TryBuildCalcPyramid Hip Roof Calculator (Square Building, No Ridge)
Size a pyramid hip roof instantly.
🕒 Last updated: September 4, 2026
Inputs
ℹ️Hip Roof: a standalone rectangular building hipped on all 4 corners. Hip & Valley: a wing/addition meeting a main roof — 2 valleys at its base, 2 hips at its far end. The rafter geometry is identical either way; only the corner labeling differs.
ℹ️Either dimension can go in either field — whichever is smaller automatically governs pitch, hip run, and jack run.
ℹ️If equal to the width, this becomes a pyramid hip roof with no ridge.
ℹ️Rise per 12 inches of run, applied uniformly to all roof planes — this calculator assumes equal pitch throughout.
ℹ️Horizontal projection of the rafter tail past the outer wall face, before any fascia trim.
ℹ️Hip/valley rafters commonly get bumped up one size from the commons, since they span considerably further for the same building width.
Waste
ℹ️Accounts for damaged pieces and layout adjustments on common and jack rafters — 10% is a common estimating default. Not applied to the fixed 4 hip/valley rafters.
Cost
Total Rafters Needed
79
71 common/jack (+10% waste) + 4 king common + 4 hip
Hip Rafter Length
20.23 ft
242.73" including overhang tail
Common Rafters
Run: 143.25" (11.94 ft)
Line length: 172.17"
Total (with 12" overhang): 186.59" (15.55 ft)
Plumb cut angle: 33.69°
Count: 4 (0 in-line + 4 king common)
Hip Rafters
Run: 202.59" (16.88 ft)
Line length: 223.97"
Plumb cut angle: 25.24° (shallower than common — longer diagonal run)
Count: 4
Jack Rafters
Per side: 8 (8 sides total)
Shortest: 33.65" — Longest: 168.26"
Increases by 19.23" per step, from the corner toward the common rafter.
Count: 64
Ridge Board
Not applicable — a pyramid hip roof (equal width and length) has no straight ridge; all 4 hips converge at a single apex.
Birdsmouth (Common Rafter Seat Cut)
Seat cut: 3.5"
Notch depth: 1.94" (max 1.81")
Heel height: 2.33"
Height above plate: 6.38"
Notch depth exceeds the commonly-required 1/4-of-depth limit — verify against your adopted code edition, or use a deeper rafter/thinner plate.
Hip and jack rafters have their own compound seat/side cuts, not computed here — lay these out with a speed square or rafter table referencing the angles above.
Assumptions Used
Standard US light-frame stick construction, equal pitch on all roof planes. The shorter of your two entered dimensions always governs the ridge height, hip run, and jack rafter run — the longer dimension only sets the ridge length. Common rafter count includes king common rafters — the rafter from the center of each hip end wall (or each wall, for a pyramid hip) straight to the ridge end or apex — in addition to the in-line commons along the ridge. Hip and valley rafters are geometrically identical pieces of lumber (a valley is simply a hip turned inward at a roof intersection instead of an outside building corner), computed with direct trigonometry, not a code-table lookup. Jack rafter lengths follow the standard carpentry-table method (spacing × common rafter unit length factor per step) rather than a lookup table. Compound side-cut and backing-bevel angles — where a hip or jack rafter meets the ridge or another hip — are not computed here; lay those out with a speed square or rafter table referencing the plumb-cut angles shown above, the same scope boundary as this site's plain Rafter Calculator. This is a quantity and geometry takeoff only, not a substitute for an engineered design where required (long spans, unusual loads, or a girder/hip beam condition).
Bill of Materials
Main material: 4 pcs + recommended tools
+−
Bill of Materials
Main material: 4 pcs + recommended tools
Computed items reflect your entered dimensions and spacing; consumables below are general recommendations — actual needs vary by product, wind/seismic zone, and site conditions.
For Your Job
Common Rafters
Hip Rafters
Jack Rafters
Rafter Ties / Connectors
General Tools & Consumables
Rafter ties / hurricane clips
Ridge board hangers/straps
Roof sheathing (OSB/plywood)
Framing nailer or hammer
Speed square / rafter square
Tape measure
Chalk line
4 ft level
Temporary bracing lumber
Safety harness & fall protection
Plan-view diagram simplified for clarity (not to scale) — jack rafter positions shown schematically, not an exact count match.
Looking for the verification checklist, reference tables, tips, or common mistakes?See the complete Hip Roof / Hip & Valley Rafter Calculator.
Pyramid hip roof sizing
A pyramid hip roof happens when a building's width and length are equal — instead of a straight ridge, all 4 hip rafters converge directly at a single center apex.
This page defaults to a 24×24 ft square building at an 8/12 pitch — edit the inputs above to match your actual building (keep both dimensions equal for a true pyramid).
Hip Roof Calculator Formula: How Is It Determined?
Common, hip/valley, and jack rafter geometry, calculated separately and combined into a material takeoff.
Step 1 — Common Rafter (governs pitch height)
Run = (Width − Ridge Thickness) ÷ 2
Rise = Run × (Pitch ÷ 12)
Line Length = Run ÷ cos(Angle)
Ridge Length = Length − Width (0 if equal — a pyramid hip)
The shorter of your two entered dimensions ("Width") governs the ridge height and every downstream hip/jack calculation — the longer dimension only sets how much straight ridge exists between the hips.
Step 2 — Hip / Valley Rafter
Hip Run = Common Run × √2
Hip Rise = Common Rise (same ridge height)
Hip Length = √(Hip Run² + Hip Rise²)
Hip Angle = arctan(Hip Rise ÷ Hip Run) — shallower than the common angle
A hip or valley rafter travels diagonally across a square corner — its run is the common run scaled by √2, with the same rise, giving a longer, shallower-angled piece of lumber. This is why hip and valley rafters use identical math regardless of whether the corner is convex (hip) or concave (valley).
Step 3 — Jack Rafters
Common Difference = Spacing × Common Unit Length Factor
Jacks per Side = ceil(Common Run ÷ Spacing) − 1
Jack Length (step n) = n × Common Difference
Each jack rafter is one fixed length increment shorter than the next, all the way down to the corner — the standard carpentry-table method for jack rafter differences, applied here as direct trigonometry.
Worked Example
This example walks through your current inputs above, using the same steps as the Formula section.
Input Values Used
| Input | Value | Why it is used |
|---|---|---|
| Width / Length | 24 ft / 24 ft | Sets common run, hip run, and ridge length |
| Pitch | 8/12 (33.69°) | Sets rise for all rafter types |
| Spacing | 16" O.C. | Sets rafter counts |
Step 1 — Common Rafter
| Calculation | Result |
|---|---|
| Run | 143.25" |
| Rise | 95.5" |
| Total length (with overhang) | 186.59" |
| Ridge length | 0 ft (pyramid — no ridge) |
Step 2 — Hip Rafter
| Calculation | Result |
|---|---|
| Run | 202.59" |
| Angle | 25.24° |
| Total length (with overhang) | 242.73" |
Step 3 — Jack Rafters & Totals
| Calculation | Result |
|---|---|
| Jacks per side (8 sides total) | 8 |
| In-line common rafters | 0 |
| King common rafters | 4 |
| Total rafters (with 10% waste on in-line commons/jacks) | 79 |
Therefore, this 24×24 ft 8/12 pitch hip roof needs approximately 79 rafters total (4 common, 4 hip, 64 jack).
Related Calculators
Disclaimer: This calculator provides approximate results for planning and estimation purposes only. Actual requirements may vary based on site conditions, materials, workmanship, and local building regulations. Always consult a qualified engineer, architect, or construction professional before making final decisions.