Roof Pitch Calculator

Rise	4 in
Run	12 in

Rise

4 in

Run

12 in

Last updated: 2026-06-16

Roof pitch describes how steeply a roof slopes. In North America it is most commonly expressed in X-in-12 notation: a "4-in-12" pitch rises 4 units vertically for every 12 units of horizontal run. The same slope can also be stated as an angle in degrees or as a decimal ratio, and all three forms appear in architectural drawings, building codes, and contractor quotes.

Rise, run, and pitch ratio

The pitch ratio is the simplest form: rise divided by run. A 4-in-12 pitch has a ratio of 4 ÷ 12 = 0.333. To convert any ratio to X-in-12 notation, multiply by 12. To convert to degrees, apply the arctangent:

\begin{aligned} \text{pitch ratio} &= \frac{\text{rise}}{\text{run}} \\[6pt] \text{pitch (X-in-12)} &= \text{pitch ratio} \times 12 \\[6pt] \theta &= \arctan\!\left(\frac{\text{rise}}{\text{run}}\right) \end{aligned}

For a 6-in-12 pitch the calculation runs:

\begin{aligned} \text{pitch ratio} &= \frac{6}{12} = 0.500 \\[6pt] \theta &= \arctan(0.500) \approx 26.6° \end{aligned}

The slope factor and material quantities

The slope factor converts horizontal (plan) area to actual sloped surface area. It equals the length of the hypotenuse of the rise-run triangle divided by the run:

$\text{slope factor} = \frac{\sqrt{\text{rise}^2 + \text{run}^2}}{\text{run}}$

For the same 6-in-12 pitch:

\begin{aligned} \text{slope factor} &= \frac{\sqrt{6^2 + 12^2}}{12} = \frac{\sqrt{180}}{12} \approx 1.118 \end{aligned}

A plan area of 100 m² therefore corresponds to about 111.8 m² of actual roofing surface. This multiplier applies to shingles, underlayment, metal panels, and any other material sold by area. Ordering without accounting for the slope factor leads to shortfalls, particularly on steeper roofs where the difference is most pronounced.

Pitch categories

Roofs are broadly grouped by pitch. Flat and low-slope roofs (below about 4-in-12) require special waterproofing membranes because water drains slowly. Conventional pitches (roughly 4-in-12 to 9-in-12) suit asphalt shingles and most tile systems. Steep roofs above 9-in-12 call for special installation methods and fastener patterns, and they place greater wind and structural loads on the framing.

For related area calculations, see the Flooring Calculator.

Frequently Asked Questions (FAQ)

What is roof pitch?

Roof pitch describes how steeply a roof rises relative to its horizontal span. The most common way to express it in North America is the X-in-12 system: a 4-in-12 pitch rises 4 inches for every 12 inches of horizontal run. Internationally, pitch is also expressed as a ratio (4:12 = 0.333) or as an angle in degrees (roughly 18.4° for a 4-in-12 pitch). Pitch affects drainage, material choice, attic height, and structural loads.

How do you convert roof pitch to degrees?

Divide the rise by the run to get the pitch ratio, then take the arctangent of that ratio. For a 6-in-12 pitch, the ratio is 6 ÷ 12 = 0.5 and the angle is arctan(0.5) ≈ 26.6°. Most scientific calculators have an arctangent (atan or tan⁻¹) button. This calculator does the conversion automatically.

What is the slope factor and why does it matter?

The slope factor is the ratio of the actual sloped roof surface length to the horizontal run: it equals the hypotenuse of the pitch triangle divided by the run, or equivalently 1 / cos(angle). For a 4-in-12 pitch the slope factor is about 1.054, meaning the sloped surface is about 5.4% longer than the footprint. Multiply the plan (horizontal) area of the roof by the slope factor to find how many square metres or square feet of roofing material are needed.

Disclaimer

Results are estimates for planning purposes. Actual roof dimensions, material quantities, and structural requirements depend on the specific roof geometry, local building codes, and site conditions. Verify measurements and specifications against applicable regulations and consult a qualified contractor before construction.

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