**How to calculate real distance on a map**

When
you are using a compass, the needle pointing north is actually not pointing to
north. The needle is in fact pointing to the Magnetic North pole which is
situated roughly north-east of Canada. It shifts every year by approximately 55km.

There
is always a difference between the True North, which is at the North Pole, and
the magnetic north. However, this difference (angle) changes every year. This
change is known as the

**.***magnetic declination*
When
using a topographic map true north are always at the top of the map. To measure
the bearing from one point to the next, the protractor must be aligned so that
0° point to the top of the map. Draw a straight line from your starting point
to the end point. Place the protractor on the map, with 0° pointing to the top
of the map. Use the line connecting the two points to read the degrees from the
protractor. Remember to measure in a clockwise direction from the top.

Let us assume the true bearing is 75°. If a person starts to drive in in a bearing
of 75° he will still miss his final destination. Why? You still have to add the
difference between True North and Magnetic North, also known as the

**. Every year the magnetic north shifts, either in a westerly or easterly direction. For an observer in South Africa the Magnetic North will always be west from True North (North Pole). At the bottom of a topographic map (e.g. 1:50 000) you will see a north-south arrow. Next to the north-south arrow the mean***magnetic declination***and the mean annual change will be indicated. For example: “***magnetic declination**Mean magnetic declination 16°3’ West of True North (July 2005). Mean annual change 2’ Westwards (2002-2006)*.”
So,
how do you calculate the magnetic bearing?

**Determine the true bearing**

__Step 1:__
E.g. 75°

**Determine the difference in years between the current year and the year the**

__Step 2:__*Magnetic declination*was measured (on topographic map)

E.g.
2014 – 2005 = 9 years

**Calculate the total magnetic change**

__Step 2:__
E.g. 9 years x 2’ West = 18’ West (On the topographic map the change is 2’ West every year)

**Calculate the current magnetic declination**

__Step 3:__
E.g. 16°3’ West

__+ 0°18’ West__

*When the mean annual change is west you +, and if the*

*change is East, you –.*

16°21’ West

*Therefore, the magnetic declination for 2014 is 16°21’ west from True North.*

**Calculate the magnetic bearing**

__Step 4:__
E.g. True Bearing + Current Magnetic
Declination

= 75° + 16°21’

=

**91°21’**

**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

__Step 3:__Gradient calculation

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

Gradient =

__Vertical difference__

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.

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

__Step 1:__**Now you will apply the information to the Distance formula. Distance = 3,9km and Speed = 14km/h**

__Step 2:__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)