What this area calculator does
This calculator gives the area of eleven common flat shapes: square, rectangle, triangle, circle, ellipse, parallelogram, rhombus, trapezoid, regular polygon, circular sector and ring. Pick the shape, type its dimensions and the area appears straight away, together with the perimeter and the other measures that go with it, such as the diagonal of a rectangle or the side of a rhombus.
It is useful for homework, but also for everyday jobs: how many square metres of tiles for a room, how much paint for a wall, how big a plot of land is, or how much fabric a round tablecloth needs. A drawing with the same letters as the input boxes shows what each dimension means.
Every length must be in the same unit. If you enter metres, the area comes out in square metres (m²).
How to use this calculator
- Choose a shape in the grid. The drawing changes to match it.
- Fill in the boxes. Each one is named after the letter on the drawing, for example radius (r) or height (h).
- Pick the length unit: millimetres, centimetres, metres, kilometres, inches or feet.
- Read the area, the perimeter and the extra measures. The result updates as you type, so there is no button to press.
When you change shape, the values that still make sense are kept. For a circle, a sector or a ring, the angle is in degrees. For a parallelogram or a trapezoid, the slanted sides are optional: leave them empty and you still get the area, add them and you also get the perimeter. The Share button copies a link that reopens the same shape and numbers.
The area formulas
These are the formulas used, with the letters shown on the drawings:
A = π × r² · A = π × a × b · A = D × d ÷ 2
A = (B + b) × h ÷ 2 · A = π × r² × θ ÷ 360 · A = π × (R² − r²)
- Square: side times itself. Rectangle: length times width.
- Triangle: base times height divided by two. The height must be perpendicular to the base.
- Parallelogram: base times height, not base times the slanted side.
- Rhombus: half the product of its two diagonals. Trapezoid: the average of the two bases times the height.
- Circle: pi times the radius squared. Ellipse: pi times its two semi-axes.
- Sector: the circle's area multiplied by the fraction θ ÷ 360. Ring: the outer disc minus the inner disc.
- Regular polygon: half the perimeter times the apothem, the distance from the centre to the middle of a side.
Worked examples
Example 1: tiling a rectangular living room
- Choose Rectangle and the metre unit. Enter L = 5.5 and l = 4.
- Area: 5.5 × 4 = 22 m². Perimeter: 2 × (5.5 + 4) = 19 m, useful for skirting boards.
- Add 10% for cuts and breakage: 22 × 1.1 = 24.2 m².
- A tile of 40 cm by 40 cm covers 0.16 m², so 24.2 ÷ 0.16 = 151.25, rounded up to 152 tiles.
22 m² of floor, about 152 tiles of 40 × 40 cm.
Example 2: a plot of land shaped like a trapezoid
- Choose Trapezoid and the metre unit. Enter B = 30, b = 18 and h = 20.
- Area: (30 + 18) × 20 ÷ 2 = 48 × 10 = 480 m².
- One hectare is 10,000 m², so the plot is 480 ÷ 10,000 = 0.048 ha.
- Enter the two slanted sides, for example 21 m and 22 m, to get the fencing length: 30 + 18 + 21 + 22 = 91 m.
480 m², or 0.048 ha, with 91 m of fence around it.
Key concepts
Area and perimeter
Area is the amount of surface inside a shape. Perimeter is the length of its outline. Doubling every side of a shape doubles its perimeter but multiplies its area by four, which is why a plot twice as wide is not simply twice the price.
Square units
An area is counted in squares: 1 m² is a square of 1 m by 1 m, which is 10,000 cm². To switch between units, convert the lengths first, or use the unit converter.
Height is not a side
In a triangle, a parallelogram or a trapezoid, the height is the straight distance between the base and the opposite side, drawn as a dashed line. It is shorter than the slanted sides, unless the shape has a right angle.
From area to volume
Many solids are a flat shape with a height: a cylinder is a circle with a height, a box is a rectangle with a height. Once you have the base area, the volume calculator gives the capacity, and the surface area calculator gives the material needed to cover it.
Tips and common mistakes
Practical tips
- For an irregular room, split it into rectangles and triangles, calculate each one and add the areas.
- To find the area of an L-shaped floor, subtract the missing rectangle from the large one.
- Add 5 to 10% to a tiled, painted or fabric area to cover cuts and waste.
- To work out a triangle from its three sides, use the triangle calculator.
Common mistakes
- Entering the diameter where the radius is asked: the radius is half of the diameter.
- Mixing units, such as a length in metres and a width in centimetres.
- Using the slanted side instead of the height in a parallelogram or a trapezoid.
- Forgetting that the result is in square units, not in the unit of the lengths.
Frequently asked questions
How do I find the area of a circle from its diameter?
Divide the diameter by two to get the radius, then use pi times the radius squared. A diameter of 6 m gives a radius of 3 m and an area of about 28.27 m².
What is the difference between a circle and a disc?
Strictly, the circle is the curved line and the disc is the surface inside it. In everyday language, and in this calculator, the area of a circle means the area of the disc.
Why does the ellipse perimeter have a ≈ sign?
No simple exact formula exists for it. The calculator uses Ramanujan's approximation, which is extremely close for usual ellipses.
How do I convert m² to hectares?
Divide by 10,000. A plot of 2,500 m² is 0.25 hectare. The unit converter handles other land units too.
Can I find the area of any polygon?
This tool handles regular polygons, where all sides are equal. For another polygon, cut it into rectangles and triangles and add their areas.
Does the calculator work with feet and inches?
Yes. Choose feet or inches as the unit and the area is given in ft² or in².