Calculating a hip roof: area, coefficients and what it will cost
Calculating the area of a four-slope roof is easier than it seems: the number of slopes doesn’t affect it at all. But it does affect the money, and strongly — for a different reason.
The area of any pitched roof with the same pitch equals the projected area divided by the cosine of the angle. For a 10×12 m house with 0.5 m overhangs and a 30° pitch that is 165 m² — for both the hip and the gable roof. The hip roof costs about 11% more, not because of the area but because of the four sloping edges: tiles are cut along them and accessories run along them.
What a hip roof is
A hip roof has four slopes. Instead of the two vertical gables of a gable roof, the ends of the house are also covered by slopes. These end slopes are called hips.
The bold line in the middle is the ridge. The four lines to the corners are the sloping edges, also called hips. The two large slopes are trapezoids, the two end slopes (hips) are triangles.
The ridge of a hip roof is shorter than the house. On a rectangular house with the same pitch on all slopes its length equals the difference between the sides: on a 10×12 m house the ridge is only 2 metres. The closer the house is to a square, the shorter the ridge; on a square house it shrinks to a point and the roof becomes a pyramid roof.
How the area is calculated
Here is the main time-saver: the number of slopes does not affect the roof area. If all slopes have the same pitch, the area equals the projected area divided by the cosine of the pitch angle. Gable, hip, pyramid — with an equal pitch on the same house the area will be the same.
The slope is the hypotenuse. The dotted line is the height, the bottom line is the slope’s projection onto the ground. The steeper the pitch, the longer the slope for the same projection, and the more material.
The projection is not the footprint but the dimensions of the house including overhangs. An overhang is usually 0.4–0.6 m on each side: it carries water away from the walls and foundation. On a 10×12 m house, 0.5 m overhangs add a metre to each side, and the projection becomes 11×13 = 143 m². That is already 19% more than the footprint — overhangs are the thing most often forgotten.
Pitch coefficients
So you don’t have to work out cosines, here are ready multipliers. Multiply the projected area by them.
| Pitch | Multiplier | Area with a 143 m² projection |
|---|---|---|
| 15° | 1,035 | 148 m² |
| 20° | 1,064 | 152 m² |
| 25° | 1,103 | 158 m² |
| 30° | 1,155 | 165 m² |
| 35° | 1,221 | 175 m² |
| 40° | 1,305 | 187 m² |
| 45° | 1,414 | 202 m² |
The spread between a shallow and a steep roof is more than 50 m² on the same house. So it’s worth getting the pitch from the designer rather than guessing by eye: a 10° error costs about 15% of the estimate.
Enter the resulting square metres, choose the “hip” shape and see the calculation based on open price lists. No call and no phone number.
Calculate a roof →Example: a 10×12 metre house
- House dimensions 10×12 m, overhangs of 0.5 m. Projection: 11×13 = 143 m².
- Pitch 30°, multiplier 1.155. Roof area: 143 × 1.155 = 165 m².
- Cutting waste on a hip roof is about 10%. You need material for 182 m².
If you don’t know the pitch yet, the calculator has a “I only know the house dimensions” mode: it multiplies the footprint by 1.5. The coefficient is generous because the pitch and overhangs are unknown — in our example it gives 180 m² instead of 165. The difference is about 9% on the high side. If you know the area exactly, enter it and the calculation will be closer to reality.
Why a hip roof costs more than a gable roof
Same area, different bill. Let’s compare the same house with 180 m² of roofing under KAZROOF Standart composite tiles at 7,960 ₸/m².
| Item | Gable | Hip |
|---|---|---|
| Area incl. waste | 193 m² (+7%) | 198 m² (+10%) |
| Tiles | 1 536 280 ₸ | 1 576 080 ₸ |
| Accessories | 276 530 ₸ (18%) | 441 302 ₸ (28%) |
| Materials total | 1 812 810 ₸ | 2 017 382 ₸ |
| Installation rate | 5,500 ₸/m² | 6,500 ₸/m² |
The difference in materials is 204,572 ₸, about 11%. With installation the gap grows: the rate is a thousand higher per square metre, which is roughly another 226 thousand on the same house.
The reason is the four sloping edges. Along each of them the tiles are cut at an angle, on both sides of the edge — hence 10% waste instead of 7%. And each edge has to be covered with an accessory, like the ridge. Instead of four edges a gable roof has two straight gables, where cutting runs in a straight line and accessories are simpler.
What else to know before deciding
- A mansard is almost ruled out. The hips cut off the ends of the attic, and there is nowhere to put vertical windows in the gables. Light will come only through roof windows in the slopes — they cost more than ordinary ones and require careful waterproofing.
- Snow and wind. Four slopes handle wind loads better — there is nothing to blow off, no vertical surfaces. For open plots outside the city this is a real advantage.
- Valleys cost more than edges. If a bay window or garage is attached to a hip roof, valleys appear — internal joints where water from two slopes runs down. A leak almost always starts there, and you must not save on this junction.
- Check that it really is a hip roof. A half-hip (Dutch) roof — with shortened hips and part of a gable left — is calculated closer to a complex roof than to a simple four-slope one.
In the calculator you can switch the shape and see what a gable and a hip roof cost for the same area. And view the roof in 3D at the same time.
Open the calculator →Frequently asked questions
The roof area equals the projected area divided by the cosine of the pitch angle. The projection is the house dimensions plus overhangs. For a 10×12 m house with 0.5 m overhangs the projection is 11×13 = 143 m²; at a 30° pitch the roof area is 143 × 1.155 = 165 m². The formula is the same as for a gable roof: the number of slopes doesn’t affect the area.
On the same house with 180 m² of roofing, a hip roof costs 2,017,382 ₸ versus 1,812,810 ₸ for a gable roof under KAZROOF Standart composite tiles. The difference is about 11%. It comes from more cutting (10% versus 7%) and accessories (28% versus 18% of the tile cost).
It’s not the area that gets more expensive but the joints. A hip roof has four sloping edges, along which every row of tiles is cut at an angle on both sides, and all four edges have to be covered with accessories. A gable roof has two straight gables instead.
The waste and accessory coefficients, installation rates and tile price are the same ones the calculator on the site uses. A calculation by area is an estimate: it does not account for the individual junctions, valleys and abutments of your project. The engineer confirms the exact bill of materials from the drawing.