You're pricing a reroofing job and need the roof pitch, actual rafter run and rise before the supplier can quote the ridge capping and valley iron. The client only knows the building span and wants a 22-degree pitch.
Roof Pitch Calculator
Roofing
Rise = Run × tan(pitch) · Rafter = Run ÷ cos(pitch)
Common pitches: 15° (low), 22.5° (standard), 30° (steep), 45° (Dutch gable).
Reference: ABCB — NCC Housing Provisions
Results are estimates for planning purposes. Verify with current standards and a qualified professional.
1 What this calculator does
Calculates roof pitch angle, rise, run (half-span) and rafter length from the building span and pitch angle. Also converts between pitch angle (degrees) and pitch ratio (rise:run). Supports metric and imperial.
2 Formula & professional reasoning
Run = Span / 2 (half the building span)
Rise = Run x tan(Pitch angle in degrees)
Rafter length = Run / cos(Pitch angle in degrees)
Pitch angle (deg) = atan(Rise / Run) x (180 / Pi)
Slope ratio (imperial) = Rise per 12 units of run
The run is always half the span for a simple gable roof -- the rafter starts at the wall plate and meets the ridge at the centre. Trigonometry (SOH CAH TOA) gives rise (opposite side = run x tan) and rafter length (hypotenuse = run / cos). The same triangle applies to hip rafters and valley rafters with different effective runs. Always add eave overhang length after calculating the structural rafter length.
3 Worked examples
⚠️ Illustrative example only — not clinical or professional instruction.
Basic
Standard gable -- 22 degree pitch
Given: Building span: 10.0m | Pitch: 22 degrees
Working:
Run: 10.0/2 = 5.0m | Rise: 5.0 x tan(22°) = 5.0 x 0.4040 = 2.020m | Rafter: 5.0/cos(22°) = 5.0/0.9272 = 5.393mAnswer: Run: 5.0m | Rise: 2.02m | Rafter length: 5.39m (to birdsmouth)
💡 Add 600mm eave overhang: rafter to order = 5.39 + 0.6/cos(22°) = 5.39 + 0.65 = 6.04m. Order 6.3m lengths.
Standard
Steep roof from rise:run ratio
Given: Span: 8.4m | Rise:Run = 7:12 (imperial ratio)
Working:
Angle: atan(7/12) x (180/Pi) = atan(0.583) = 30.26° | Run: 8.4/2 = 4.2m | Rise: 4.2 x tan(30.26°) = 2.451m | Rafter: 4.2/cos(30.26°) = 4.859mAnswer: Pitch: 30.3° | Rise: 2.45m | Rafter: 4.86m
💡 A 7:12 pitch is steep (30.3 degrees). Require appropriate safety equipment and check if tile manufacturer has a minimum pitch specification.
Advanced
Checking pitch against product minimum
Given: Proposed pitch: 12 degrees | Metal roofing minimum: 5 degrees | Concrete tile minimum: 15 degrees
Working:
12 degrees > 5 degrees -- metal OK | 12 degrees < 15 degrees -- concrete tile NOT suitableAnswer: 12-degree pitch suitable for metal roofing but NOT for concrete tiles
💡 Always check roofing product data sheets for minimum pitch requirements before specifying materials. A pitch too shallow for the product voids warranties and risks leaks.
4 Sanity check
Common roof pitch ranges
Low pitch: 5-15 degrees | Medium: 15-30 degrees | Steep: 30-45 degrees | Very steep: 45+ degrees
Typical minimum pitches by product
Metal sheeting: 5 degrees | Corrugated iron: 7 degrees | Concrete tile: 15-18 degrees | Terracotta tile: 17.5 degrees | Slate: 22 degrees
Always check the product data sheet -- minimums vary by manufacturer.
Eave overhang not included in base rafter length
Base rafter length is from birdsmouth to ridge plumb cut | Add overhang length separately before ordering
Imperial slope ratio
7:12 = 7 inches of rise per 12 inches of run = 30.3 degrees | 4:12 = 18.4 degrees | 6:12 = 26.6 degrees
5 Common errors
| Error | Cause | Consequence | Fix |
|---|---|---|---|
| Not adding eave overhang to the rafter length before ordering timber | Using the calculated structural length as the order length | Rafters too short -- every rafter needs to be replaced or spliced at cost | Calculate base structural length (birdsmouth to ridge) then add overhang on the hypotenuse: overhang addition = overhang horizontal length / cos(pitch). Add at least 100mm for plumb cut waste. |
| Specifying a pitch below the product minimum | Not checking manufacturer data sheets before design | Roof leaks, warranty voided, potential liability | Check minimum pitch for the specified roofing product before finalising design. If pitch is borderline, go to the next steeper standard product. |
| Using the building width instead of the span for gable roof rafter calculations | Confusing width and span | Rafters ordered 2x too long -- expensive waste | For a standard gable roof, the run = span / 2 (half the building width). The rafter goes from the wall plate to the ridge, not from wall to wall. |
| Not checking structural adequacy of rafter size for the span | Calculating length without cross-checking against span tables | Undersized rafters fail under wind and snow load | Use AS 1684 span tables (or local building code equivalent) to verify the rafter cross-section is adequate for the calculated length, roof load and spacing. Calculator gives length only -- structural sizing requires span tables. |
6 Reference & regulatory links
7 Professional workflow
Common tools used alongside this one: