Calculating Slope and Common Slopes in Architecture

Architects constantly provide slope information on their drawings using gradients, degrees, or percentages depending on the application. For instance, roofs are noted using gradients, but cross-slopes on sidewalks are usually notated in degrees. It is helpful to understand how to calculate each method.

There are three different ways to indicate the slope of a surface relative to the horizontal plane: degrees, gradient, and percentage.

Calculating a Slope Gradient

Calculating a Slope Gradient diagram
Calculating a Slope Gradient

Slope gradients are written as Y:X, where Y is a single unit in rise and X is the run.  Both numbers must use the same units.  For instance, if you travel 3 inches vertically and 3 feet (36 inches) horizontally, the slope would be 3:36 or 1:12.  This is read as a "one in twelve slope."

Calculating the Slope Percentage

Calculating Slope Percentage
Calculating Slope Percentage

Slope percentage is calculated in much the same way as the gradient.  Convert the rise and run to the same units and then divide the rise by the run.  Multiply this number by 100 and you have the percentage slope.  For instance, 3" rise divided by 36" run = .083 x 100 = an 8.3% slope.

Calculating a Slope in Degrees

Calculating a Slope in Degrees diagram
Calculating a Slope in Degrees

The most complicated way to calculate slope is in degrees and it requires a bit of high-school math.  The tangent of a given angle (in degrees) is equal to the rise divided by the run.  Therefore, the inverse-tangent of the rise divided by the run will give the angle.

Table of Common Slopes in Architecture

The table below shows some common slopes.  1:20 sloped floors do not require handrails, but anything steeper than 1:20 is considered a ramp and requires handrails.  1:12 sloped ramps are the maximum slope allowed by ADA codes and they require handrails. Federal ADA codes indicate that the maximum cross-slope of an accessible route is 1:48, which is slightly more than 2%. However, we have seen some jurisdictions that allow a maximum cross slope of 1:50.

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 are identified using the gradient method described above where the rise varies, but the run is usually 12. In some very steep roofs, you may see the gradient inverted so that the run varies, but the rise is held as 12.

Low Slope Roofs

Low slope roofs have gradients of 3:12 or less. They should have a membrane roof system to ensure watertightness.

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.

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%

Roofs can be steeper than shown in the table above. In fact, a roof can be almost vertical.

Plumbing Pipe Slopes

As discussed in our pipe slope article, draining and sewer pipe slopes tend to be minimal. The idea is to keep water and solids flowing. There are three common slopes used, which are referenced in the International Plumbing Code.

Minimum SlopeMinimum Slope %Slope GradientPipe Diameter
1/4" per foot2.08%1/4 : 122 1/2" or smaller
1/8" per foot1.04%1/8 : 123" to 6"
1/16" per foot0.52%1/16 : 128" or larger
Article Updated: July 23, 2022

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