Area is the measure of the size of a two-dimensional surface — the amount of space enclosed by a shape's boundary. You can picture it as the quantity of paint needed to cover a floor, or the amount of land a plot occupies. The Area Calculator computes the area of seven of the most common geometric shapes from a few simple measurements, so you never need to remember a formula or reach for a geometry textbook. Choose the shape that matches what you are measuring, enter its dimensions in any unit you like, and the area appears instantly.
What Is Area?
Area describes how much two-dimensional space a figure covers. Its standard unit is the square meter, but any unit of length produces a corresponding unit of area: square centimeters, square feet, square yards and so on. Doubling every dimension of a shape does not double its area — it quadruples it, because area grows with the square of the linear scale. This is why a floor plan twice as long and twice as wide needs four times as much carpet. Understanding whether you are dealing with one, two or three dimensions is the first step in choosing the right calculation: lengths are one-dimensional, areas are two-dimensional, and volumes, which the companion Volume Calculator handles, are three-dimensional.
Rectangle and Square
A rectangle is a four-sided shape with four right angles, and its area is the simplest to calculate: multiply the length by the width. The length is normally the longer side and the width the shorter one, though the formula works either way. A square is simply a rectangle whose length and width are equal, so its area is the side length multiplied by itself. Rectangle math is everywhere — room floors, plots of land, sheets of material, screens and photographs. If you are measuring a room to buy flooring, measure the length and width of the floor in the same unit, multiply them, and the result is the floor area you need to cover. For an L-shaped room, split the space into two rectangles, calculate each, and add the results.
Triangle
A triangle has three straight edges, and its area can be found in several ways depending on what you know. This calculator uses Heron's formula, which needs only the three edge lengths — perfect when you can measure the sides but not the height. Heron's formula works in two steps: first compute the semi-perimeter s, which is half the sum of the three sides, then apply the formula area = √(s(s−a)(s−b)(s−c)). For example, a triangle with edges of 3, 4 and 5 units has a semi-perimeter of 6, giving an area of exactly 6 square units. One important detail: three lengths only form a triangle if each edge is shorter than the sum of the other two. If your numbers cannot form a triangle, the calculator shows an area of zero rather than a meaningless result.
Trapezoid
A trapezoid is a four-sided shape with at least one pair of parallel sides. The parallel sides are called the bases and the distance between them, measured perpendicular to the bases, is the height. Its area is the average of the two bases multiplied by the height: area = (b1 + b2)/2 × h. Intuitively, the formula takes the average length of the parallel sides and treats the trapezoid like a rectangle of that width. This shape shows up in ramps, roof cross-sections, side views of furniture and land parcels with slanted boundaries. The height must be the perpendicular distance between the bases — measuring a slanted side instead will overstate the area.
Circle
A circle is defined by its radius, the distance from the center to any point on the edge. Its area is π times the radius squared, where π (pi) is the mathematical constant approximately equal to 3.14159. Doubling the radius of a circle quadruples its area, exactly as with the rectangle. Circular areas appear constantly in real life: table tops, manholes, gardens with circular beds, water tanks seen from above and round planters. If you know the diameter rather than the radius — the distance across the circle through the center — divide it by two first. Since the radius is squared, a small measurement error has a larger effect than it would in a linear calculation, so measure carefully.
Sector
A sector is a slice of a circle, bounded by two radii and the arc between them — like a wedge of pie. Its area depends on both the radius and the angle of the slice. Since the sector is a fraction of the whole circle, its area is that fraction of the circle's area: area = (θ/360) × πr², where θ is the angle in degrees. A 90-degree sector of a circle is one quarter of the full circle, a 180-degree sector is a half, and so on. This calculator takes the angle in degrees directly. Sectors appear in slicing problems, pizza and cake portions, pie charts and land plots shaped like a wedge. Enter the radius and the angle at the point of the slice, and the tool does the rest.
Ellipse
An ellipse is a stretched circle with two radii instead of one: the semi-major axis, its longest radius, and the semi-minor axis, its shortest. Its area is simply π times the product of the two: area = πab. When both axes are equal, the ellipse becomes a circle and the formula reduces to the circle formula. Ellipses appear in architecture — arches, tabletops and decorative gardens — and in astronomy, where planetary orbits are elliptical. Because the two axes are perpendicular and measured from the center, make sure you enter the full half-lengths, not the full diameters: the semi-axes are half the width and half the length of the oval.
Parallelogram
A parallelogram has two pairs of parallel sides, with opposite sides equal in length. Its area uses the base and the height, where the height is the perpendicular distance between the base and the opposite side: area = base × height. Note that the height is not the slanted side — measuring the slanted edge and using it as the height is one of the most common errors in geometry. You can think of a parallelogram as a rectangle that has been pushed sideways without changing its height, which is exactly why the formula matches the rectangle's. Rhombuses, rhomboids and rectangles are all special cases. Parallelogram-shaped surfaces appear in roofs, decorative tiles, furniture and angled facades.
Finding the Area of Complex Shapes
Not every surface is one of these seven shapes. The standard trick is decomposition: split a complex shape into simple ones, calculate each area, and add them together. An L-shaped room becomes two rectangles; a plot of land with a curved side becomes a rectangle plus a sector or a set of triangles; a floor with a round column in the middle is a rectangle minus a circle. This approach is also the basis of estimating land area, where surveyors frequently break irregular parcels into triangles, the most flexible building block of area calculation. For very irregular boundaries, you can approximate by choosing simple shapes that closely follow the outline — the more pieces you use, the better the estimate.
Units and Conversion
The area result comes out in the square of whatever unit you enter: enter meters and get square meters, enter feet and get square feet. If you need a different unit, use a length conversion factor and square it. For example, one foot equals 0.3048 meters, so one square foot equals 0.3048², about 0.0929 square meters. Common area units include the hectare (10,000 square meters) and the acre (about 4,047 square meters, or 43,560 square feet), which are used mainly for land. Since squaring amplifies rounding, convert lengths to the target unit before squaring rather than converting the final area with a rounded factor.
Common Mistakes to Avoid
Three errors cause almost all wrong area results. The first is mixing units: multiplying meters by centimeters produces a number that is neither square meters nor square centimeters — convert everything to one unit first. The second is using the wrong height: for triangles, trapezoids and parallelograms the height must be perpendicular to the base, not a slanted side. The third is confusing radius with diameter in circles and sectors. Checking these three details, and letting this calculator handle the arithmetic, will keep your measurements dependable.
A fourth, subtler mistake is trusting a single measurement. Surfaces that look rectangular are rarely perfectly so — walls bulge, floors slope and plots of land shift. When precision matters, take the measurement in at least two places and average the readings, and round final results sensibly rather than to many decimal places that the original measurements never justified. For estimates like painting, flooring or fencing, adding a small allowance for waste and overlaps on top of the calculated area is standard practice and saves an extra trip to the store.
Key Assumptions
- All dimensions are entered in the same unit; the result is in that unit squared.
- The triangle formula assumes the three edges can form a triangle; otherwise the area is 0.
- The sector angle is in degrees, with a full circle equal to 360°.
- Ellipse inputs are the semi-axes (half the full widths), not the full diameters.
- For combined shapes, compute each part separately and add the areas.