Calculating Slopes and Common Slopes in Architecture

Architects provide slope information on drawings using percentages, degrees or gradients depending on the application. Roofs are often noted with gradients. However, cross-slopes along sidewalks are typically indicated in degrees. It’s helpful to know how to calculate each method.

Three methods can be used for indicating the slope of a surface relative the horizontal plane: percentage, gradient and degrees.

Calculating a Slope Gradient

Slope gradients can be written as Y.X. where Y is one unit of rise and X the run.  Both numbers must use identical units.  For example, if you travel 3 in vertically and 3 in horizontally (36 inches), the slope would be either 3:36, or 1:12.  This is also known as “one in twelve slope”.

Calculating the Slope Percentage

The slope percentage can be calculated in the same way that the gradient.  Divide the run by the rise to convert the rise and run into the same units.  This will give you the percentage slope.  For example, a 3″ rise divided 36″ run =.083×100 = 8.3% slope.

Calculating a Slope In Degrees

Calculating slope in degrees is the most difficult way. This requires some high school math.  The run divided by the rise is the tangent.  Thus, the angle is the inverse-tangent from the rise divided with the run.

TCommon Slopes in Architecture

Below is a table that shows common slopes.  Handrails are not required for sloped floors that are 1:20. However, any slope higher than 1:20 will be considered a ramp.  Handrails are required for sloped ramps with a maximum slope of 1:12. Federal ADA codes state that the maximum cross-slope for an accessible route is 1 to 48, which is slightly less than 2%. Some jurisdictions allow a maximum cross-slope of 1:50, however.

DEGREESGRADIENTPERCENT
0.6°1 : 95.491.0%
1 : 57.291.7%
1.15°1 : 502%
1.19°1 : 482.08%
2.86°1 : 205%
4.76°1 : 128.3%
7.13°1 : 812.5%
10°1 : 5.6717.6%
14.04°1 : 425%
15°1 : 3.7326.8%
26.57°1 : 250%
30°1 : 1.7357.7%
45°1 : 1100%
56.31°1: 0.67150%
60°1 : 0.6173.2%
 63.43°1 : 0.5200%
78.69°1: 0.2500%
89.43°1 : 0.11000%
90°1 : 0 inf.

 

Roof Slopes

Roof slopes can be identified by the gradient method. The run is 12 in the case of roof slopes where the rise is variable. On very steep roofs, the gradient may be inverted so the run is variable but the rise remains 12.

Low Slope Roofs

Low slope roofs are characterized by a gradient of 3:12 or less. A membrane roof system is recommended to ensure watertightness.

ROOF GRADIENTDEGREESPERCENT
1/4 : 121.19°2.08%
1/2 : 122.39°4.17%
1 : 124.76°8.3%
2 : 129.46°16.67%
3 : 1214.04°25%

Steep Slope Roofs

Anything above 3:12 is considered a steep roof and can be covered with metal panels, shingles, or tiles — these roofs shed water and are not considered watertight.

ROOF GRADIENTDEGREESPERCENT
4 : 1218.43°33.33%
5 : 1222.62°41.67%
6 : 1226.57°50%
7 : 1230.26°58.33%
8 : 1233.69°66.67%
9 : 1236.87°75%
10 : 1239.81°83.33%
11 : 1242.51°91.67%
12 : 1245°100%

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