The scale is used to express distance on a map. Some maps use a linear scale also
known as a scale bar, such as the one shown here. Some maps use a word
statement to express scale. For example, one centimeter equals one kilometer.
Other maps use a representative fraction.
Topographic maps produced by the United States Geological Survey
use 1:24,000. This means that 1 inch on the
map equals 24,000 inches in the real world.
Another common representative fraction used is 1 to 63,360.
That is, one inch to one mile.
Other countries scale their maps in metrics.
Represenative fractions such as 1 to 50,000,
1 to 250,000 and 1 to 1 million are commonly used.
For example, on a map with a scale of 1 to 50,000, one centimeter equals 50,000 centimeters in reality.
Maps are often known as large scale or small scale.
Large scale maps are called large scale because features will appear bigger on the map
Street maps for example are large scale maps.
On small scale maps, features will appear smaller.
Maps of the world are considered small scale maps.
We can also use the scale of a map to measure distance. I have a topographic
map here of Ruapehu ski fields, with a scale of 1 to 12,500.
There is also a scale bar on this map.
Now I recently climbed to the dome shelter here
on Mount Ruapehu from the top of the T bar here which
comes from the Knoll ridge cafe.
Now I want to measure how far it is from this T bar to the dome.
However the route I took actually was not straight because I
went up this valley here, and when I came up onto this Ridge called Restful Ridge,
and eventually I walked along the top of a ridge here until I got to the dome shelter.
So what I got here is I've got a piece of wiry string and I'm going to
bend this string, so that you start here from the top of the T bar, will bend it
till we get up to the ridge, and you got where I turned and right here there's the
dome shelter.
I'm holding in my left hand the bent piece of string. Where my left
hand is actually pinching, that is where the dome shelter was, and this end of the
string is where the end of the t-bar was, and now I've got this 30 centimeter ruler
and I'm going to straighten the string alongside the ruler.
I'm going to see how long this string actually is.
Now after straightening the string out and
measuring it against the ruler, it comes to 16 centimeters. Now what happens after
this depends on the type of scale I'll use to do the calculation.
Now if we're going to use the scale bar we've got to measure it with a ruler. Now you can see
here on the scale bar that 0 to 1,000 meters is the same as 8 centimeters on
the ruler. Now I measured out 16 centimeters for the journey that
I climbed, and 16 centimeters works out to be 2 kilometers on the scale bar.
If I'm going to use the representative fraction of 1 to 12,500 , I will
simply multiply the distance I ruled on the ruler by this denominator.
So I will go, um 16 centimeters multiplied by 12,500 and
this you can see comes to 200,000 centimeters, and when you convert 200,000
centimeters into kilometers it comes to 2 kilometers, which is the same as what I
measured out when I used the scale bar.
You can also use scale to estimate the area.
For example, I want to estimate the size of Gedge City on this fictional map.
Count the number of good squares that are completely contained within the boundaries of Gedge city.
Record this number.
I've counted 19 full squares in Gedge city.
Then count how many parts squares there are and add them up.
This square for example, occupies an estimated 40% of the square.
So I will count this as 0.4 of the square.
Now add up the part squares.
I've added them up to 9.1.
Then add the two totals together.
19 plus 9.1 equals 28.1.
Calculate the area in square kilometers of each grid square .
This is done by simply multiplying the length by the width of the square.
If the area of each square was one square kilometer multiply
this figure by the total number of squares.
1 times 28.1 equals 28.1 square kilometers.
If each square were two square kilometers you would say
2 times 28.1 equals 56.2 square kilometers.