## Pages

### Mapwork calculations

How to calculate real distance on a map

This is a very easy calculation! With a ruler and calculator you can do this in three easy steps.

Use the following formula:

You will divide by a 1000 if you need the real distance in meters OR divide by a 1000 000 if you need the real distance in kilometres!

E.g. on a 1:50 000 Topographic map the map distance between Point A and Point B is 47mm.What is the real distance in kilometres?

Distance = Map distance in mm x map scale

1000 000

= 47mm x 50 000

1000 000

= 2,35km

You can also take the map distance in centimetres and multiply it by 0.5

E.g. 4.7cm x 0.5 = 2.35km

How to calculate gradient on a topographic map

How do you calculate the gradient between two points on a 1:50 000 topographic map?

Use the following formula

Step 1: Determine the difference in altitude between the two points

E.g. point A = 1120m and Point B = 1380m

Difference in height = 1380m – 1120m = 260m

Step 2: Calculate the horizontal distance by using the following formula

Distance = Map distance in mm x map scale

1000 OR 1 000 000

Divide by a thousand if you want the distance in meters OR a 1 000 000 if you need the answer in kilometres

In this instance we will need the distance in meters!

E.g. the map distance between Point A and Point B is 23mm

Distance = 23mm x 50 000

1000

= 1150000

1000

= 1150m

Gradient can be expressed in a fraction (e.g. 1:25) format or as a percentage (%)

Horizontal distance

= 260m

1150m

= 260m ÷ 260

1150m ÷ 260

= 1 .

4,42

1:4.42

Therefore, for every 4.42 meters you are moving horizontally the height will change by 1 meter. This is quite steep!!

How to calculate Time

E.g. A cyclest is cycling from point A to point B at an average speed of 14km/h. How long will it take the cyclest to cover the distance? The mapdistance between point A and point B is 78mm and the mapscale is 1:50 000.

Step 1: Calculate the distance between point A and point B in kilometers, because the speed is in kilometers per hour.

Step 2: Now you will apply the information to the Distance formula. Distance = 3,9km and Speed = 14km/h

You will notice that every decimal has been converted into a smaller unit. E.g. 3,58 hours, is 3hours (,58 x 60 = 34,8 minutes and .8 minutes x 60 = 48 seconds)