Roof Pitch Multiplier: How to Get Roof Square Footage
Multiply the roof's flat footprint (including overhangs) by the pitch multiplier to get the real roof surface area. The multiplier is √(rise² + 144) ÷ 12: 1.054 for 4/12, 1.118 for 6/12, 1.202 for 8/12 and 1.414 for 12/12.
Roof pitch multiplier chart
| Pitch | Multiplier | Extra area |
|---|---|---|
| 2/12 | 1.014 | +1% |
| 3/12 | 1.031 | +3% |
| 4/12 | 1.054 | +5% |
| 5/12 | 1.083 | +8% |
| 6/12 | 1.118 | +12% |
| 7/12 | 1.158 | +16% |
| 8/12 | 1.202 | +20% |
| 9/12 | 1.250 | +25% |
| 10/12 | 1.302 | +30% |
| 11/12 | 1.357 | +36% |
| 12/12 | 1.414 | +41% |
| 14/12 | 1.537 | +54% |
| 16/12 | 1.667 | +67% |
| 18/12 | 1.803 | +80% |
Where the multiplier comes from
Picture one foot of roof seen from the side: 12 inches of run across the bottom, the rise up the side, and the roof surface as the slope. The slope's length is √(rise² + 12²), so for every 12 inches of footprint the roof surface is that many inches long. Divide by 12 to get the multiplier.
multiplier = √(rise² + 144) ÷ 12 (or 1 ÷ cos(angle))
For a 6/12 roof: √(36 + 144) = √180 = 13.42, and 13.42 ÷ 12 = 1.118.
Step by step: roof area and squares
- Measure the footprint. Measure the outside of the house and add the overhangs on every side. A 40 × 30 foot house with 1-foot overhangs is 42 × 32 = 1,344 square feet. Measuring the floor plan alone undercounts.
- Find the pitch. See how to measure roof pitch.
- Multiply the footprint by the multiplier from the chart.
- Add waste: about 10% for a simple gable roof, 15% for hips, valleys and dormers.
- Divide by 100 to get roofing squares. Multiply squares by 3 for bundles of standard shingles.
Worked example
A 1,500 square foot footprint with a 6/12 pitch:
- Roof area: 1,500 × 1.118 = 1,677 square feet
- With 10% waste: 1,845 square feet
- Squares: 18.5
- Bundles: 18.5 × 3 = 55.4, so order 56 bundles
Roofs with more than one pitch
Work out each section separately with its own multiplier, then add them. A porch roof at 3/12 on a 7/12 house is a separate footprint and a separate calculation.
Hip roofs
If all the planes share the same pitch, the multiplier works for hip roofs too: footprint × multiplier gives the full surface area. The hips and valleys themselves are longer than the common rafters, but that affects cuts and waste, not the area. Use the higher waste figure.
Order shingles by the wrapper: most are 3 bundles per square, but some heavier styles are 4 or 5. Starter strip and ridge cap are usually ordered separately by the linear foot.
Questions
What is the multiplier for a 6/12 roof pitch?
1.118. Multiply the flat footprint area, including overhangs, by 1.118 to get the real roof surface area.
What is the multiplier for a 4/12 roof pitch?
1.054. A 4/12 roof has only about 5% more surface than its footprint.
How many squares is a 2,000 square foot roof?
20 squares. One roofing square is 100 square feet of roof surface. Add 10 to 15% for waste before ordering.
How many bundles of shingles per square?
Three for most 3-tab and architectural shingles. Some heavy designer shingles are four or five per square, so check the wrapper.
Does a hip roof use the same multiplier?
Yes. If every plane has the same pitch, footprint × pitch multiplier gives the area for gable and hip roofs alike. Hips and valleys add waste, not area.