Area calculator
Pick a shape and enter its measurements. Get the area of a rectangle, square, triangle, circle, trapezoid, parallelogram or ellipse, or the surface area of a cube, box, cylinder, cone, sphere or pyramid. The formula is worked out with your numbers, and the answer is shown in square units, acres and hectares, with the perimeter where the shape gives one.
Answers update as you type. A triangle works from its base and height or its three sides
Use the same unit for every measurement.
- Area
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A = l × w
Enter each measurement to see the area.
In other units
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How to find area
Area is the space inside a flat shape, measured in square units such as square feet (ft²) or square meters (m²). For a rectangle, multiply length × width. A triangle is half of a rectangle with the same base and height, and a parallelogram is a rectangle with one end cut off and moved to the other, so it’s base × height too.
Use one unit for every measurement, and the area comes out in that unit squared. Square units grow fast: 1 square foot is 144 square inches, 1 square yard is 9 square feet, and an acre is 43,560 square feet.
For worked examples of each formula, read how to find volume and area.
Area formulas
The formula for each flat shape the calculator covers.
| Shape | Formula | What the letters mean |
|---|---|---|
| Rectangle | A = l × w | Length times width. A square is the same with both equal: A = a². |
| Triangle (Base and height) | A = b × h ÷ 2 | The height is measured at a right angle to the base, not along a side. |
| Triangle (Three sides) | A = √(s × (s − a) × (s − b) × (s − c)) | Heron’s formula, for when you know the three sides. s is half the perimeter. |
| Circle | A = π × r² | r is the radius, half the diameter. |
| Trapezoid | A = (a + b) ÷ 2 × h | a and b are the two parallel sides; h is the distance between them. |
| Parallelogram | A = b × h | The height is at a right angle to the base, not the slanted side. |
| Ellipse | A = π × a × b | a and b are half the longest and shortest widths. |
Area of a circle
Multiply π by the radius squared. A circle 10 in across has a radius of 5 in, so its area is π × 5² = 78.54 square inches, and the distance around it is 31.42 in. If you measured across the circle, choose Diameter: squaring the diameter instead of the radius is the most common mistake, and gives an answer four times too big.
Area of a triangle
With the base and the height, the area is base × height ÷ 2. When you only know the three sides, choose Three sides and the calculator uses Heron’s formula: a triangle with sides 3, 4 and 5 has s = 6 and an area of √(6 × 3 × 2 × 1) = 6. Three lengths only make a triangle when the longest is shorter than the other two together.
Area of a trapezoid
Average the two parallel sides, then multiply by the height between them. A trapezoid with parallel sides of 6 and 10 and a height of 4 has an area of (6 + 10) ÷ 2 × 4 = 32. Outside North America the shape is usually called a trapezium.
Surface area formulas
The total area of every face of a solid, as if you unfolded it flat.
| Shape | Formula | What the letters mean |
|---|---|---|
| Cube | A = 6 × a² | Six square faces. |
| Rectangular box | A = 2 × (l × w + l × h + w × h) | Three pairs of rectangles: top and bottom, front and back, the two ends. |
| Cylinder | A = 2 × π × r² + 2 × π × r × h | Two circles plus the side, which unrolls into a rectangle 2 × π × r long and h high. |
| Cone | A = π × r² + π × r × s | The base plus the side. s is the slant height, √(r² + h²). |
| Sphere | A = 4 × π × r² | Exactly four times the area of a circle with the same radius. |
| Square pyramid | A = a² + 2 × a × s | The square base plus four triangles. s is the slant height, √((a ÷ 2)² + h²). |
Surface area
Surface area adds up the area of every face, which is what you need for paint, wrapping or sheet material. A cylinder 3 cm in radius and 10 cm high has two circles of π × 3² and a side of 2 × π × 3 × 10, for 245.04 cm² in total. For a cone or pyramid the calculator works out the slant height from the height you enter, so you don’t have to measure along the slope.
For the space inside a solid, use the volume calculator.
Heron’s formula as given by Wolfram MathWorld. Conversion factors from NIST’s Guide to the SI, Appendix B: an acre is 43,560 square feet and a hectare 10,000 square meters.
Questions about area
How do you find the area of a circle from the diameter?
Halve the diameter to get the radius, then multiply π by the radius squared. A circle 8 ft across has a radius of 4 ft and an area of π × 4² = 50.27 square feet. You can also use π × d² ÷ 4, which gives the same answer.
How do I find the area of a triangle without the height?
If you know all three sides, use Heron’s formula: choose Triangle, then Three sides. If you know two sides and the angle between them, the area is a × b × sin(C) ÷ 2. For a right triangle, the two shorter sides are the base and the height.
How do I work out the square feet of a room?
Measure the length and the width in feet and multiply them: a room 12 ft by 15 ft is 180 square feet. For an L-shaped room, split it into two rectangles, find each area and add them. Buy about 10% more flooring than the area to allow for cuts.
How many square feet are in an acre?
An acre is 43,560 square feet, or about 4,047 square meters. A hectare is 10,000 square meters, about 2.47 acres. Measure a plot in feet or meters and the calculator shows the acres and hectares under In other units.
What’s the difference between area and surface area?
Area measures a flat shape. Surface area is the total area of all the faces of a solid, such as the six faces of a box. Both are in square units. The space inside a solid is its volume, in cubic units.
How do I find the area of an irregular shape?
Split it into shapes the calculator covers, such as rectangles, triangles and half circles, find the area of each and add them. For a shape with a curved edge, many small rectangles or triangles give a close estimate.