This slope rises 0.5 for every 1 of run: 26.57° from horizontal, a 50 % grade, or a 6/12 roof pitch. Its sloped length is 13.4164 cm.
Multiply a horizontal run by this to get the sloped length.
Every way of stating a slope comes from one ratio, m = rise ÷ run. The angle from horizontal is arctan m, the percent grade is 100m, the roof pitch is 12m (units of rise per 12 of run), and the rafter factor √(1 + m²) turns a horizontal run into the sloped length. Enter a rise and run, or any one of the other forms, and the rest follow.
The default rise of 6 over a run of 12 is a 6/12 roof: 26.57°, a 50% grade and a rafter factor of 1.1180, so 12 cm of run needs 13.4164 cm of rafter. Ramps and roads use the same numbers: the steepest ramp the 2010 ADA Standards allow, 1:12, is an 8.33% grade, or 4.76°.
Percent grade is not an angle: a 100% grade is 45°, and a vertical face has no finite grade or pitch, so angles must lie between −90° and 90°. A negative rise describes a downhill slope.
照合元：Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2)
照合元：tan 45° = 1; Python 3.8 math.sqrt(2)
照合元：Python 3.8 math: degrees(atan(0.08)); 12 × 0.08; 1/0.08
照合元：Python 3.8 math: degrees(atan(4/12)), sqrt(1 + 1/9)
Take the arctangent of the grade divided by 100: θ = arctan(grade/100). An 8% road grade is arctan 0.08 = 4.57°, and a 100% grade is 45°, not 90°. The reverse is grade = 100 × tan θ, so a 30° slope is a 57.7% grade.
26.57°. A pitch of x/12 means x units of rise for every 12 of run, so the angle is arctan(x/12): 4/12 is 18.43°, 6/12 is 26.57°, 8/12 is 33.69° and 12/12 is 45°. The rafter factor for 6/12 is √1.25 = 1.118, so 12 ft of horizontal run needs 13.42 ft of rafter before any overhang.
1:12 under the 2010 ADA Standards for Accessible Design (§405.2): one unit of rise for every 12 of run, an 8.33% grade or 4.76°. Each ramp run may rise at most 30 in (§405.6), so a 30 in rise needs a run of at least 30 ft. Other countries set their own limits in their building codes.
Divide the vertical rise by the horizontal run, both in the same unit: m = rise/run. A roof that rises 6 in over 12 in of run has m = 0.5. Measure the run horizontally, not along the surface: the sloped length here is 13.42 in, and dividing by it gives 0.447, the sine of the angle rather than the slope.
精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：8。 例えば、「Rise 6, run 12 (a 6/12 roof)」はPython 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2)と照合しています。
OpenStax College Algebra 2e, §4.1 — slope as rise over run; US Access Board, ADA Standards §405.2 — ramp slope 1:12 (8.33 %).
この計算機には、独立した出典の解答を使った計算例が 8 件あります。テストに組み込まれており、ここでも実行できます。