Obtain the pitch, or slope angle, of a roof by calculating the ratio of the change in the roof's height to the corresponding horizontal distance. Roof pitch is expressed in ratios of 12 because it is measured by the foot. For example, a roof with a 6:12 pitch rises 6 inches for every horizontal foot.
- Measure the roof
If measuring a physical roof, get a ladder, and place it on a solid surface. Climb up to the roof with a carpenter's square set to a foot of length. Place it above the roof so it forms a right triangle with the slope of the roof.
- Determine pitch
Look at the measurement where the carpenter's square meets the roof, and make a note of this number. For example, assume the roof has a pitch of 4 inches. The roof should intercept the carpenter's square at the 4-inch mark. This is a ratio of 12, so it would be a 4:12 pitch.
- Convert the fraction to a decimal
Dividing 4 by 12 yields a decimal result of 0.3333. This number is needed for the next step.
- Take the inverse tangent of this decimal
Open a calculator application or use a scientific calculator. Enter the decimal, then press the key labeled "tan(-1)," "arctan" or similar. The decimal 0.333 converts to an angle of 18.434 degrees.