The following are calculators for the area of seven common shapes. Fill in the fields for the shape you need and click Calculate. Each dimension can use its own unit; the result is shown in the units you enter and can be converted to acres and every other supported unit.
The area calculator computes the area of the seven most common two-dimensional shapes — the rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram — from the dimensions you enter. Each shape has its own dedicated calculator above, so you simply fill in the fields for the figure you are working with and click Calculate. Every dimension can use its own unit (feet, yards, inches, miles, meters, kilometers, or centimeters), and the result is shown in the unit you enter along with an instant conversion to acres and every other supported unit. Whether you are measuring a room, a plot of land, a garden bed, a piece of fabric, or a circular table, this tool gives fast, accurate answers.
Area is one of the most useful measurements in everyday life and in nearly every trade. It tells you how much carpet or tile to buy, how much paint a wall needs, how much fertilizer a lawn requires, and how large a parcel of land is. Because different shapes use different formulas, having all of them in one place — with automatic unit conversion — removes the guesswork and the arithmetic.
Area is the amount of two-dimensional space a flat shape occupies, measured in square units. If a surface is one meter long and one meter wide, it has an area of one square meter (1 m²). Because area is a two-dimensional quantity, it always scales with the square of length: double every dimension of a shape and its area increases fourfold, not twofold. This square-law relationship is why unit conversions for area involve larger factors than you might expect — there are 10,000 square centimeters in a single square meter, not 100.
Each calculator on this page uses the standard, textbook formula for its shape. Here is what each one computes and why.
A rectangle has four right angles, with opposite sides equal. Its area is simply the length times the width: Area = l × w. A square is a special rectangle where length and width are equal, so its area is the side squared. This is the most common area calculation of all — rooms, walls, sheets of material, screens, and building footprints are usually rectangles.
This calculator finds a triangle's area from the lengths of its three sides using Heron's formula. First it computes the semi-perimeter, s = (a + b + c) / 2, then the area as Area = √[s(s − a)(s − b)(s − c)]. Heron's formula is powerful because it needs only the three side lengths — no angles or height required. (When you know the base and the perpendicular height instead, the area is simply ½ × base × height.) The three sides must satisfy the triangle inequality — each side shorter than the sum of the other two — or no triangle exists.
A trapezoid (called a trapezium in British English) has one pair of parallel sides, called the bases (b1 and b2), separated by a perpendicular height h. Its area is the average of the two bases times the height: Area = ½ × (b1 + b2) × h. Trapezoids appear in land parcels, roof cross-sections, and many structural shapes.
A circle is defined by its radius r, the distance from the center to the edge. Its area is Area = π × r², where π (pi) is approximately 3.14159. If you know the diameter instead, halve it to get the radius. Circles describe wheels, pipes, tanks, plates, and countless round objects.
A sector is a "pie slice" of a circle — the region between two radii and the arc between them. Its area depends on the central angle A. When the angle is measured in degrees, Area = A / 360 × π × r², because the sector is that fraction of the full circle. When the angle is in radians, the formula simplifies to Area = ½ × r² × A. This calculator accepts either degrees or radians.
An ellipse is a stretched circle with two perpendicular semi-axes: the semi-major axis a (the longer one) and the semi-minor axis b (the shorter one). Its area is Area = π × a × b. When a and b are equal, the ellipse becomes a circle and the formula reduces to πr². Note that the calculator asks for the semi-axes — the distances from the center to the edge — not the full widths.
A parallelogram has two pairs of parallel sides. Its area is the base times the perpendicular height (not the slanted side length): Area = b × h. The height must be measured at a right angle to the base. A rectangle is a special parallelogram with right angles.
Because area is a squared quantity, its units are squared too. This calculator supports seven linear units — inches, feet, yards, miles, centimeters, meters, and kilometers — and returns the area in the square of whichever unit you choose, plus a conversion to acres. A few key equivalences are worth remembering:
The calculator handles all of these conversions automatically. Enter your measurements in any supported unit — you can even mix units within a single shape — and use the "Show result in other units" panel to see the area expressed in acres, square feet, square meters, and more.
For a simple rectangular room, measure the length and width and multiply. For an irregular space, the most reliable approach is to divide it into simple shapes — rectangles, triangles, and trapezoids — calculate each area separately, and add them together. To subtract a feature such as a column or an alcove, calculate its area and subtract it from the total. When measuring land, pace off or tape the boundaries and sketch the plot, then break it into triangles (which need only side lengths, thanks to Heron's formula) or trapezoids. Always double-check that you are using the perpendicular height, not a slanted edge, for triangles, trapezoids, and parallelograms.
Area calculations underpin an enormous range of tasks:
The seven calculators here cover the shapes you meet most often, and many other figures reduce to them. A square is just a rectangle with equal sides, so enter the same value for length and width. A rhombus is a parallelogram with four equal sides, so the base-times-height formula applies; alternatively, a rhombus's area equals half the product of its two diagonals. A kite's area is also half the product of its diagonals. A regular polygon — such as a pentagon or hexagon — can be split into identical triangles from its center, so you can find its area by computing one triangle and multiplying by the number of sides, or use the formula ½ × perimeter × apothem. Even a full circle's close relatives fall out of these tools: a semicircle is half a circle's area, and a quarter circle is a 90° sector. Because complex outlines can nearly always be decomposed into rectangles, triangles, trapezoids, and circular pieces, the shapes on this page are enough to measure the great majority of real surfaces you will encounter.
These three measurements are often confused. Perimeter is the distance around the edge of a shape, measured in linear units (feet, meters). Area is the two-dimensional space inside the shape, measured in square units. Volume is the three-dimensional space a solid occupies, measured in cubic units. A room's perimeter tells you how much baseboard to buy; its floor area tells you how much flooring; its volume tells you how much air an HVAC system must heat or cool. This page calculates area; for solids, use a volume calculator instead.
Measuring area is one of the oldest applications of mathematics. The ancient Egyptians calculated the areas of fields to reassess land taxes after the Nile's annual floods erased boundary markers — the very word "geometry" comes from Greek roots meaning "earth measurement." Babylonian tablets show area calculations for rectangles and triangles thousands of years ago. The Greek mathematician Heron (Hero) of Alexandria, writing in the first century CE, recorded the elegant formula for a triangle's area from its three sides that this calculator still uses today. The Greeks also refined the understanding of the circle and the constant π, with Archimedes bounding its value with remarkable accuracy. Centuries later, the invention of integral calculus gave mathematicians a general method to find the area of virtually any curved region, placing all of these classical formulas on a rigorous modern footing.
You can enter each dimension in inches, feet, yards, miles, centimeters, meters, or kilometers. The result is shown in the square of the unit you choose, and the "Show result in other units" panel converts it to acres and all the other units automatically. You can even mix units within one shape.
Use Heron's formula, which is exactly what the triangle calculator here does. Compute the semi-perimeter s = (a + b + c) / 2, then the area = √[s(s − a)(s − b)(s − c)]. No angles or height are needed.
One acre equals 43,560 square feet, or about 4,046.86 square meters. A square mile contains 640 acres. The calculator shows the acre equivalent of any area you compute.
The radius — the distance from the center to the edge. If you measured the diameter (the full width across the center), divide it by two to get the radius before entering it.
The semi-major and semi-minor axes are the distances from the center of the ellipse to its edge along the long and short directions. The full major and minor axes are twice those values. The ellipse calculator asks for the semi-axes, so enter the half-widths.
Divide it into simple shapes — rectangles, triangles, and trapezoids — calculate the area of each, and add them together. Subtract the areas of any cut-outs. For very irregular regions, splitting into many triangles works well because each triangle needs only its three side lengths.
This Area Calculator is provided for educational and general informational purposes. Results are computed with standard geometric formulas and displayed to high precision; round them as appropriate for your project. For construction, land surveying, or other critical work, always verify measurements and calculations independently.