Calculate the area of any shape instantly. Formulas shown with every result for square, rectangle, triangle, circle and more.
Area is the measure of the two-dimensional space enclosed within a shape, expressed in square units. Calculating area accurately is fundamental in construction, land measurement, flooring, painting, gardening, engineering and mathematics. Each geometric shape has its own specific formula derived from its properties. Our area calculator handles eight common shapes with the formula displayed alongside every result so you can understand and verify the calculation.
The area formulas for the eight shapes in our calculator cover the vast majority of real-world area calculation needs. Square: A = s^2 where s is the side length. Rectangle: A = l x w where l is length and w is width. Triangle: A = 0.5 x b x h where b is base and h is the perpendicular height from that base to the opposite vertex. Circle: A = pi x r^2 where r is radius (pi = 3.14159). Trapezoid: A = 0.5 x (b1 + b2) x h where b1 and b2 are the parallel sides and h is the perpendicular distance between them. Parallelogram: A = b x h where b is base and h is perpendicular height (not the slant side). Ellipse: A = pi x a x b where a is the semi-major axis and b is the semi-minor axis. Sector (pie slice): A = 0.5 x r^2 x theta where theta is the central angle in radians. Use our percentage calculator to find what percentage one area is of another, and our square root calculator when working with areas and side lengths together (since side = square root of area for a square).
| Shape | Formula | Variables | Example (result) |
|---|---|---|---|
| Square | A = s^2 | s = side length | s=5: A = 25 sq units |
| Rectangle | A = l x w | l = length, w = width | 8x5: A = 40 sq units |
| Triangle | A = 0.5 x b x h | b = base, h = height | b=10 h=6: A = 30 sq units |
| Circle | A = pi x r^2 | r = radius | r=7: A = 153.94 sq units |
| Trapezoid | A = 0.5(b1+b2)xh | b1,b2 = parallel sides | 8+12, h=5: A = 50 sq units |
| Parallelogram | A = b x h | b = base, h = perp. height | b=9 h=4: A = 36 sq units |
| Ellipse | A = pi x a x b | a,b = semi-axes | a=6 b=4: A = 75.40 sq units |
| Sector | A = 0.5 x r^2 x theta | r = radius, theta = radians | r=5, 90deg: A = 19.63 sq units |
The base-times-height formula requires knowing the perpendicular height, which is not always directly measurable. When you know all three side lengths but not the height, use Heron's formula: first calculate the semi-perimeter s = (a + b + c) / 2, then Area = square root of (s x (s-a) x (s-b) x (s-c)). Example: a triangle with sides 5, 7 and 8 has s = 10, and Area = sqrt(10 x 5 x 3 x 2) = sqrt(300) = 17.32 square units. When you know two sides and the included angle, use the formula: Area = 0.5 x a x b x sin(C) where C is the angle between sides a and b. All three methods give the same result for any given triangle. Use our square root calculator when applying Heron's formula manually, and our ratio calculator for scaling triangle dimensions proportionally.
Students and professionals frequently confuse circle area and circumference. Circumference measures the distance around the outside of a circle (C = 2 x pi x r or pi x diameter) and is a linear measurement in regular units. Area measures the space inside the circle (A = pi x r^2) and is a square measurement. A circle with radius 5 has a circumference of 31.42 units but an area of 78.54 square units. Doubling the radius quadruples the area (because r is squared) but only doubles the circumference. This is why a pizza with double the radius gives four times the area, not twice — a fact that has practical relevance for anyone comparing differently-sized circular items by price.
Area conversions are more complex than linear conversions because the conversion factor must be squared. Converting 1 foot to metres is x0.3048, but converting 1 square foot to square metres is x(0.3048^2) = x0.0929 — not simply x0.3048. This catches many people out. One acre equals 43,560 square feet or 4,047 square metres. One hectare equals 10,000 square metres or 2.471 acres. One square kilometre equals 100 hectares or 247.1 acres. One square mile equals 640 acres or 258.999 hectares. For land measurements, real estate and agricultural applications, our area calculator supports multiple input units so you can enter dimensions in their natural unit without manual conversion.
| From | To sq metres | To sq feet | To acres | To hectares |
|---|---|---|---|---|
| 1 sq foot | 0.0929 | 1 | 0.000023 | 0.0000093 |
| 1 sq metre | 1 | 10.764 | 0.000247 | 0.0001 |
| 1 sq yard | 0.836 | 9 | 0.000207 | 0.0000836 |
| 1 acre | 4,047 | 43,560 | 1 | 0.4047 |
| 1 hectare | 10,000 | 107,639 | 2.471 | 1 |
| 1 sq km | 1,000,000 | 10,763,910 | 247.1 | 100 |
Flooring and tiling: measure room length and width in feet, calculate area, add 10% for waste and cuts. A 12ft x 15ft room needs 180 sq ft of flooring plus 18 sq ft waste allowance = 198 sq ft. Paint coverage: one gallon of paint typically covers 350-400 sq ft with one coat. A room with four walls each 12ft wide and 9ft tall has total wall area of 432 sq ft — approximately 1.1-1.2 gallons per coat. Garden lawn: measure in metres. A 10m x 15m lawn is 150 sq metres. Most grass seed bags state coverage in sq metres. Land purchase: agents list land in acres. Multiply acres by 43,560 to get sq ft or by 4,047 to get sq metres. A 0.25 acre plot is 10,890 sq ft or just over 1,000 sq metres. Our unit converter handles any additional measurement conversions you need alongside area calculations.
Real-world spaces are rarely perfect geometric shapes. An L-shaped room, an irregular garden, or an oddly-shaped plot of land all require breaking the shape down into regular components. The standard approach is to divide the irregular shape into rectangles, triangles and/or other known shapes, calculate the area of each component, then add them together. For an L-shaped room, divide it into two rectangles, calculate each, and sum. For an irregular polygon where you know the coordinates of each vertex, use the Shoelace theorem: Area = 0.5 x absolute value of the sum of (x_i x y_(i+1) minus x_(i+1) x y_i) for all vertices in order. This formula works for any polygon regardless of the number of sides or complexity of shape, provided you know the coordinate positions of each corner. Use our fraction calculator if your measurements involve fractional units.
Real estate and land measurement use a specific vocabulary for area that differs from standard geometric units. In the US, residential lot sizes are typically expressed in square feet for smaller urban and suburban lots, or in acres for larger suburban, rural and agricultural plots. One acre is exactly 43,560 square feet or 4,047 square metres — a size roughly equivalent to a standard American football field minus the end zones. Commercial and industrial real estate is typically measured in square feet for individual units or acres for larger parcels. Agricultural land in the US is measured in acres; internationally in hectares (1 hectare = 10,000 square metres = 2.471 acres). Floor area ratio (FAR) or floor space index (FSI) divides the total built floor area by the land area to express development density — a FAR of 2.0 means total floor area across all floors equals twice the land area. Understanding area in these real-world contexts makes our area calculator directly applicable to property evaluation, renovation planning and land purchase decisions. Use our percentage calculator to calculate what percentage of a plot is built upon versus open space, or to find the price per square foot of any property. Our unit converter handles acre-to-square-foot and hectare-to-square-metre conversions for any land measurement you need alongside area calculations.
Area is a two-dimensional measurement (length x width), while volume adds a third dimension (length x width x height). Knowing the area of a shape is often the first step in calculating the volume of a corresponding three-dimensional solid. A rectangle with area 20 sq ft extruded to a depth of 8 ft becomes a rectangular box with volume 160 cubic feet. A circle with area 78.54 sq ft is the cross-section of a cylinder — multiply by the cylinder's height to get volume. This relationship is practical in construction: calculating the volume of concrete needed for a rectangular slab requires the slab area multiplied by its thickness. Calculating the volume of water in a circular pond requires the pond's circular area multiplied by its average depth. The area formula is always the foundation of the volume calculation for any shape with a consistent cross-section. Use our square root calculator when working backwards from area to find a dimension, and our fraction calculator when your measurements involve fractional units.