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Area Calculator
Calculate area for 8 common shapes with unit conversion
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Length Unit
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Triangle Method
Dimensions
Shape Diagram
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Enter dimensions above and press Calculate
Results and unit conversions will appear here
Calculating…
Area
= m² / ft²
Formula Used
Area in All Units
mm²
cm²
m²
ft²
yd²
acre
km²
in²
hectare
Additional Properties
Worked Example
Formula
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The formula behind each of the eight shapes
Each shape uses its own standard formula, and the tool shows which one it applied. A square is side multiplied by itself; a rectangle is length multiplied by width; a parallelogram is base multiplied by perpendicular height.
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.
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
Consider a raised bed shaped as a trapezoid, with parallel sides of 8 metres and 5 metres and a perpendicular height of 4 metres between them.
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.
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
Mix your units and the answer will be wrong in a way that looks plausible. Every dimension for a given shape must be entered in the same unit, so convert a measurement taken in centimetres before typing it alongside one taken in metres. Angles are the exception: the included angle for a triangle and the sector angle are entered in degrees and converted internally.
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.
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.
Frequently Asked Questions
Eight in total: square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram and circular sector. Each one asks only for the dimensions it needs, such as a radius for a circle or the two parallel sides and height for a trapezoid, and the tool displays the formula it applied alongside the answer.
Yes. Choose the triangle shape and the three-side method, which uses Heron's formula. Enter sides of 13, 14 and 15 and the semi-perimeter is 21, giving an area of 84 square units. The three lengths must form a valid triangle, so any two added together have to exceed the third.
You do not need to. Every calculation is converted automatically into square metres, square centimetres, square inches, square feet, square yards, hectares and acres. A hectare is 10,000 square metres and an acre is 4,046.86 square metres, so small areas appear as very small decimal fractions of each.
Always the perpendicular height, measured at a right angle from the base to the opposite side or vertex. A sloping edge is longer than the perpendicular height, so using it produces an area that is too large. If you only know the slope and an angle, use the two-sides-and-included-angle method instead.
The area is the finished surface only, with no allowance for cuts, breakages or overlaps. A common rule is to add about 10 per cent for straightforward tiling, flooring or turf, and 15 to 20 per cent for diagonal layouts, patterned tiles or awkward shapes, then round up to whole packs or rolls.