For a roof slope of 3 in 12, the factor to convert plan area to actual area is

For a roof slope of 3 in 12, the factor to convert plan area to actual area is

• A. 1.014
• B. 1.031
• C. 1.054
• D. 1.083

Answer: (B)

Converting plan area to actual roof area uses the secant of the roof angle, since the sloped surface is longer than its horizontal projection. For a 3 in 12 in pitch, rise/run = 3/12 = 0.25, so the angle θ from horizontal has tan(θ) = 0.25. The area factor is 1/cos(θ) = sqrt(1 + tan²(θ)) = sqrt(1 + 0.25²) = sqrt(1.0625) ≈ 1.0308. Rounding gives 1.031. So you multiply the plan area by about 1.031 to get the actual roof area.

Converting plan area to actual roof area uses the secant of the roof angle, since the sloped surface is longer than its horizontal projection. For a 3 in 12 in pitch, rise/run = 3/12 = 0.25, so the angle θ from horizontal has tan(θ) = 0.25. The area factor is 1/cos(θ) = sqrt(1 + tan²(θ)) = sqrt(1 + 0.25²) = sqrt(1.0625) ≈ 1.0308. Rounding gives 1.031. So you multiply the plan area by about 1.031 to get the actual roof area.