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# Calculating Slope and Common Slopes in Architecture – Archtoolbox

Architects constantly provide gradient information on their drawings using gradients, degrees, or percentages depending on the application. For case, roof are noted using gradients, but cross-slopes on sidewalks are normally notated in degrees. It is helpful to understand how to calculate each method acting .
There are three different ways to indicate the slope of a surface relative to the horizontal airplane : degrees, gradient, and share .

gradient gradients are written as y : ten, where Y is a single unit in rise and ten is the run. Both numbers must use the lapp units. For case, 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
Slope percentage is calculated in a lot the like way as the gradient. Convert the upgrade and run to the lapp units and then divide the arise by the guide. Multiply this number by 100 and you have the percentage slope. For exemplify, 3 ” resurrect divided by 36 ” run = .083 x 100 = an 8.3 % gradient.

## Calculating a Slope in Degrees

Calculating a Slope in Degrees
The most complicated way to calculate slope is in degrees and it requires a moment of high-school mathematics. The tangent of a given angle ( in degrees ) is equal to the rise divided by the campaign. therefore, the inverse-tangent of the rise divided by the run will give the slant.

## Table of Common Slopes in Architecture

The table downstairs shows some park 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 utmost 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 hybridization slope of 1:50.

0.6° 1 : 95.49 1.0%
1 : 57.29 1.7%
1.15° 1 : 50 2%
1.19° 1 : 48 2.08%
2.86° 1 : 20 5%
4.76° 1 : 12 8.3%
7.13° 1 : 8 12.5%
10° 1 : 5.67 17.6%
14.04° 1 : 4 25%
15° 1 : 3.73 26.8%
26.57° 1 : 2 50%
30° 1 : 1.73 57.7%
45° 1 : 1 100%
56.31° 1: 0.67 150%
60° 1 : 0.6 173.2%
63.43° 1 : 0.5 200%
78.69° 1: 0.2 500%
89.43° 1 : 0.1 1000%
90° 1 : 0  inf.

## Roof Slopes

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

### Low Slope Roofs

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

1/4 : 12 1.19° 2.08%
1/2 : 12 2.39° 4.17%
1 : 12 4.76° 8.3%
2 : 12 9.46° 16.67%
3 : 12 14.04° 25%

### Steep Slope Roofs

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

4 : 12 18.43° 33.33%
5 : 12 22.62° 41.67%
6 : 12 26.57° 50%
7 : 12 30.26° 58.33%
8 : 12 33.69° 66.67%
9 : 12 36.87° 75%
10 : 12 39.81° 83.33%
11 : 12 42.51° 91.67%
12 : 12 45° 100%
source : https://thefartiste.com
Category : Tech