# 屋根勾配の計算：角度・勾配率・高さ

> 高さと水平距離から角度、勾配の百分率、屋根勾配（12に対するx）、斜面の長さ、垂木長さの係数を求めます。

操作できるページ：https://www.calcopenly.com/ja/geometry/slope-roof-pitch-calculator
分野：幾何の計算機

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.

## 入力

- **既知の値** (選択肢：Rise and run, 角度, Percent grade, Roof pitch)
- **Rise**: Negative for a downhill slope
- **Run (horizontal distance)**
- **Angle from horizontal**: Between −90° and 90°
- **成績**: Rise per 100 of run
- **Pitch**: Rise for every 12 of run, as in a 6/12 roof
- **結果の単位** (選択肢：ミリメートル (mm), センチメートル (cm), メートル (m), キロメートル (km), インチ (in), フィート (ft), ヤード (yd), マイル (mi))

## 結果

- 角度 (°) — 主な結果
- 成績
- Roof pitch (in 12)
- Ratio (rise : run)
- Rise per unit of run
- Rafter length factor
- Slope length

## 計算式

$$
\begin{gathered} m = \frac{\text{rise}}{\text{run}},\quad \theta = \arctan m,\quad \text{grade} = 100m\,\% \\[6pt] \text{pitch} = 12m \text{ in } 12,\quad \text{factor} = \sqrt{1 + m^2} \end{gathered}
$$

## 計算例

### Rise 6, run 12 (a 6/12 roof)

- 既知の値: Rise and run
- Rise: 6 cm
- Run (horizontal distance): 12 cm
- 結果の単位: センチメートル (cm)
- **角度: 26.565051 °**
- **成績: 50%**
- **Roof pitch: 6 in 12**
- **Ratio (rise : run): 1 : 2**
- **Rafter length factor: 1.118034**
- **Slope length: 13.416408 cm**
- 照合元：Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2)

### 45°

- 既知の値: 角度
- Angle from horizontal: 45 °
- **成績: 100%**
- **Roof pitch: 12 in 12**
- **Ratio (rise : run): 1 : 1**
- **Rafter length factor: 1.414214**
- 照合元：tan 45° = 1; Python 3.8 math.sqrt(2)

### 8 % road grade

- 既知の値: Percent grade
- 成績: 8%
- **角度: 4.573921 °**
- **Roof pitch: 0.96 in 12**
- **Ratio (rise : run): 1 : 12.5**
- 照合元：Python 3.8 math: degrees(atan(0.08)); 12 × 0.08; 1/0.08

### 4/12 roof pitch

- 既知の値: Roof pitch
- Pitch: 4 in 12
- **角度: 18.434949 °**
- **成績: 33.333333%**
- **Rafter length factor: 1.054093**
- 照合元：Python 3.8 math: degrees(atan(4/12)), sqrt(1 + 1/9)

### ADA ramp 1:12

- 既知の値: Rise and run
- Rise: 1 cm
- Run (horizontal distance): 12 cm
- 結果の単位: センチメートル (cm)
- **成績: 8.333333%**
- **角度: 4.763642 °**
- **Ratio (rise : run): 1 : 12**
- 照合元：ADA §405.2 maximum ramp slope 1:12; Python 3.8 math: degrees(atan(1/12))

### Flat ground (edge case)

- 既知の値: Rise and run
- Rise: 0 cm
- Run (horizontal distance): 5 cm
- 結果の単位: センチメートル (cm)
- **角度: 0 °**
- **成績: 0%**
- **Roof pitch: 0 in 12**
- **Rafter length factor: 1**
- **Slope length: 5 cm**
- 照合元：Zero rise: tan θ = 0

## よくある質問

### How do you convert percent grade to degrees?

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.

### What angle is a 6/12 roof pitch?

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.

### What is the maximum slope for a wheelchair ramp?

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.

### How do you calculate rise over run?

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.

### 「屋根勾配の計算：角度・勾配率・高さ」の精度はどのくらいですか？

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。

### この計算方法の出典は何ですか？

OpenStax College Algebra 2e, §4.1 — slope as rise over run; US Access Board, ADA Standards §405.2 — ramp slope 1:12 (8.33 %).

## 出典

- [OpenStax College Algebra 2e, §4.1 — slope as rise over run](https://openstax.org/books/college-algebra-2e/pages/4-1-linear-functions)
- [US Access Board, ADA Standards §405.2 — ramp slope 1:12 (8.33 %)](https://www.access-board.gov/ada/#ada-405)