Area Calculator

This free area calculator lets you find the area of nine standard two-dimensional shapes, including rectangles, squares, triangles, circles, ellipses, parallelograms, trapezoids, rhombuses, and circular sectors. Enter your measurements, choose the correct shape, and click Calculate to get instant results for design, construction, or classroom use.

This free area calculator determines the area of common shapes, including rectangles, circles, triangles, and more — but sometimes your task requires a more tailored tool. When measuring outdoor zones, the Land Area Calculator is ideal. Indoors, the Flooring Area Calculator and Square Footage Calculator simplify planning. If you're working on sloped structures or exteriors, tools like the Roof Area Calculator and Fence Paint Calculator offer shape-specific accuracy. You can also estimate surface coverage with the Wall Paint, Ceiling Paint, and Surface Area Calculator. Each one applies the same core geometry in ways that fit real design, construction, or renovation workflows.

How to Choose the Right Shape

Use a rectangle or square when edges are straight and all corners are 90°. Choose a triangle if the region tapers to a point. Use a parallelogram or trapezoid if opposite sides are slanted. Select a circle or ellipse for smooth curves, and a sector when only part of a circle is involved.

For irregular areas, break the region into a combination of rectangles, triangles, or circular parts, calculate each area separately, and then add the results. This approach lets you approximate complex shapes using the standard forms covered by this calculator.

Examples

Rectangle Example (Room)

Formula: area = length × width

If a room is 12 m long and 5 m wide, the area is calculated as 12 × 5 = 60 m². This simple rectangle model applies whenever opposite sides are equal and all angles are 90°, such as rooms, cabinets, and floor layouts.

Square Example (Garden)

Formula: area = side × side

If a garden plot has a side length of 8 m, the area is 8 × 8 = 64 m². A square is a special case of a rectangle where all sides are equal.

Triangle Example (Roof Panel)

Formula: area = ½ × base × height

For a triangular roof panel with a 10 m base and 6 m height, the area is ½ × 10 × 6 = 30 m². This applies to any triangle where the height is measured perpendicular to the base.

Circle Example (Water Tank Base)

Formula: area = π × radius²

If a circular tank base has a radius of 7 m, the area is π × 7² ≈ 153.94 m². Circles require only the radius to determine the enclosed area.

Ellipse Example (Running Track)

Formula: area = π × a × b

For an elliptical track with a semi-major axis of 6 m and semi-minor axis of 4 m, the area is π × 6 × 4 ≈ 75.40 m². Ellipses are used when boundaries follow smooth, elongated curves.

Trapezoid Example (Ramp)

Formula: area = ½ × (base₁ + base₂) × height

If a ramp cross-section has bases of 10 m and 6 m, with a height of 4 m, the area is ½ × (10 + 6) × 4 = 32 m². Trapezoids apply when only one pair of opposite sides is parallel.

Parallelogram Example (Shed Wall)

Formula: area = base × height

For a slanted shed wall with a base of 9 m and a perpendicular height of 5 m, the area is 9 × 5 = 45 m². Parallelograms cover any shape with parallel opposite sides and an angled top edge.

Rhombus Example (Tile)

Formula: area = ½ × diagonal₁ × diagonal₂

If a rhombus tile has diagonals of 10 m and 6 m, the area is ½ × 10 × 6 = 30 m². This diagonal method works when the slant height is hard to measure.

Sector Example (Pizza Slice)

Formula: area = (θ ÷ 360) × π × radius²

For a pizza slice with a 5 m radius and a 90° angle, the area is (90 ÷ 360) × π × 5² ≈ 19.63 m². Sectors apply only when the boundary contains two radii meeting at the center plus an arc.

Rectangle

A rectangle is a four-sided polygon with four right angles, where opposite sides are both parallel and equal in length. It is the default shape used when a surface has straight edges, fixed corners, and perpendicular boundaries. A rectangle’s area is calculated by multiplying its length and width, making it ideal whenever two perpendicular measurements are known.

Rectangles are chosen when the sides meet at 90° and the edges do not taper or slope. If all four sides are equal, the shape becomes a square—a special case of a rectangle. When only two perpendicular sides are known or when a surface can be broken into right-angled sections, the rectangular model provides the most reliable and consistent area estimate.

You should not use a rectangle when opposite sides are not parallel, when angles deviate from 90°, or when the boundary forms a slanted quadrilateral—in these cases, a parallelogram or trapezoid is more accurate. Rectangles also act as base units for decomposing complex shapes in architecture, flooring, interior layouts, and construction planning.

A set designer working for a television studio needed to prepare the layout for an indoor living room scene. The director required removable walls, even lighting coverage, and symmetrical prop placement. The stage floor formed a perfect rectangle measuring 36 feet in length and 24 feet in width, giving an area of 36 × 24 = 864 sq ft.

This 864-square-foot boundary allowed the crew to position furniture, design the lighting grid, and install overhead scaffolding without misalignment. Because the area was determined from a simple rectangular layout, calculating lumens per square foot and electrical load became straightforward—showing how the rectangle is often the most practical and dependable shape for real-world planning.

Square

A square is a special type of rectangle in which all four sides are equal and all angles are exactly 90°. It is used when the boundary has perfect symmetry and every edge measures the same length. Because only one measurement is required, a square provides the simplest and most reliable area calculation among all quadrilaterals with right angles.

Squares are chosen when identical edges, right-angle corners, and uniform spacing are needed in architecture, floor layouts, tiling, artwork grids, digital UI elements, and structural design. A square is also a special case of two other shape families: it is a rectangle with equal sides and a rhombus with right angles.

A square should not be used if any side differs in length, if angles shift away from 90°, or if the boundary forms a slanted quadrilateral. In those cases, a rectangle, rhombus, or parallelogram is more accurate. Squares are also commonly used to break down irregular shapes into equal units for measurement, layout planning, or modular design.

A modern art gallery in New York was curating an exhibition of framed square paintings. To arrange them evenly across a wall, the curator needed to know the exact space each piece would occupy. Each painting measured 48 inches on all sides, so the area was calculated as 48 × 48 = 2,304 in².

Knowing the area of each square allowed the team to space the artwork consistently, maintain alignment across the display grid, and determine the total number of pieces that could fit without overcrowding. The square’s uniform edges made the layout predictable and repeatable — demonstrating how simple geometry supports practical design decisions.

Triangle

A triangle is a three-sided polygon where the sum of the interior angles is always 180°, and any two sides must be long enough to form a valid third side. Triangles are used when a surface tapers to a point or when only three boundary edges define the region. Depending on the measurements available, the area can be found using base-height, side-length, or coordinate-based methods.

Heron’s formula applies when all three side lengths are known and no height is given. If the height is available, the simpler formula ½ × base × height is preferred. For plots of land or sloped roof sections defined by corner coordinates, the coordinate-geometry method provides the most accurate boundary measurement.

A triangle should not be used when the sides violate the triangle inequality or when the boundary forms four or more edges—in those cases, a quadrilateral or polygon shape is required. Triangles are also essential in structural design because their rigid shape resists distortion, allowing engineers to combine multiple triangles to form stable trusses, roofs, supports, and land-survey grids.

An architect working on an eco-friendly building needed to install solar panels on a triangular roof section. The roof edges measured 20 ft, 22 ft, and 18 ft, so the architect used Heron’s formula: s = (20 + 22 + 18) ÷ 2 = 30, and area = √30 × (30 − 20)(30 − 22)(30 − 18) = √30 × 10 × 8 × 12 = √28800 ≈ 169.7 sq ft.

Knowing the exact triangular area helped the crew determine panel count, weight distribution, and hardware spacing. The precise calculation avoided excess material costs and ensured the mounting system aligned cleanly with the sloped roof geometry—illustrating how accurate triangle measurements support practical construction decisions.

Parallelogram

A parallelogram is a four-sided polygon in which both pairs of opposite sides are parallel and equal in length. It is used when a surface has slanted boundaries but maintains parallel edges. Its area is calculated by multiplying the base by the perpendicular height, making the height measurement crucial because the side length alone does not reflect the true vertical span.

Parallelograms are the preferred model when the shape resembles a tilted rectangle, when angles are not 90°, or when loads and surfaces follow a sloped direction. If all angles become right angles, the parallelogram becomes a rectangle. If all four sides become equal, it becomes a rhombus; if the sides are equal and all angles are 90°, it becomes a square.

A parallelogram should not be used if opposite sides are not parallel or if the shape forms a trapezoid with only one pair of parallel sides. It is also unsuitable when the height is measured along the slanted edge rather than perpendicular to the base—this produces incorrect area values. In architecture, fabric pattern drafting, framework design, and land surveying, parallelograms help model sloped forces, angled wall sections, and shear-resistant structures.

A signage company was asked to build a slanted roadside billboard mounted between two tilted steel beams. The ad surface formed a parallelogram measuring 15 feet along the base and 10 feet in perpendicular height, so the engineer calculated its area as 15 × 10 = 150 sq ft.

This 150-square-foot area helped the team print the banner at the correct dimensions, trim the vinyl sheet precisely, and plan the load distribution across the tilted support beams. Using a parallelogram model allowed the designers to match the billboard’s slanted geometry, improving wind resistance and visual alignment with the roadside angle.

Circle

A circle is a perfectly round, two-dimensional shape in which every boundary point is the same distance from the center. This constant distance is the radius, and it defines the circle completely. The area of a circle is calculated using the radius and the mathematical constant π (pi), making it suitable whenever the boundary curves evenly around a single central point.

A circle should be used only when the outline is uniformly curved and the radius is consistent in all directions. If the boundary stretches more along one axis than the other, the shape becomes an ellipse. If only a portion of the circle is needed—such as a slice, arc, or curved gate panel—the correct form is a sector, not a full circle.

Circles should not be used if the boundary is irregular, off-center, or formed by two different radii. They are chosen for engineering, landscaping, mechanical design, fountains, circular pads, round tanks, and any design where symmetry, rotation, or radial layout is required. Because the radius uniquely determines the entire shape, circles provide predictable measurements for spatial planning and structural balance.

An urban landscape architect was commissioned to design a circular fountain at the center of a new city plaza. The fountain had a radius of 12 feet, so the designer calculated its area as π × 12² = π × 144 ≈ 452.39 sq ft.

This area helped the team reserve floor space, design the water flow system, and plan the stone tiling around the fountain. The circular layout created a visually balanced focal point that complemented the open plaza—showing how accurate circle measurements guide both engineering and aesthetic decisions.

Ellipse

An ellipse is a two-dimensional shape formed when a boundary curves smoothly around two focal points instead of one central point. It resembles a stretched or flattened circle. An ellipse has two key measurements: the semi-major axis (the longest radius) and the semi-minor axis (the shortest radius). These axes define the shape completely and are used to calculate its area.

An ellipse should be used when the boundary extends farther in one direction than the other, creating unequal radii. If both radii are equal, the shape becomes a circle. When only part of the ellipse is needed—such as an arched panel or curved entryway—a sector or custom spline should be used instead. The ellipse model is chosen for smooth, symmetric curves that lack sharp corners but still follow a predictable geometric rule.

An ellipse should not be used if the boundary is irregular, has varying curvature, or does not align with consistent major and minor axes. It is frequently applied in architecture, orbital mechanics, racetracks, amphitheaters, garden paths, and structural layouts that require gentle curvature, visual symmetry, and efficient space planning.

A landscape designer planned an elliptical walkway loop around a central garden bed with a semi-major axis of 25 feet and a semi-minor axis of 15 feet. Using the formula, the area was calculated as π × 25 × 15 = π × 375 ≈ 1,178.1 sq ft.

This precise area measurement helped the team order the correct quantity of paving tiles, create a balanced path width, and estimate installation costs. The elliptical layout guided visitors naturally through the garden and added visual elegance to the space—showing how geometry supports both design flow and practical planning.

Trapezoid

A trapezoid is a four-sided polygon with at least one pair of parallel sides, called the bases. It is used when the boundary slopes on one side while the opposite sides do not remain parallel. The perpendicular distance between the two bases defines the height, and this height is essential because the slanted side lengths cannot determine the area on their own.

A trapezoid should be used when only one pair of opposite sides is parallel. If both pairs become parallel, the shape becomes a parallelogram; if the angles also become 90°, it becomes a rectangle; and if all sides are equal with right angles, it becomes a square. The trapezoid model is also ideal when the top and bottom edges differ in length, producing a tapered or sloped geometry.

A trapezoid should not be used if neither pair of sides is parallel or if the height is mistakenly measured along the slanted edges instead of perpendicularly. Trapezoids are commonly used in bridge supports, retaining walls, ramps, roof cross-sections, irrigation channels, garden edging, and structural elements where a sloped boundary or tapered load path is required.

A homeowner needed to build a retaining wall in a sloped backyard. The wall’s trapezoidal cross-section had a top base of 6 ft, a bottom base of 12 ft, and a vertical height of 5 ft, so the area was calculated as (6 + 12) ÷ 2 × 5 = 9 × 5 = 45 sq ft.

This area calculation allowed the builder to estimate material volume, plan the concrete footprint, and ensure stability across the sloped soil line. The trapezoidal shape provided structural strength while matching the natural incline—illustrating how geometric modeling supports sound engineering and practical landscape design.

Rhombus

A rhombus is a quadrilateral in which all four sides are equal in length, while opposite angles are equal but not necessarily 90°. It is used when a shape is slanted like a parallelogram but maintains equal side lengths. The area can be calculated using base × height or more commonly using the diagonals, which is especially useful when the rhombus is tilted or part of an irregular layout.

A rhombus should be used when all sides are equal but the angles are not 90°. If the angles become right angles, the rhombus becomes a square. If only opposite sides are equal while all four sides differ, the shape becomes a general parallelogram. The diagonal formula is preferred when the height is unknown or difficult to measure, since the diagonals intersect at right angles inside the rhombus.

A rhombus should not be used if the shape has unequal side lengths or if only one pair of sides is parallel—in those cases, a parallelogram or trapezoid is more accurate. Rhombuses are commonly used in tiling, textile patterns, logo design, architectural motifs, and land survey plots where equal side lengths and diagonal alignment define the geometry.

An interior designer was tasked with laying decorative tiles in the shape of a rhombus inside a courtyard feature. Each tile had diagonals of 10 inches and 16 inches, so the area was calculated as (10 × 16) ÷ 2 = 160 ÷ 2 = 80 in².

Knowing the exact area helped the designer estimate tile quantity, plan spacing, and avoid excess material waste. The rhombus tiles added a geometric flair to the courtyard, balancing symmetry and style while maintaining precise measurement throughout the installation.

Sector

A sector is the region of a circle enclosed by two radii and the connecting arc. It represents a specific slice of the full circular area and is defined by the radius and the central angle. The area of a sector is calculated as the corresponding fraction of the circle’s total area, based directly on the angle.

A sector should be used when the boundary is defined by two radii meeting at the center and the curved perimeter is part of a circle. If the boundary does not originate from the center, the shape becomes a segment or an irregular arc region. If the angle is 360°, the sector becomes a complete circle; if 180°, it forms a semicircle.

A sector model is not appropriate when the sides do not pass through the circle’s center or when the shape includes straight edges that are not radii. Sectors commonly appear in pie charts, circular gauges, pizza-slice layouts, garden pathways, mechanical rotation zones, and any design involving a portion of a circular surface.

A product developer was designing packaging for a new gourmet pizza sold by the slice. Each slice was a sector with a radius of 9 inches and a central angle of 45°, so the area was calculated as (45 ÷ 360) × π × 9² = (1/8) × π × 81 ≈ 31.8 in².

This precise measurement helped ensure efficient material usage, maintain consistent portion sizes, and design packaging that fit the slice tightly. By modeling the pizza slice as a geometric sector, the team optimized both packaging and production with one clear calculation.

Area is the measure of space inside a two-dimensional shape. This calculator covers rectangles, circles, triangles, and more. For 3D extensions like volume and surface estimations, visit the Volume Calculator and Surface Area Calculator.

Irregular and Composite Areas

Many real spaces are not perfect rectangles or circles. To estimate the area of an irregular region, divide it into simple shapes such as rectangles, triangles, or circular sectors, use the calculator above for each part, and then add the individual areas together. This method is widely used in land surveying, renovation projects, and layout planning.

Common Area Units and Conversion to Square Meters

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