Roof Angle to Slope Conversion

Slope Defined

• The slope of a roof is the proportion of the height of the roof to the length from the edge to the highest point. The slope should not be confused with the pitch of the roof, which is the total rise divided by the entire span of the roof from one end to the other. On building plans in the United States, this proportion relates how high the ceiling rises over 12 inches of length. For instance, if the roof rises 12 inches in height over a 12 inch length, the slope is 12/12 or 1.

Protractor Method

• Protractors are semicircle measuring devices used to determine angles. Combine this with a ruler to convert the angle of a roof to the slope. Measure the angle of the roof with the protractor. Draw two lines at that angle on a piece of paper. Measure 12 inches on the bottom line, representing the run of the roof. Draw a line from the end of that line to the second line. This intersecting line represents the rise of the roof. Measure the distance of this line for the top number in the proportion of the slope of the roof over 12 inches. For instance, if the line intersecting the two lines of the angle measured 4 inches, the proportion for the slope is 4/12 or 1/3.

T-square Method

• Draw the roof angle on a piece of paper or hold a t-square up to the roof. Place the 12-inch base of the t-square along the bottom of the angle with the free end of the base at the angle. Where the t-square ends along the base — 12 inches away from the angle — measure the vertical rise with the other arm of the t-square. This will be the rise over the 12-inch run for the slope.

Calculator Method

• Use a scientific calculator and trigonometry to convert between the angle and the slope. Check that your calculator is set to degrees and not radians in the options. Put the angle of the roof into the calculator and press the tangent button. The tangent is a decimal proportion of the rise over the run. Multiply this decimal by the 12-inch run to find the rise for the slope of the roof over 12. For instance, if the tangent of a 30-degree angle is 0.577, multiply this by 12 to find the rise in inches over a 12-inch run. The rise will be 6.93 inches using this method.