Construction & Engineering
Construction calculators turn the dimensions written on a sketch or a tape measure into the quantities you actually have to order. Builders, landscapers, self-builders and anyone pricing up a job use them before buying materials, because over-ordering costs money and under-ordering costs a second delivery. The Area Calculator works out the surface of rectangles, triangles, circles and combinations of them, which is the figure behind almost every quote: flooring, turf, paint, plaster, paving and roofing are all sold by area. Awkward rooms are easiest handled by splitting the plan into simple shapes and adding the results, and you can work in metric or imperial units to match whatever the supplier quotes in. The Concrete Calculator goes a step further into volume, taking the length, width and depth of a slab, footing or post hole and returning the amount of concrete needed, in cubic metres or yards along with an indication of the bags or mixer loads that represents. Depth is where estimates go wrong most often, so measure it in several places on uneven ground and use the largest figure. The usual sequence is to calculate area first, then apply the thickness to get volume. Both run in your browser with no sign-up.
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Concrete Calculator
Calculate concrete volume for slabs, footings, columns, walls and stairs in yards, cubic feet, cubic metres and bags.
Area Calculator
Calculate the area of eight common shapes and see the result converted into metric and imperial units.
The formula behind each of the eight shapes
A triangle can be entered three ways. With a base and a perpendicular height the area is half the base times the height. With three sides it uses Heron's formula: take the semi-perimeter s, equal to half the sum of the three sides, then the area is the square root of s times s minus a, times s minus b, times s minus c. With two sides and the angle between them the area is half of a times b times the sine of the included angle.
A circle is pi times the radius squared. An ellipse extends that to pi times the semi-major axis times the semi-minor axis. A trapezoid is half the sum of the two parallel sides multiplied by the perpendicular height. A circular sector is half the radius squared multiplied by the angle in radians, so an angle typed in degrees is converted first by multiplying by pi and dividing by 180.
Worked example: a trapezoidal garden bed
Add the parallel sides: 8 plus 5 gives 13. Halve that to get the average parallel width of 6.5 metres. Multiply by the height of 4 metres and the area is 26 square metres.
The conversions follow from fixed factors. One square metre is 10.7639 square feet, so 26 square metres is 279.86 square feet. One square yard is nine square feet, so the same area is 31.10 square yards. A hectare is 10,000 square metres, making this 0.0026 hectares, and an acre is 4,046.86 square metres, so the bed covers 0.00642 acres.
If instead the plot were a triangle with sides of 13, 14 and 15 metres, Heron's formula would give a semi-perimeter of 21, and the area would be the square root of 21 times 8 times 7 times 6. That product is 7,056, whose square root is exactly 84 square metres.
Getting a usable number for real materials
The height used for triangles, trapezoids and parallelograms is the perpendicular height, measured at a right angle to the base, not the length of a sloping side. Using a slanted edge by mistake inflates the area. For three-sided triangle entry the three lengths must satisfy the triangle inequality, meaning any two sides added together must exceed the third, or no such triangle exists.
Two results carry small approximations worth knowing. The perimeter of an ellipse has no exact elementary formula, so it is labelled as approximate. Pi-based results are irrational and are rounded for display. For ordering materials, treat the area as a minimum: add a waste allowance, typically around 10 per cent for tiles or turf and more for diagonal or patterned layouts, and round up to whole packs.