Example

Calculate the gradient from A to B in m/ km, %, and ratio.

Calculating The Rise
Find the elevation at B and subtract the elevation at A. This will give you the change in elevation if you were to walk from Point A to Point B. Hence, B - A = 160 m - 40 m = 120 m. This is the Rise.

Calculating The Run
When you put your ruler down between Point A and B, there is a map distance of 6.7 cm. The scale is 1:30 000; therefore each centimetre on the map represents 0.3 km in reality. Hence, the actual distance between Point A and B is 6.7 cm x 0.3 km = 2.01 km. This is the Run.

1) Metres / km

Rise = 120 m
Run = 2.01 km = 60 m/km

(Note: Typically in this course, you will round the m / km to the nearest whole number.)

What this number simply means is that if you were to walk from Point A to Point B, for every kilometre that you traveled horizontally you would also be gaining 60 metres in elevation.

2) Percentage

Rise = 120 m
Run = 2.01 km Convert the bottom into kilometres.

[Recall : 1 km = 1000 metres]

Therefore, 2.01 km = 2010 metres.

Rise = 120 m
Run = 2010 m

Divide the numerator (top) by the denominator (bottom) and multiply by 100 to get a percentage.

Rise = 120 m
Run = 2010 m x 100 = 6%

(Note: Again, typically in this course, you will round the % to the nearest whole number.)

Percentage is often used to express gradient on road signs which is critical information for truck drivers.

3) Ratio

Rise = 120 m
Run = 2010 m

Reduce the fraction by dividing the top and bottom by the top number.

Rise = 120 m / 120 = 1
Run = 2010 m /120= 16.8

Express this reduced fraction as a ratio for your final answer.

Therefore, 1:16.8

(Note: Typically in this course, you will round the ratio to the nearest first decimal.)