Most often, changes in grade are described in terms of percentage of slope. Describing slope in this manner provides a common basis of understanding. In addition, discrete ranges of slopes, slope categories, are associated with different activities / program. Knowing what slope categories exist in a site or that we have to accommodate also let's us perform more detailed calculations related to, for example, stormwater run-off and erosion.

Slope, expressed as a percentage, is the number of units in the vertical direction divided by the number of units in the horizontal direction ("rise over run") -- this gives you the decimal percentage. To get the integer percentage, simply multiply by 100.

The units used in the calculation must be the same in the vertical and horizontal direction (ie, use the same units for the elevation as you do for the horizontal distance).

The terms grade, gradient, and slope are interchangeable when speaking about topography.

 

Slope Formula:

Slope is equal to “rise” over “run”

or

S = DE / L

where:
S = slope gradient [ as a decimal percentage ]
DE = difference in elevation [ in ft. or m. ]
L = horizontal length [ in ft or m. ]

To get a better understanding of how the formula works, there is a file in the "Tools" section that takes you step by step through an example problem.

Some typical slopes as expressed in percentage are shown in the following animation and are explained in more detail below.

 

2.00% is a common minimum slope for many surface types to insure positive drainage and avoid any 'ponding' or standing water.

5.00% is generally the maximum acceptable slope for pedestrian circulation routes before the path is considered 'inaccessible' for people with mobility disabilities or wheelchair users. Where slopes above 5.00% are required, a route must be planned with accessibly-designed ramps complete with handrails and landings (see the Ramps page for more details).

8.33% (or 12:1) is generally the maximum acceptable slope for an accessibly-designed ramp.

20.00% is a practical maximum for paved vehicular circulation routes (including bicycles). When designing steep vehicular routes, care needs to be paid to sightlines and entry-/exit-slopes (see the Vehicular Circulation page for more details).

33.33% (or 3:1) is a general maximum slope for landscaped areas. Above this, the slope becomes susceptible to erosion and maintenance equipment (like lawn mowers) have difficulty maneuvering. If designing slopes above 33.33%, special attention should be paid to erosion-control planting.

50.00% (or 2:1) is a general maximum slope for landscaped areas with erosion control planting before mechanical reinforcement is required to prevent erosion and slope instability.

100% (or 1:1) is generally the maximum slope possible with mechanical reinforcement before a retaining wall should be used (see the Retaining Walls page for more details).

Ratios:

Slopes are most commonly calculated in decimal percentage and most often labeled in integer percentage, but slopes are also frequently described by their ratio.

a slope ratio is expressed as:
horizontal change [ written first ] : vertical gain or loss [ written second ]
usually with the vertical gain or loss being calculated to 1

a slope ratio is expressed as:
L : DE
usually with DE = 1

for example, a 33.33% slope:
S = ( DE ) / ( L )
0.3333 = ( 1 ) / ( L )
L = ( 1 ) / ( 0.3333 )
L = 3.00
3:1

Degrees:

Slopes will at times be shown in angle degrees.

a slope degree is expressed as:
angle in degrees = arctan ( slope percentage )

for example, a 100% slope:
angle in degrees = arctan ( 1.00 )
angle in degrees = 45°

Some typical slopes as expressed in percentage, ratio and degrees are shown below:

Link to useful GH scripts & Rhino files