A road or river follows bends, so its length on the ground is longer than the straight line between its ends. Measure the curve in short pieces, add them, then convert once.
This lesson sits in topographic scale, distance and area. You need the conversion from a representative fraction to ground distance first.
Which method works for a curved route?
There are two reliable ways. Both give the length of the route on the map, which you then convert with the scale.
| Method | How it works | Good for |
|---|---|---|
| Paper strip | Mark the start, pivot the strip along each bend, then read the marked length against the ruler | Long roads and rivers |
| Segments | Cut the curve into short, near-straight pieces and add the ruler readings | Short routes in an exam |
Pick one and use it for the whole route. Mixing methods makes errors harder to trace.
Worked example: an original winding road
An original map has an RF of 1:50 000. A road runs from Kampung A to a junction at B. Its four segments measure 2.0 cm, 3.5 cm, 1.5 cm and 2.5 cm. The straight line from A to B is 6.0 cm.
Step 1: add the segments. 2.0 + 3.5 + 1.5 + 2.5 = 9.5 cm on the map.
Step 2: convert. At 1:50 000, 1 cm is 500 m, or 0.5 km. So 9.5 × 0.5 = 4.75 km along the road.
For comparison, the straight line gives 6.0 × 0.5 = 3.0 km. The road is 1.75 km longer than the straight line.
The mistake that shortens the route
A common slip is to measure A to B with one straight ruler line and write 3.0 km. The working is neat, so it is easy to miss that the question asked for the road.
The word to watch is “along”. “Distance along the road” or “length of the river” means you follow the bends. “Straight-line distance” means you may use the ruler directly.
A sense check you can do in ten seconds
The route must be longer than the straight line. If your winding route comes out equal or shorter, you missed a bend or dropped a segment.
In the example, 4.75 km is larger than 3.0 km, so the answer passes. Here 4.75 ÷ 3.0 is about 1.6, a sensible ratio for a bendy road.
Check yourself
An original map has an RF of 1:25 000. A track has three segments of 3.2 cm, 2.4 cm and 4.0 cm. The straight line between its ends is 7.0 cm. Find the length of the track in kilometres, and say how much longer it is than the straight line.
Answer
Map total: 3.2 + 2.4 + 4.0 = 9.6 cm.
At 1:25 000, 1 cm is 250 m, or 0.25 km. So 9.6 × 0.25 = 2.4 km.
The straight line is 7.0 × 0.25 = 1.75 km, so the track is 2.4 − 1.75 = 0.65 km longer.
What to study next
Move on to estimating an irregular area with a stated grid method, which uses the same scale step on squares instead of lines. Or test yourself on the full practice set.
If you want a teacher to check your method on your own textbook maps, see online one-to-one Geography tuition.