Conical and Turret Roof Calculator
Last reviewed How we calculate
Turrets, towers, gazebos and silos often have cone-shaped roofs. The shape is easy to describe but hard to estimate by eye, because a cone has much more surface than the circle it covers. This works out the area from the diameter and the height.
Cone-shaped roof area
Surface area, slope length and equivalent pitch for a cone-shaped turret, tower or gazebo roof.
This calculator needs JavaScript to work. The measurements below are the ones you would need to do the sum by hand.
Roof area
- Squares to order, with waste
- Slope length, eave to tip
- Equivalent pitch
- Roof angle
- Circumference at the eave For drip edge and starter.
The area is exact for a true cone. Turret roofs are usually covered with small units such as shingles, slate or shakes cut to taper, or with metal cut into tapered panels, and both take far more labor and waste than a flat roof face of the same area.
How the calculation works
The slope length of a cone, from the eave to the tip, is the square root of the radius squared plus the height squared. The roof area is pi times the radius times that slope length. The equivalent pitch is the height over the radius, times 12, so a cone can be compared with an ordinary roof.
A worked example
A turret roof 12 ft across at the eave and 10 ft high has a slope length of 11.66 ft and an area of about 219.8 sq ft. With 20 percent waste that is 2.64 squares. Its equivalent pitch is 20 in 12, about 59 degrees, and the eave is 37.7 ft round.
Why cones take so much waste
Every course on a cone is shorter than the one below it, so every piece is cut to a taper and very little of an offcut can be used again. Shingles, slate and shakes all work, and metal can be cut into tapered panels, but all of them take far more labor and material than a flat roof face of the same area.
Frequently asked questions
How do I find the height of a turret roof?
If you know its pitch, the height is the radius times the pitch over 12. Otherwise estimate it from the ground against known heights, such as the wall below or a window, and check it before ordering.
Can shingles go on a cone-shaped roof?
Yes, but each course has to be cut to a taper, and small cones are fiddly. Slate, wood shakes and metal cut into tapered panels are common alternatives.
How much waste should I allow for a cone?
More than for a flat roof face: 20 per cent is a sensible starting point, and small or steep cones can need more.