Boneyard Tools

Roof pitch as ratio, degrees and grade

How the x:12 ratio, the angle in degrees and the percent grade describe the same roof slope, and when each one is the right number to use.

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The x:12 ratio framers actually use

Carpenters describe a roof by how many inches it rises over a fixed 12 inch run, written as a ratio like 6:12 or 8:12. The run is always 12 because a framing square and most rafter tables are built around that base, so the first number alone tells a crew everything about the slope. This calculator normalizes whatever run you enter back to 12, which means a 5 over 10 measurement and a 6 over 12 measurement both report as 6:12. Keeping the run fixed makes two roofs directly comparable at a glance.

Turning the ratio into an angle

The pitch ratio is really the tangent of the roof angle, so the angle in degrees is the arctangent of rise divided by run. A 6:12 roof works out to 26.57 degrees, a 12:12 roof to exactly 45 degrees, and a gentle 3:12 to about 14.04 degrees. Degrees are handy when you are setting a miter saw, cutting a bevel, or checking a slope against a building code table that is written in degrees rather than ratios.

Percent grade and the slope factor

Percent grade expresses the same slope as rise divided by run times 100, so a 6:12 roof is a 50 percent grade and a 12:12 roof is 100 percent. Grade shows up in drainage notes and accessibility rules more than in framing. The slope factor is a different multiplier: it is the length of the sloped rafter per unit of flat run, so multiplying your building's plan area by the slope factor gives the true surface area you need to cover.

From slope to rafter length

Because a rafter is the hypotenuse of the rise and run triangle, its length equals the horizontal run times the slope factor. Enter the run in feet in the rafter field and the tool returns that sloped length, for example 22.3607 feet for a 20 foot run on a 6:12 roof. That figure is the theoretical line length, so remember to add your eave overhang and subtract half the ridge thickness before you mark and cut real lumber.

Frequently asked questions

Is a 6:12 pitch the same as a 26.57 degree roof?

Yes. The ratio, the angle and the grade are three ways of stating one slope. A 6:12 roof is 26.57 degrees and a 50 percent grade at the same time.

Does the slope factor include the overhang?

No. The slope factor only converts flat run into sloped length. You add the overhang length separately and trim for the ridge board after the tool gives you the base rafter figure.

Which number should I give a shingle supplier?

Give them the pitch ratio and your building's flat area. They apply the slope factor to work out the true roof area, then add waste for hips, valleys and starter courses.