Relationship between degrees, percent slope, and ratio to express slope gradient

Slope gradient is a key factor in influencing the relative stability of a slope. It determines the degree to which gravity acts upon a soil mass. Slopes are often irregular and complex, with gradients varying greatly throughout a given shoreline profile. Each slope profile section should be treated as a separate management and restoration site unit. Slope gradient can be expressed in several ways. The slope determination formulas (Figure 1) and common slope gradients table (Figure 2) illustrate the three commonly used notations (ratio, percent and angle).

Figure 1. Slope determination formulas
HD = Horizontal distance, VD = Vertical distance.
Formula Example Result
Slope ratio (H:V) HD:VD 100:50 2:1
Slope percent (%) (VD ÷ HD) × 100 (50 ÷ 100) × 100 50%
Slope angle (°) ArcTan (VD ÷ HD) ArcTan (50 ÷ 100) 26.6°
Slope determination formulas
Figure 2. Common slope gradients
Angle (°) Percent (%) Ratio (H:V)
2.5 5.0  
5.7 10.0 10:1
10.0 17.6  
14.0 25.0 4:1
18.0 33.5 3:1
19.3 35.0  
20.0 36.4  
24.2 45.0  
26.1 49.0  
26.6 50.0 2:1
30.0 57.7  
33.0 66.7 1.5:1
35.0 70.0  
38.6 80.0  
42.0 90.0  
45.0 100.0 1:1
55.0 142.8  
60.0 173.2