SME
Cartography
Scale and coordinate systems
Use this for “Two bridges are 4.2 cm apart on a 1:24,000 map. How far apart are they on the ground?”
Diagram
dₘₐₚ = 4.2 cm on the top line sits over 1,008 m on the bottom line: each 1 above is 240 below.
This is an example. Type your own values to start a new problem.
d (m)
=
dₘₐₚ (cm)
×
S
S is the scale’s second number: S = 24,000 on a 1:24,000 map.
Formulas
d
=
dₘₐₚ
×
S
100
1,008
=
4.2
×
24,000
100
Assumptions
•
A representative fraction has no units: at 1:24,000, 1 cm on the map is 24,000 cm on the ground.
•
The map distance is measured in a straight line on the map, so the ground distance is straight too.
•
A large scale (1:10,000) shows a small area in detail; a small scale (1:1,000,000) shows a large area.
Step-by-step
WE KNOW
dₘₐₚ = 4.2 cm, S = 24,000
FIND
ground distance (d)
Step 1 · Find ground distance (d)
Use d = dₘₐₚ × S ÷ 100
Each
map
centimetre
stands
for
S
centimetres
of
ground;
÷
100
turns
centimetres
into
metres.
d
=
4.2
×
24,000
100
4.2 × 24,000 = 100,800 cm on the ground
d
=
1,008
m
Check
Put the numbers back in. Both sides should match.
1,008
=
4.2
×
24,000
100
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.