The Rake Wall Calculator calculates the length of every stud in a rake wall — a wall whose top follows a sloped roofline, such as a gable end or shed wall.
Each stud grows by the same amount per foot of run: length = short height + distance × slope, where slope = (tall height − short height) ÷ run. The calculator lists each stud’s position and length at your spacing, the pitch (rise per 12 of run) and the length of the sloped top plate.
Rake Wall Calculator
Stud lengths for a rake (sloped-top) wall at every stud position, plus the roof pitch.
Formula
- Slope: s = (H₂ − H₁) ÷ run
- Stud length at distance x: L(x) = H₁ + x × s
- Pitch: 12 × s (inches of rise per 12 in of run)
- Top plate length: √(run² + (H₂ − H₁)²)
Where H₁ = short-end height and H₂ = tall-end height.
How the Calculation Works
Step 1: Find the rise over the whole wall and divide by the run to get the slope.
Step 2: Place studs at every spacing interval from the short end, plus one at the tall end.
Step 3: Multiply each stud’s distance by the slope and add the short height.
Variables Explained
| Input | Meaning |
|---|---|
| Wall run | Horizontal length of the wall |
| Short-end height | Height at the low end, to the underside of the sloped plate |
| Tall-end height | Height at the high end |
| Stud spacing | On-center distance between studs |
Example Calculation
Given: run 12 ft, heights 8 ft and 12 ft, studs at 16 in
Slope: (12 − 8) ÷ 12 = 0.333 (a 4 in 12 pitch)
Each 16 in (1.333 ft) of run adds 0.444 ft (5⅓ in) of height
| Stud | Position | Length |
|---|---|---|
| 1 | 0 ft | 8.00 ft |
| 2 | 1.33 ft | 8.44 ft |
| 3 | 2.67 ft | 8.89 ft |
| … | … | … |
| 10 | 12 ft | 12.00 ft |
Top plate: √(12² + 4²) ≈ 12.65 ft
Pitch Reference Table
| Pitch | Angle | Stud increase per 16 in |
|---|---|---|
| 3 in 12 | 14.04° | 4 in |
| 4 in 12 | 18.43° | 5.33 in |
| 6 in 12 | 26.57° | 8 in |
| 8 in 12 | 33.69° | 10.67 in |
| 12 in 12 | 45° | 16 in |
Material Estimation Notes
Lengths are measured along each stud’s centerline to the underside of the sloped top plate. Deduct the bottom plate thickness as needed and cut the stud tops to the pitch angle. The long point of an angled cut sits slightly beyond the centerline length.
Frequently Asked Questions
How do you calculate stud lengths for a rake wall?
Find the slope (rise ÷ run), then each stud = short height + distance from the short end × slope.
How much does each stud increase?
Stud spacing × slope. At 4 in 12 and 16 in spacing, that is 5⅓ in.
What angle do I cut rake wall studs?
The roof angle: arctan(rise ÷ run). 4 in 12 is about 18.4°.
How long is the sloped top plate?
√(run² + rise²).
Can I use this for a gable end wall?
Yes — calculate each half of the gable as a separate rake wall from the eaves to the peak.