Angle to Roof Pitch: Quick Conversion Guide

This calculator converts a roof angle in degrees to the standard roof pitch ratio (rise over run), and also shows the pitch as a percentage and the slope in degrees. You enter the angle in degrees, and you get the pitch ratio (e.g., 6/12), the pitch percentage, and the slope angle back. This is useful for roofers, builders, and DIYers who need to match plans or materials that use different pitch notations.

Formula

The roof pitch is the ratio of the vertical rise to the horizontal run. In the US, it is commonly expressed as a ratio of rise in inches per 12 inches of run (e.g., 6/12). The angle (in degrees) is related to the pitch by the tangent function:

tan(angle) = rise / run

For a 12-inch run, the rise is: rise = 12 × tan(angle)

So the pitch ratio is rise/12. The percentage pitch is tan(angle) × 100.

Worked Example

Using the default angle of 30°:

1. Convert 30° to radians: 30 × π/180 = 0.5236 radians.
2. Calculate tan(0.5236) = 0.5774.
3. Rise per 12 inches: 0.5774 × 12 = 6.93 inches.
4. Pitch ratio = 6.93/12 (rounded to 6.93/12).
5. Percentage pitch = 0.5774 × 100 = 57.7%.

The calculator shows a pitch of 6.93/12 and a percentage of 57.7% for a 30° angle.

Why Roof Pitch Matters

Roof pitch affects water runoff, snow load, available attic space, and the type of roofing material you can use. Low-pitch roofs (under 2/12) require special waterproofing, while steep pitches (above 9/12) may need additional fastening for shingles. Knowing the pitch in the format your supplier or contractor uses is essential for ordering materials and ensuring proper installation.

How to Measure Roof Pitch

If you have the angle, you can convert it directly with this calculator. If you have the rise and run, you can find the angle using the inverse tangent:

• Measure the vertical rise over a 12-inch horizontal run.
• Use a speed square or digital level to get the angle directly.
• For existing roofs, use a pitch gauge or a smartphone app with a level.

Always measure from the roof surface, not the ceiling, and ensure the run is exactly horizontal.

Common Conversions

Here are some typical angles and their corresponding pitches:

• 4.76° = 1/12
• 9.46° = 2/12
• 14.04° = 3/12
• 18.43° = 4/12
• 22.62° = 5/12
• 26.57° = 6/12
• 30.26° = 7/12
• 33.69° = 8/12
• 36.87° = 9/12
• 39.81° = 10/12

These are rounded to two decimal places; the exact values come from the tangent function.

Choosing the Right Pitch

The ideal pitch depends on your climate and architectural style. In snowy regions, a steeper pitch (6/12 or more) helps shed snow. In windy areas, a lower pitch reduces wind uplift. A pitch between 4/12 and 9/12 is common for residential roofs. Below 2/12, use a membrane roof instead of shingles. Above 12/12, consider the cost of additional framing and safety measures.

Common Mistakes and Misconceptions

One common mistake is confusing the angle with the pitch percentage. A 45° roof is not a 45% pitch; it is a 100% pitch because rise equals run. Another error is mixing units: the run is always 12 inches, not 12 feet or 1 foot. Always ensure your angle is in degrees, not radians, when using the calculator. Also, note that the pitch ratio is often written as a fraction like 6/12, but it is not a true fraction—it is a ratio of inches per foot.

Limitations of the Formula

The tangent function works for any angle from 0° to 90°, but roof pitches above 45° become impractical for most buildings. For very steep roofs, the rise per 12 inches becomes large, and the tangent function grows quickly. The calculator uses a standard mathematical tangent, which is accurate for all angles, but real-world measurements may have slight errors due to surface irregularities. Always verify with a physical measurement before cutting materials.

Frequently Asked Questions

What is the difference between roof pitch and slope?

Roof pitch is the ratio of rise to run, usually expressed as inches per foot (e.g., 6/12). Slope is the tangent of the angle, often given as a percentage (rise/run × 100). Both describe the same steepness, but pitch is common in the US, while slope is used in engineering and metric contexts.

How do I convert pitch to angle?

Use the inverse tangent: angle = arctan(rise / run). For a 6/12 pitch, angle = arctan(6/12) = 26.57°. You can also use this calculator in reverse by entering the angle you want to achieve.

Can I use any angle for a roof?

Practically, angles between 2° and 60° are used, but very low angles require special membranes, and very high angles are expensive and unsafe. Building codes often specify minimum pitches for certain materials. Always check local codes.

What is a 4/12 pitch in degrees?

A 4/12 pitch means 4 inches of rise per 12 inches of run. The angle is arctan(4/12) = 18.43°. This is a common residential pitch.

Why is pitch expressed as a ratio of 12?

The 12-inch run is a convenient standard because it matches common measuring tools like speed squares and makes calculations easy. It is a US convention; metric countries often use degrees or percentages.

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in a | Angle | degrees | 30 | 0
out pitch | Pitch (rise/run) | - | round(tan(a * pi / 180) * 12, 2) | 2
out percent | Pitch (%) | % | tan(a * pi / 180) * 100 | 1
out angle | Angle | degrees | a | 0