Scale and Maps

A scale tells you how big something is drawn compared with its real size. Writing it as a ratio like 1 : 50\,000 means 1 unit on the map stands for 50 000 of the same units in real life. The two sides use the same unit, so 1 cm on the map is 50 000 cm in the world.

That gives two simple moves. To find a real distance, take the map distance and multiply by the scale:

\text{real} = \text{map} \times n

To find a map distance, take the real distance and divide by the scale:

\text{map} = \text{real} \div n

The one thing to watch is units. Keep both sides in the same unit while you work, then convert the answer if you want different units. Remember 1\text{ km} = 100\,000\text{ cm}, so a map scale is often quoted as a friendly pair like 1\text{ cm} : 2\text{ km}.

A scale 1 : n links the drawing to reality:

real distance = n \times \text{map distance};
map distance = \text{real distance} \div n;
convert units carefully — keep both sides in the same unit, using 1\text{ km} = 100\,000\text{ cm};
a larger n means more is squeezed into each unit, so the map is more zoomed out.

Map versus real life

The little rectangle is the field on the map; the big one is the field in real life. Both keep the same shape — only the scale bar changes the numbers.