Roof area calculator with pitch

Enter the house size and the pitch to get the true roof area, the pitch factor, the ridge, hips or barges and the spouting run — the numbers a re-roof quote is built on.

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Roof area calculator

How to work out a roof’s real area

A roof is bigger than the floor it covers. Measure the roof in plan (the house plus the eave overhang all round), then divide by the cosine of the pitch — the pitch factor. For any roof where every plane has the same pitch, gable or hip, that one step gives the true sloped area:

True roof area = plan area ÷ cos(pitch)

A 14 × 9 m house is 126 m² in plan. At 25° the factor is 1.103, so the roof is 139.0 m² — 13 m² more than the floor. Price the iron, underlay and labour on the plan area and you’re 10% short before you’ve allowed any waste.

Pitch factor table

Pitch	Pitch factor	Every 100 m² of plan is
5°	1.004	100.4 m²
10°	1.015	101.5 m²
15°	1.035	103.5 m²
20°	1.064	106.4 m²
22.5°	1.082	108.2 m²
25°	1.103	110.3 m²
27.5°	1.127	112.7 m²
30°	1.155	115.5 m²
35°	1.221	122.1 m²
40°	1.305	130.5 m²
45°	1.414	141.4 m²

Plain trigonometry (1 ÷ cos of the pitch), so it holds for any roofing material.

Ridges, hips, barges and spouting

Rafter (eave to ridge) = half the roof width ÷ cos(pitch); the rise = half the width × tan(pitch).
Gable roof: the ridge runs the full length; four barges each the rafter length; spouting along both long sides.
Hip roof (equal pitch all round): ridge = length − width; four hips, each √(2 × (width÷2)² + rise²); spouting all the way round.

Valleys, dormers, L- and T-shapes and roofs at different pitches break the simple formulas. That’s what Toolie’s Roof Designer is for: type an L, draw the outline or trace an aerial, and it solves every plane — true area, ridge, hips, valleys, barges, aprons and gutters — then prices the re-roof on it.

Toolie Roof Designer solving an L-shaped hip roof: plan 174 m2, true 192 m2, hips, valleys and ridge

Before you order sheets

Check the minimum pitch for the profile in the NZ Metal Roof and Wall Cladding Code of Practice and the manufacturer’s literature — low-pitch roofs need the right profile and laps.
Order by the run, not the area: sheets are cut to length per plane, and hips and valleys add cutting waste.
Corrosion zone: coastal sites change the coating and fixings — Toolie reads it from the site address.
Consent: replacing roof cladding with a comparable material is generally exempt work under Building Act Schedule 1 (check the conditions); a heavier roof or a structural change can need consent. See the NZ Building Code guide.

Common questions

How do I calculate roof area from the floor area?

Take the roof's plan area (the house plus the eave overhang all round) and divide by the cosine of the roof pitch. A 126 m2 plan at 25 degrees is 126 / 0.906 = 139.0 m2 of roof.

What is a roof pitch factor?

It is 1 divided by the cosine of the pitch: the number you multiply the plan area by to get the sloped area. It is 1.035 at 15 degrees, 1.103 at 25 degrees, 1.155 at 30 degrees and 1.305 at 40 degrees.

Is a hip roof bigger than a gable roof?

Not in area if both have the same pitch over the same plan: the true area is plan area divided by cos(pitch) either way. A hip roof has more hip and spouting length and more sheet cutting, so it costs more to build.

How long is a hip rafter?

On an equal-pitch hip roof each hip is the square root of 2 times (half the width) squared, plus the rise squared. For a 9 m wide roof at 25 degrees that is about 6.70 m.

Does this work for an L-shaped roof?

Not exactly. Valleys and different-length wings break the simple formulas. Toolie's Roof Designer solves L-shapes, drawn outlines and aerial traces plane by plane.

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