1. Gradient is a measurement of the steepness of the land or simply slope
Formula
Rise = Change in the Vertical Distance Run = Change in the Horizontal Distance

2. Gradient
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.

3. Gradient
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.

4. Gradient
Expressed in 3 ways
m/ km
Percentage %,
ratio

5. Gradient 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.

6. Gradient
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.

7. Gradient 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.)

8. Gradient
Gradient Handout

9. Gradient B - A Rise = (180-150)m_ = 30m = 26m/km
Run (2.9cm*0.4)km 1.16km
30m = 30m * 100 = 3%
1.16km 1160m
30m ÷ 30 = 1 = 1:38.7
1160m

10. Gradient B - A Rise = (75-225)m_ = -150m = - 114 m /km
Run (6.6cm*0.2)km 1.32km
Note: The negative indicates that the slope is going downhill.
-150m = -150m * 100 = -11% or simply 11%
1.32km 1320m
-150m ÷ 150 = -1 = -1:8.8 or simply 1:8.8
1320m
Note: The negative is typically left out for the % and ratio. Apply the negative though for the m/km.