By Zencalcy Editorial TeamLast reviewed About us
Roof pitch is written as rise over 12 inches of run, but roofers, engineers and material estimators each use a different expression of the same angle. This calculator converts between them and gives the slope multiplier you need to turn a plan area into actual roof area.
Pitch, angle, grade and the slope multiplier in one place.
angle = atan(rise ÷ 12) multiplier = 1 ÷ cos(angle) grade = tan(angle) × 100
A 4/12 pitch is 18.43° with a 1.054 multiplier; a 6/12 is 26.57° with 1.118; a 12/12 is 45° with 1.414. The multiplier is the number you multiply the footprint area by to get the sloped roof area.
| Symbol | Meaning |
|---|---|
| rise | Vertical rise per 12 inches of horizontal run. |
| θ | Roof angle in degrees. |
| m | Slope multiplier (1/cos θ). |
6 ÷ 12 = 0.5, so the angle is 26.57°, the grade is 50% and the slope multiplier is 1.118 — a 1,000 sq ft footprint has 1,118 sq ft of roof.
Continue with the Rafter Length Calculator, Roof Truss Calculator, Roofing Calculator, or the Roof Shingle Calculator — or browse more roofing and all construction calculators.
18.43°. A 6/12 is 26.57° and a 3/12 is 14.04°.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Estimate decking boards by length, screws, hidden fasteners and waste
Calculate concrete blocks needed for wall construction
Calculate full deck materials list including boards, joists, beams, posts, and cost estimates
Price hardwood the way the lumber yard does — by board footage.
Turn measured dimensions into the cubic yards concrete and gravel are sold in.
How many gallons it takes to cover an area at a given depth.
Content updated: September 2026