Calculate 4/12 roof rise, run, rafter length, angle, slope multiplier, surface area, roofing squares, overhangs, and waste in imperial or metric units.
- All Construction Calculators
- Metal Roof Cost Calculator
- Roof Panel Length Calculator
- Roof Waste Calculator
4/12 Roof Pitch Formulas
A 4/12 pitch means the roof rises 4 inches vertically for every 12 inches of horizontal run. Choose one of the three calculation modes above. Optional overhang, waste and precision settings remain active when their panel is closed. The geometric formulas are:
Rise = Run ÷ 3
Rafter excluding overhang = Run × √10 ÷ 3
Rafter including overhang = (Run + horizontal eave overhang) × √10 ÷ 3
Roof angle = arctan(1/3) = 18.43°
Roof area = adjusted horizontal width × adjusted horizontal length × √10 ÷ 3
- Run — horizontal distance from outside wall to roof centerline (half the span on a symmetric gable).
- Rise — vertical distance from wall plate to ridge.
- Rafter Length — sloped length from wall plate to ridge, before any overhang.
- Length × Width — building footprint covered by the roof.
- 1.0541 — the slope multiplier for 4/12, equal to √160 / 12, or √10 / 3. Calculations use the unrounded multiplier.
The area formula assumes a simple gable with no dormers, hips, or valleys. Add overhang to the run before multiplying if you want rafter length to the fascia. For materials, multiply the sloped area by 1 plus your waste factor.
Reference Values for 4/12 Pitch
Common conversions and run-to-rise values you can use without re-running the calculator:
| Property | Value |
|---|---|
| Rise per 12 in run | 4 in |
| Roof angle | 18.43° |
| Percent grade | 33.3% |
| Slope multiplier | 1.0541 |
| Radians | 0.3217 rad |
| Walkability | Pitch alone does not establish safe roof access |
| Run (ft) | Rise (ft) | Rafter (ft) |
|---|---|---|
| 8 | 2.67 | 8.43 |
| 10 | 3.33 | 10.54 |
| 12 | 4.00 | 12.65 |
| 14 | 4.67 | 14.76 |
| 16 | 5.33 | 16.87 |
| 20 | 6.67 | 21.08 |
Worked Example and FAQ
Example: A gable roof spans 24 ft with a 1 ft overhang. Run to wall is 12 ft, so the ridge rise is 12 × 4/12 = 4 ft. Rafter length to the wall is 12 × 1.0541 = 12.65 ft. Adding the overhang, total rafter is 13 × 1.0541 = 13.70 ft. For a 40 ft long building with no overhangs in the area calculation, sloped roof area is 24 × 40 × √10/3 = 1,011.93 sq ft, or about 10.12 squares. If the area also includes a 1 ft eave overhang on each side, zero gable overhang and zero waste, it is 26 × 40 × √10/3 = 1,096.26 sq ft. Rafter overhang and area overhang are separate inputs.
Is 4/12 considered low slope? The term depends on the context. OSHA defines a low-slope roof as 4/12 or less for its construction fall-protection rules. Roofing-material requirements use their own slope ranges; follow the specific manufacturer instructions and applicable local code, including underlayment requirements.
Can you walk on a 4/12 roof? Pitch alone does not determine whether roof access is safe. Condition, weather, height and the work being done matter. OSHA requires specified fall protection for covered roofing work on low-slope roofs with unprotected edges at least 6 ft above a lower level; footwear alone is not sufficient. See OSHA 1926.501(b)(10) and the low-slope definition.
Why use 1.0541 instead of measuring the rafter? The multiplier comes from the Pythagorean theorem applied to the 4-12 triangle. Multiplying any horizontal run by 1.0541 gives the sloped distance over that run for a 4/12 pitch.
