All-In-One Roof Calculator
Pitch + Rafters + Hips & Valleys + Heights + Area + BS 5534 Materials — in one pass
🛡️ UK Material Compatibility (BS 5534) — tap to expand
📐 View Complete Mathematical Proofs & Step-by-Step Workings
- Pitch angle: θ = arctan(Rise ÷ Run) = arctan(1.500 ÷ 3.000) = 26.5651°
- Conversions: 6.00:12 • 1 : 2 • 50.00% • factor 1 ÷ cos(θ) = 1.1180
- Effective run: 4.000 m half-span − 0.019 m (half ridge board) = 3.981 m
- Common rafter line: Run ÷ cos(θ) = 3.981 ÷ 0.8944 = 4.451 m
- Overhang tail: 0.300 m ÷ cos(θ) = 0.335 m → total timber = 4.786 m
- Cuts: plumb cut = 90° − θ = 63.4° • seat cut = θ = 26.6°
- Rise: Span ÷ 2 × tan(θ) = 2.000 m → apex = 2.400 + 2.000 = 4.400 m
- True area: plan area 91.16 m² × pitch factor 1.1180 = 101.92 m²
- Covering: 101.92 m² × (1 + 10.0%) × 10/m² = 1,122 tiles
Master Tool: This aggregate calculator combines every individual roof calculation into one pass. Enter your pitch in any format (rise & run, degrees, X-in-12, or slope %), add the building dimensions, and it simultaneously returns the pitch conversions, true rafter timber lengths and cut angles, hip and valley geometry, ridge and apex heights, the true 3D sloped roof area, and the full BS 5534 material schedule with wastage and estimated cost.
Why One Aggregate Calculator?
Every roof calculation is derived from the same two numbers: a horizontal run and a vertical rise. Traditional single-purpose tools make you re-enter the same dimensions five times — once for the pitch, again for the rafters, again for the area, and again for the tiles. Because each output is a deterministic transform of the same inputs, one master calculator can cascade every result at once with zero re-entry and zero transcription errors between tools.
What This Tool Calculates
| Section | Outputs | Governing Standard |
|---|---|---|
| Pitch | Angle (°), X-in-12, slope ratio 1:X, gradient %, pitch multiplier, rise per metre, solar PV yield | Euclidean trigonometry |
| Carpentry | Effective run, common rafter line length, overhang tail, total timber length, plumb & seat cuts, ridge board length, hip pitch, hip/valley rafter lengths, jack rafter count and decrement | NHBC 7.2 / BS EN 1995-1-1 |
| Heights | Rise above wall plate, total apex height, Permitted Development envelope check | UK PD Class A limits |
| Area | Plan footprint, plan with overhangs, true sloped surface area (m² & ft²), per-slope breakdown | Secant multiplier method |
| Materials | Tiles/slates net & gross, batten linear metres, membrane rolls, ridge/hip capping and tiles, fixings, cost estimate, minimum-pitch compliance check | BS 5534:2014+A2:2018 |
How the Hip Rafter Mathematics Works
On a hipped roof with 45° corners, the hip rafter travels diagonally in plan, so its horizontal run is the half-span multiplied by √2 while it rises the same height as the common rafters. The hip is therefore always at a shallower pitch than the main slopes:
Jack rafters stepping into the hip at spacing s shorten by s × pitch factor each step — the calculator applies this decrement automatically at your chosen 400/600mm spacing.
Worked Example: 8m × 10m House at 35°
Complete Schedule Produced By One Calculation
- Pitch: 35.00° = 8.40:12 = 70.00% = 1 in 1.43, factor 1.2208, rise 700mm per metre
- Common rafter: effective run 3.981m (allowing 38mm ridge board) → line length 4.860m + 0.37m tail = 5.226m total timber
- Cuts: plumb cut 55.0°, seat cut 35.0°
- Heights: rise 2.801m above plate; with a 2.4m wall plate the apex reaches 5.201m
- Area: 80m² footprint → 105.6m² + overhangs → ≈126m² true sloped area
- Materials: ≈1,380 interlocking concrete tiles at 10% waste, ≈390m battens, 3 membrane rolls — all from the single input set above
Frequently Asked Questions
Which roof types does the all-in-one calculator support?
Symmetrical dual-pitch gable roofs, four-slope hipped roofs (with hip, valley and jack rafter geometry), and mono-pitch / lean-to extensions. Asymmetric dual-pitch roofs can be solved per-slope with the dedicated pitch calculator.
Do I measure the run or the span?
For gable and hip roofs the run is half the span (wall plate to ridge centreline). For a lean-to, the run is the full horizontal depth of the mono roof. In Rise & Run mode you can enter any directly measured run — a 1 metre level and tape check in the loft is the fastest site method.
Does the tile quantity include wastage?
Yes. The net quantity is the exact mathematical coverage; the gross quantity adds your chosen wastage allowance (default 10%, adjustable 0–30%) for cuts, breakages, verges and valleys per standard UK estimating practice under BS 5534.
Can I share or print a full calculation?
Yes. Copy Full Report places the entire multi-section schedule on your clipboard, Share Link encodes every input parameter into the URL, and Print Sheet produces a hard copy with every results section expanded for on-site use.
Is the apex height check a planning approval?
No. The 4.0m / 3.0m checks are indicative Permitted Development envelope guides only. Planning status depends on site constraints, conservation areas, and local authority policy — always confirm with your LPA before construction.
📚 Primary Technical Sources & British Standards
- BS 5534:2014+A2:2018: Code of practice for slating and tiling for pitched roofs and vertical cladding. British Standards Institution.
- BS 5250:2021: Management of moisture in buildings — Code of practice. British Standards Institution.
- BS 6229:2018: Flat roofs with continuously supported flexible waterproof coverings — Code of practice.
- NHBC Standards Chapter 7.2: Pitched Roofs — Minimum pitches, rafter timber sizing, batten gauges and fixing specifications.
- UK Manufacturer Technical Literature: Marley Technical Handbooks, BMI Redland Fixing Guides, CUPA Pizarras Slate Technical Manuals.
Last technical audit date: 17 August 2026.