TryBuildCalcHip Roof / Hip & Valley Rafter Calculator (Hip, Valley, Jack & Common Rafters)
Find your hip and valley rafter lengths and counts 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
123
117 common/jack (+10% waste) + 2 king common + 4 hip
Hip Rafter Length
22.41 ft
268.88" including overhang tail
Common Rafters
Run: 167.25" (13.94 ft)
Line length: 186.99"
Total (with 12" overhang): 200.41" (16.70 ft)
Plumb cut angle: 26.57°
Count: 28 (26 in-line, 13 per side + 2 king common)
Hip Rafters
Run: 236.53" (19.71 ft)
Line length: 250.88"
Plumb cut angle: 19.47° (shallower than common — longer diagonal run)
Count: 4
Jack Rafters
Per side: 10 (8 sides total)
Shortest: 31.31" — Longest: 192.3"
Increases by 17.89" per step, from the corner toward the common rafter.
Count: 80
Ridge Board
Length: 16 ft
Stock: 12 ft boards
Count: 2
Birdsmouth (Common Rafter Seat Cut)
Seat cut: 3.5"
Notch depth: 1.57" (max 1.81")
Heel height: 1.75"
Height above plate: 6.36"
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: 28 pcs + recommended tools
+−
Bill of Materials
Main material: 28 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
Ridge Board
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.
What Is a Hip Roof / Hip & Valley Rafter Calculator?
A hip roof calculator finds the number and length of common, hip (or valley), and jack rafters needed for a stick-framed hip roof — either a standalone rectangular building hipped on all 4 corners, or a hip-and-valley wing/addition meeting a main roof. It starts from your building's two dimensions and roof pitch, applies direct trigonometry (not a code-table lookup) to find each rafter type's run, rise, and length, and uses the standard on-center spacing formula for piece counts.
This calculator does not design your roof structure. It gives rafter length, count, and plumb-cut angle only — compound side-cut and backing-bevel angles (where a hip meets the ridge, or a jack meets a hip) are a carpentry-square/rafter-table layout step, the same scope boundary already drawn for this site's plain Rafter Calculator.
Why hip and valley rafters are different from a common rafter:
- A hip/valley rafter's horizontal run is √2 times the common rafter's run — it travels diagonally across a square corner, not straight in from the wall
- A hip and a valley rafter are dimensionally identical pieces of lumber — only whether the corner is convex (hip) or concave (valley) differs
- Jack rafters step down in length toward each corner in a fixed arithmetic series, not a fixed count like commons
- A square building produces a pyramid hip roof — all 4 hips converge at a single apex with no ridge board at all
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 | 28 ft / 44 ft | Sets common run, hip run, and ridge length |
| Pitch | 6/12 (26.57°) | Sets rise for all rafter types |
| Spacing | 16" O.C. | Sets rafter counts |
Step 1 — Common Rafter
| Calculation | Result |
|---|---|
| Run | 167.25" |
| Rise | 83.63" |
| Total length (with overhang) | 200.41" |
| Ridge length | 16 ft |
Step 2 — Hip Rafter
| Calculation | Result |
|---|---|
| Run | 236.53" |
| Angle | 19.47° |
| Total length (with overhang) | 268.88" |
Step 3 — Jack Rafters & Totals
| Calculation | Result |
|---|---|
| Jacks per side (8 sides total) | 10 |
| In-line common rafters | 26 |
| King common rafters | 2 |
| Total rafters (with 10% waste on in-line commons/jacks) | 123 |
Therefore, this 28×44 ft 6/12 pitch hip roof needs approximately 123 rafters total (28 common, 4 hip, 80 jack).
Essential Checklist+−
Complete these critical checks before approving the work or proceeding to the next construction stage.
✓Dimension & Pitch Inputs+-
- Building (or wing) width and length confirmed from actual field measurements or plans, not assumed
- Roof pitch entered matches the actual design intent, and is the SAME on both roof planes
- Rafter spacing matches the roof sheathing's span rating and the actual roof load for this project
- Local building code edition, wind/seismic zone, and snow load confirmed before finalizing
✓Hip / Valley Geometry & Cuts+-
- Confirmed this calculator gives hip/valley rafter LENGTH and plumb-cut angle only, not compound side-cut/backing-bevel angles
✓Jack Rafter Layout+-
- Jack rafter length series (shortest to longest) verified against actual layout before cutting
✓Code, Safety & Sign-Off+-
- Birdsmouth notch depth checked against the commonly-required 1/4-of-depth limit for this rafter size
- Any hip/valley beam carrying unusually long spans or heavy point loads reviewed by a structural engineer
Full QC Checklist+−
Verification checklist for stick-framed hip and valley rafter material takeoffs — covering dimension/pitch inputs, hip-valley geometry, jack rafter layout, and code/safety confirmation. Use the Essential Checklist for critical checks before finalizing, expand to Full QC Checklist for complete verification.
✓Dimension & Pitch Inputs+-
- Building (or wing) width and length confirmed from actual field measurements or plans, not assumed
- Roof pitch entered matches the actual design intent, and is the SAME on both roof planes
- Correct roof section type selected (Hip Roof vs. Hip & Valley wing/addition)
- Rafter spacing matches the roof sheathing's span rating and the actual roof load for this project
- Local building code edition, wind/seismic zone, and snow load confirmed before finalizing
- Same overhang entered applies correctly to both common AND hip/jack rafter tails for a continuous fascia line
✓Hip / Valley Geometry & Cuts+-
- Confirmed this calculator gives hip/valley rafter LENGTH and plumb-cut angle only, not compound side-cut/backing-bevel angles
- Hip/valley rafter total length checked against available stock lengths before ordering
- If width and length are equal (a pyramid hip), confirmed there is no ridge board and all 4 hips converge at a single apex
- Structural support for the hip rafter's load path (down to a corner post/header) verified where needed
- Hip/valley rafter lumber size confirmed adequate for its actual (longer) span, not just matched to the common rafter size
- Common rafter count confirmed to include king common rafters, not just the in-line commons along the ridge
✓Jack Rafter Layout+-
- Jack rafter length series (shortest to longest) verified against actual layout before cutting
- Jack rafter side-cut angle (where it meets the hip/valley) confirmed separately, not computed by this calculator
- Jack rafter count and lengths confirmed to apply identically on both walls meeting each hip/valley corner
- Jack rafters (like commons) installed crown-up, and checked individually before cutting the full series
✓Code, Safety & Sign-Off+-
- Birdsmouth notch depth checked against the commonly-required 1/4-of-depth limit for this rafter size
- Any hip/valley beam carrying unusually long spans or heavy point loads reviewed by a structural engineer
- Permit and framing inspection requirements confirmed before roof sheathing covers the rafters
- Unequal pitches, irregular building shapes, or any non-standard condition reviewed by a designer or structural engineer
- Total rafter count reconciled against the actual architectural roof plan before ordering lumber
Framing Reference Tables
Common roof pitches and their angle/diagonal-length factor for both common and hip/valley rafters.
| Pitch | Common Angle | Common Factor (per ft run) | Hip/Valley Angle | Hip/Valley Factor (per ft run) |
|---|---|---|---|---|
| 3/12 | 14.0° | 1.031 | 10.0° | 1.016 |
| 4/12 | 18.4° | 1.054 | 13.3° | 1.027 |
| 6/12 | 26.6° | 1.118 | 19.5° | 1.061 |
| 8/12 | 33.7° | 1.202 | 25.2° | 1.106 |
| 9/12 | 36.9° | 1.250 | 27.9° | 1.132 |
| 12/12 | 45.0° | 1.414 | 35.3° | 1.225 |
Roof Section Types
| Type | Description |
|---|---|
| Hip Roof | A standalone rectangular building hipped on all 4 corners — 4 hip rafters, common rafters over any ridge-length portion, jacks throughout. |
| Hip & Valley (Wing/Addition) | A wing or addition meeting a main roof — 2 valley rafters at the base (where it meets the main roof), 2 hip rafters at its far/outer end, common and jack rafters as with a standalone hip roof. |
| Pyramid Hip | The special case where width equals length — all 4 hips converge directly at a single apex point, with no ridge board at all. |
When should you use this hip roof calculator?
- Planning rafter counts and lengths for a new hip roof, garage, or hip-and-valley addition before ordering lumber.
- Finding hip/valley rafter length and cut angle for layout, before committing to a stock or spliced/engineered length.
- Sizing jack rafters for a hip or valley corner, including the full decreasing length series.
- Comparing how pitch, dimensions, or spacing changes total rafter count before finalizing a design.
- Cross-checking a framing crew's lumber order against an independent estimate before ordering.
Quick Framing Tips
- Cut and test-fit the first hip rafter before batch-cutting the rest — small pitch or measurement errors compound fast on a diagonal member.
- Lay out jack rafters from the corner outward, marking each position on the wall plate before cutting the full length series.
- Use a speed square or rafter table for the compound side cuts on hip and jack rafters — this calculator gives length and plumb-cut angle only.
- Consider bumping the hip/valley rafter up one lumber size from the commons — it spans considerably further for the same building width.
- Brace the first hip and its adjoining commons immediately after setting — an unbraced hip corner is unstable until the ridge and opposite hip are also up.
- A 10% waste factor is a reasonable estimating default for common/jack rafters — increase it for a roof with more than one hip-and-valley intersection.
Common Mistakes
- Sizing the hip/valley rafter identically to the common rafter without checking its own (longer) actual span.
- Entering the building's longer dimension as "Width" by mistake — this calculator sorts them automatically, but double-check the result matches your actual building orientation.
- Skipping the compound side-cut layout on hip and jack rafters — a plumb cut alone doesn't fit correctly at the hip/ridge connection.
- Applying a waste factor to the 4 fixed hip/valley rafters — they're a fixed count, not a spacing-formula quantity.
- Assuming unequal roof pitches at a hip or valley intersection — this calculator (and the standard hip framing method) assumes equal pitch on all planes.
- Forgetting that a square building produces a pyramid hip roof with no ridge board — ordering a ridge board anyway wastes material.
- Not verifying structural support (post/header) below a hip's concentrated load path, especially on wider spans.
Limitations
- US light-frame stick-built residential practice only, at a single uniform pitch on all roof planes — unequal pitches, steel framing, and non-US conventions are not modeled.
- Does not compute compound side-cut or backing-bevel angles for hip or jack rafters — only the plumb-cut angle and lengths, the same scope boundary as this site's plain Rafter Calculator.
- Handles one rectangular roof section (or one hip-and-valley wing) at a time — a building with multiple wings, dormers, or intersecting roof sections needs each section calculated separately.
- Does not verify structural adequacy of hip/valley beams or headers under concentrated corner loads — get an engineered review for wide spans or heavy roof coverings.
- Does not count roof sheathing, underlayment, roofing material, or fasteners beyond the rafter-tie connector count.
- Jack rafter count assumes the run to each corner is exactly the common rafter's own run — dormers, skylights, or other openings near a hip are not accounted for.
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.