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Length

It’s easy to convert between length units, especially if you understand the method being used in the following example.

Example:
You want to convert 22 miles to inches.

Let’s say you don’t know the direct conversion factor between miles and inches, but you know that:

1 mile=1760 yards

and

1 inch=frac{1}{36} yards

Then you can calculate the conversion factor F between miles and inches:

F=frac{1760}{frac{1}{36}}=1760*36=63360

So 22 miles is equal to:

22 miles*63360=1393920 inches

Imperial units and US costemary units

In USA the official system of measurement is the imperial units, where the yard, defined exactly as 0.9144 meter, is the base unit.

The relationship between the different units in the imperial system is as follows:

One mile is 5280 yards, one yard is 3 feet, one foot is 12 inches and one inch is 1000 thou.

Though United Kingdom and the Commonwealth nations officially have adopted the metric system, the imperial units are still used for some purposes.

NameThou (th)Inch (in)Foot (ft)Yard (yd)Mile (mi)Nautical mile
Footfrac{1}{12000}
frac{1}{12}
1352806076.12
Meter0.00002540.02540.3048 *0.9144 *1609.3441852 *

* exact

Conversion of length units

Please enter a length and select the units you want to convert between.

th = thou
in = inch
ft = foot
yd = yard
mi = mile
nmi = nautical mile
km = kilometer
hm = hectometer
dam = dekameter
m = meter
dm = decimeter
cm = centimeter
mm = millimeter

Original length: 
Original unit: 
Desired unit: 

The meter compared to other metric units

The convenience of the metric system is that it’s very easy to convert between the different units within the system, because the conversion factors are just different powers of 10.

See the table below, where the different metric units are compared to the meter.


1 km1 hm1 dam1 m1 dm1 cm1 mm
1000 m100 m10 m1 m0.1 m0.01 m0.001 m
10310210110010-110-210-3

Example:

You want to convert from kilometers (km) to centimeters (cm).
As you can see in the table above, it applies that:

1km=10^3m
and
1cm=10^{-2}m

In order to find the conversion factor of the two units, you need to divide 103 by 10-2. Instead of making the division you can just use one of the laws of exponents saying that frac{x^m}{x^n}=x^{m-n}.

Conversionfactor=frac{10^3}{10^{-2}}=10^{3-(-2)}=10^{3+2}=10^5.

So the conversion factor between kilometers and centimeters is 105, that is, you move the decimal point in a distance given in kilometers 5 spaces to the right in order to convert it to centimeters.

Astronomic units

In astronomy the official units of length is parsec, light-year and light-seconds:

NameParsecLight-yearLight-second
DescriptionThe heliocentric parallax of one arc secondThe distance the light travels in one yearThe distance the light travels in one second
Miles19,173,511,691,720 miles5,878,625,373,184 miles186282 miles
Meter30,856,776,000,000,000 meter9,460,730,472,580,800 meter *299,792,458 meter *

* exact