Dachneigung berechnen: Winkel, Gefälle und Steigung

Aus Höhe und waagerechter Strecke Winkel, Steigung in Prozent und Dachneigung (x zu 12) sowie schräge Länge und Sparrenfaktor berechnen.

Aktualisiert 28. September 2026Geprüfte Beispiele: 8

Winkel

Maximale Nachkommastellen: 4; Zum nächsten Wert, bei Gleichstand von null weg

Note: 50%
Roof pitch: 6in 12
Ratio (rise : run): 1 : 2
Rise per unit of run: 0.5
Rafter length factor: 1.118034
Slope length: 13.4164cm

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.

Slope profile, to scale

So wird gerechnet S

Slope
$m = \frac{\text{rise}}{\text{run}} = \frac{6}{12} = 0.5$
Winkel
$\theta = \arctan m = \arctan 0.5 = 26.565051^\circ$
Grade and pitch
$\text{grade} = 100m = 50\,\%,\qquad \text{pitch} = 12m = 6 \text{ in } 12$
Rafter factor
$\sqrt{1 + m^2} = \sqrt{1 + 0.5^2} = 1.118034$
Multiply a horizontal run by this to get the sloped length.
Slope length
$\sqrt{\text{rise}^2 + \text{run}^2} = 12 \times 1.118034 = 13.416408\,\text{cm}$

Über Dachneigung berechnen: Winkel, Gefälle und Steigung

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.

Durchgerechnete Beispiele

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

Bekannte Größe: Rise and run
Rise: 6 cm
Run (horizontal distance): 12 cm
Ergebniseinheit: Zentimeter (cm)

Winkel: 26.565051 °
Note: 50%
Roof pitch: 6 in 12
Ratio (rise : run): 1 : 2
Rafter length factor: 1.118034
Slope length: 13.416408 cm

Prüfquelle: Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2)

45°

Bekannte Größe: Winkel
Angle from horizontal: 45 °

Note: 100%
Roof pitch: 12 in 12
Ratio (rise : run): 1 : 1
Rafter length factor: 1.414214

Prüfquelle: tan 45° = 1; Python 3.8 math.sqrt(2)

8 % road grade

Bekannte Größe: Percent grade
Note: 8%

Winkel: 4.573921 °
Roof pitch: 0.96 in 12
Ratio (rise : run): 1 : 12.5

Prüfquelle: Python 3.8 math: degrees(atan(0.08)); 12 × 0.08; 1/0.08

4/12 roof pitch

Bekannte Größe: Roof pitch
Pitch: 4 in 12

Winkel: 18.434949 °
Note: 33.333333%
Rafter length factor: 1.054093

Prüfquelle: Python 3.8 math: degrees(atan(4/12)), sqrt(1 + 1/9)

Fragen

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.

Wie genau arbeitet „Dachneigung berechnen: Winkel, Gefälle und Steigung“?

Die Genauigkeit hängt von Ihren Eingaben und den Annahmen der Methode ab. Die Dezimalrechnung nutzt 50 signifikante Stellen, doch Schätzungen, numerische Verfahren und Quelldaten können ungenauer sein. Die angezeigte Rundung beseitigt diese Grenzen nicht. Anhand unabhängiger Quellen geprüfte Rechenbeispiele: 8. Beispielsweise wird „Rise 6, run 12 (a 6/12 roof)“ anhand von Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2) geprüft.

Woher stammt die Methode?

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

Über diesen Rechner

\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}

Quellen

Anhand von Quellen geprüft

Dieser Rechner enthält 8 Rechenbeispiele mit Ergebnissen aus unabhängigen Quellen. Sie laufen in der Testsuite und können auch hier ausgeführt werden.

Slope profile, to scale

Slope