Roof Pitch & Area Calculator

Calculate roof pitch angle, roof area, and total roofing material needed for any gable, hip, or shed roof. Convert between pitch ratio, degrees, and percentage gradient.

The roof pitch and area calculator determines roof slope, rise, run, rafter length, and total roof surface area — the essential quantities needed for ordering roofing materials, calculating structural loads, and planning drainage. Roof pitch is expressed as a ratio of rise to run (e.g. 4:12 means 4 inches of rise for every 12 inches of horizontal run) in the US, or as an angle in degrees in the UK and Europe. Pitch affects everything from the minimum required tile overlap to the structural rafter size: low-pitch roofs (below 15°) require special interlocking tiles or membranes because standard plain tiles cannot shed water fast enough at shallow angles; steep roofs (above 45°) require shorter tile batten spacing to prevent tiles sliding.

Rafter length is always longer than the horizontal run due to the hypotenuse relationship — a 4m span on a 30° pitch roof has rafters approximately 4.6m long. Multiplying rafter length by the roof width and number of rafters per side gives the total roof deck area, which is then used to calculate the number of tiles, slate, or metal sheets needed.

Enter the roof span (total width from wall to wall) or half-span (from wall to ridge) and the ridge height (vertical rise from wall plate to ridge).
The calculator returns pitch angle (degrees), pitch ratio (rise:12 or rise:run), rafter length, and hip/valley lengths for hipped roofs.
Enter the building footprint dimensions (length × width) to calculate total roof deck area in m² or sq ft, accounting for the pitch multiplier (area is always larger than footprint due to slope).
Select roof shape (gable, hipped, mono-pitch, or shed) for accurate area calculation of non-rectangular roof plans.
Read the recommended tile coverage rate (tiles per m² or squares per 100 sq ft) to calculate the total tile order including the standard 10% breakage allowance.

Roof pitch and area formulas

Pitch angle (°) = arctan(Rise ÷ Run)

Pitch ratio = Rise : Run (US: expressed as Rise : 12; UK: as degrees or as a fraction)

Rafter length = √(Rise² + Run²) (Pythagorean theorem for simple gable)

Pitch multiplier = 1 ÷ cos(pitch angle) — multiply footprint area by this factor to get sloped roof area.

Roof deck area (gable) = (Building length × Run × 2) × Pitch multiplier

Common pitch multipliers: 15° = 1.035; 20° = 1.064; 25° = 1.103; 30° = 1.155; 35° = 1.221; 40° = 1.305; 45° = 1.414.

Example: 8m wide building, 2.5m rise from wall plate to ridge. Run = 4m. Pitch = arctan(2.5÷4) = 32°. Rafter length = √(2.5²+4²) = √22.25 = 4.72m. Pitch multiplier = 1 ÷ cos(32°) = 1.179. Roof deck area (10m long building) = 10 × 4 × 2 × 1.179 = 94.3 m².

Reading your roof pitch and area results

Pitch ranges and recommended applications

Pitch angle guidance: below 10° (17.5:100) = flat or near-flat roof — requires single-ply membrane, EPDM rubber, or built-up felt; 10–20° = low pitch — requires interlocking concrete tiles (min 12.5°), not plain clay tiles; 20–35° = medium pitch — suitable for most tile types; 35–45° = steep pitch — premium look, heavier structural loading, higher wind resistance; above 45° = very steep — traditional slate, thatch, or decorative tiles only. Minimum tile pitches: concrete interlocking tiles = 12.5°; clay plain tiles = 35°; natural slate = 20° (25° in exposed locations); clay Roman/pantile = 22.5°. Tile coverage for common types: plain clay tiles ≈ 60–65 tiles/m²; concrete interlocking tiles ≈ 8–16 tiles/m²; natural slate ≈ 20–28 slates/m².

Construction tips and best practices

Always verify rafter length on site before cutting — slight variations in wall plate level, ridge board position, or building squareness mean calculated lengths are a starting point, not a cut list.
Add 5–10% to tile quantities for cutting at verges, hips, valleys, and around chimneys — more for complex hip roofs with multiple intersections.
For flat/low-pitch roofs: a minimum 1:80 fall (0.72°) is required for surface drainage even on "flat" roofs to prevent ponding — BS 6229 requires 1:40 fall design minimum.
Hip roofs have approximately 30–40% more complex cutting and labour than gable roofs — factor this into budget and time estimates.
Batten spacing must match the tile manufacturer's specified gauge (the exposed tile length) — this is calculated as (rafter length − top and bottom tile overlap) ÷ number of tile courses.

The Louvre pyramid in Paris has a roof pitch of approximately 51.7° — designed to echo the proportions of the Great Pyramid of Giza (51.8°).
Traditional English cottage roofs typically use a 45° pitch (1:1 rise:run) — the steepest practical angle before structural costs increase significantly.
A typical 3-bedroom UK semi-detached house has a roof deck area of approximately 75–100 m² depending on pitch — requiring around 5,000–7,000 plain clay tiles or 600–1,400 concrete interlocking tiles.
Wind uplift force increases with the square of wind speed: a 100 km/h wind exerts approximately 4× more uplift than a 50 km/h wind — steep pitches with good sarking (underlay) and batten fixing resist wind damage significantly better than under-fixed shallow pitches.

Common mistakes to avoid

Using the footprint area as the roof deck area — always multiply by the pitch multiplier; even a 20° pitch adds 6.4% to the area, and a 35° pitch adds 22.1%.
Calculating rafter length from the span (full width) rather than the run (half-width) — the run is half the span for a symmetrical gable; using span directly doubles the rafter length calculation.
Ordering tiles without checking the minimum pitch requirement — fitting standard clay plain tiles on a 20° pitch will cause leaks; always match tile type to pitch.
Forgetting to include overhangs (eaves and verges) in the rafter length and area calculation — a 300mm eave adds 0.3m to each rafter and approximately 2.4 m² to a 10m-long gable roof.

Roof design in the UK is subject to Building Regulations Approved Document A (Structure) and must comply with BS 5534 (Code of Practice for Slating and Tiling) for tile and slate roofs. Structural calculations for new roofs and major alterations typically require a structural engineer's input and may require Building Regulations approval. Planning permission may be required for changes that alter the roofline. This calculator provides geometric estimates for planning and material ordering — it does not constitute a structural design, planning application, or compliance assessment. Always consult a qualified roofing contractor or structural engineer for building work.

Frequently Asked Questions

What is roof pitch?

Roof pitch is the steepness of a roof expressed as a ratio of rise over run. A 4/12 pitch means the roof rises 4 inches for every 12 inches of horizontal run.

How do I convert roof pitch to degrees?

Use the formula: angle = arctan(rise/run). A 4/12 pitch = arctan(4/12) ≈ 18.4°. A 12/12 pitch = arctan(1) = 45°.

How do I calculate roof area?

Calculate the footprint area (length × width of the house), then multiply by the roof pitch multiplier: Area = footprint × √(rise² + run²) / run. Add 10–15% for overlaps and waste.

What is a good roof pitch?

A pitch of 4/12 to 6/12 (18°–27°) is standard for residential roofs. Steeper pitches (above 6/12) shed water and snow better but cost more to build. Pitches below 2/12 require special low-slope roofing materials.

What is the difference between a gable and a hip roof?

A gable roof has two sloping sides meeting at a ridge, with triangular gable ends. A hip roof has four sloping sides meeting at a ridge, with no vertical gable ends — it's more complex to calculate but more wind-resistant.