}{12}$ foot, $\frac{1}{36}$ yard or $\frac{1}{63\phantom{\rule{0.17em}{0ex}}360}$ mile. This means when you convert inches to feet, yards or miles, you need to divide the number by 12, by 36 or by $63\phantom{\rule{0.17em}{0ex}}360$ respectively.
1 foot
is equal to 12 inches, $\frac{1}{3}$ yard or $\frac{1}{5280}$ mile. This means when you convert feet to inches, yards or miles, you need to multiply the number by 12, divide by 3 or divide by 5280 respectively.
1 yard
is equal to 36 inches, 3 feet and $\frac{1}{1760}$ mile. This means when you convert yard to inch, foot or mile, you need to multiply the number by 36, by 3 or divide by 1760 respectively.
1 mile
is equal to $63\phantom{\rule{0.17em}{0ex}}360$ inches, 5280 feet, or 1760 yards. This means when you convert mile to inch, foot or yard, you need to multiply the number by $63\phantom{\rule{0.17em}{0ex}}360$, by 5280 or by 1760 respectively.
Unless something is very long, length is most often measured in a combination of feet and inches. If you are 4 feet and 7 inches tall, you’ll say that you are 4 feet, 7 inches, or more commonly: 4’ 7”.
Think About This
Why would you never say you are 4 feet and 13 inches long?
Remember, there are 12 inches in one foot. So 13 inches is the same as 1 foot and 1 inch or 1’ 1”, so 4 feet and 13 inches is the same as 5 feet and 1 inch or 5’ 1”.
Another word for a measure is a unit, and this is the word that is used the most. The figure below will be very helpful when you understand how it works. The figure shows you what to multiply and divide by to go from one unit to another. For example, if you want to go from yards to feet, you have to multiply by 3.
When you need to switch from one unit to another, you can let the bubble figure help you with the calculation. Remember that there are 12 inches in 1 foot, so you have to multiply or divide by 12 when you switch between feet and inches.
Example 1
Foot $\iff $ yard:
$$\begin{array}{llll}\hfill 3000\phantom{\rule{0.17em}{0ex}}\text{ft}& =(3000:3)\phantom{\rule{0.17em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =1000\phantom{\rule{0.17em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 3\phantom{\rule{0.17em}{0ex}}\text{yd}& =(3\cdot 3)\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =9\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$Foot $\iff $ inch:
$$\begin{array}{llll}\hfill 2\phantom{\rule{0.17em}{0ex}}\text{ft}& =(2\cdot 12)\phantom{\rule{0.17em}{0ex}}\text{in}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =24\phantom{\rule{0.17em}{0ex}}\text{in}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 400\phantom{\rule{0.17em}{0ex}}\text{in}& =(420:12)\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =35\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$Inch $\iff $ yard:
$$\begin{array}{llll}\hfill 0.18\phantom{\rule{0.17em}{0ex}}\text{in}& =(0.18:36)\phantom{\rule{0.33em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.005\phantom{\rule{0.17em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 34\phantom{\rule{0.17em}{0ex}}\text{yd}& =(34\cdot 36)\phantom{\rule{0.17em}{0ex}}\text{in}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =1224\phantom{\rule{0.17em}{0ex}}\text{in}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$Mile $\iff $ yard:
$$\begin{array}{llll}\hfill 8\phantom{\rule{0.17em}{0ex}}\text{mi}& =(8\cdot 1760)\phantom{\rule{0.17em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =14\phantom{\rule{0.17em}{0ex}}080\phantom{\rule{0.17em}{0ex}}\text{yd}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 176\phantom{\rule{0.17em}{0ex}}\text{yd}& =(176:1760)\phantom{\rule{0.17em}{0ex}}\text{mi}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.1\phantom{\rule{0.17em}{0ex}}\text{mi}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$Foot $\iff $ mile:
$$\begin{array}{llll}\hfill 1320\phantom{\rule{0.17em}{0ex}}\text{ft}& =(1320:5280)\phantom{\rule{0.17em}{0ex}}\text{mi}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0.25\phantom{\rule{0.17em}{0ex}}\text{mi}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 0.25\phantom{\rule{0.17em}{0ex}}\text{mi}& =(32\cdot 5280)\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =168\phantom{\rule{0.17em}{0ex}}960\phantom{\rule{0.17em}{0ex}}\text{ft}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$Think About This
The USA and a few other countries use the imperial system, but did you know that they don’t use the whole system?
There are many imperial units that are never or rarely used in the USA. For example, a stone is 14 pounds as they know in the UK, but this is never used in the USA or in Canada. Another example is a barleycorn. Three barleycorns is the same as one inch. We still use barleycorns when we measure shoe sizes! A size 12 is 12 inches, but a size 11 is 12 inches subtracted by one barleycorn, so 11 and $\frac{2}{3}$ inches. The system in the USA, where you use only some of the imperial units, is called “United States Customary Units”.
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