Calculate roof pitch angle, roof area, and total roofing material needed for any gable, hip, or shed roof. Convert between pitch ratio, degrees, and percentage gradient.
X is what % of Y: (X ÷ Y) × 100
X% of Y: (X ÷ 100) × Y
% change from A to B: ((B − A) ÷ A) × 100
Original value before X% added: Final ÷ (1 + X/100)
Original value before X% removed: Final ÷ (1 − X/100)
Worked examples: 45 is what % of 180? (45 ÷ 180) × 100 = 25%. 15% of 240? 0.15 × 240 = 36. Price rose from 80 to 96 — % increase: ((96−80) ÷ 80) × 100 = 20%. Price was 120 after 20% tax added — original pre-tax: 120 ÷ 1.20 = 100.
Roof pitch is the steepness of a roof expressed as a ratio of rise over run. A 4/12 pitch means the roof rises 4 inches for every 12 inches of horizontal run.
Use the formula: angle = arctan(rise/run). A 4/12 pitch = arctan(4/12) ≈ 18.4°. A 12/12 pitch = arctan(1) = 45°.
Calculate the footprint area (length × width of the house), then multiply by the roof pitch multiplier: Area = footprint × √(rise² + run²) / run. Add 10–15% for overlaps and waste.
A pitch of 4/12 to 6/12 (18°–27°) is standard for residential roofs. Steeper pitches (above 6/12) shed water and snow better but cost more to build. Pitches below 2/12 require special low-slope roofing materials.
A gable roof has two sloping sides meeting at a ridge, with triangular gable ends. A hip roof has four sloping sides meeting at a ridge, with no vertical gable ends — it's more complex to calculate but more wind-resistant.