Area Calculator

The following calculator estimates the area of common geometric shapes used in measurement and design. In many cases, irregular figures can be broken down into these basic forms to calculate total area. This tool is widely used in applications such as land assessment, construction layouts, and classroom instruction.

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.

Examples

Rectangle Example (Room)

Formula: Area = length × width

Example: If length = 12 m and width = 5 m, then Area = 12 × 5 = 60 m²

Square Example (Garden)

Formula: Area = side × side

Example: If side = 8 m, then Area = 8 × 8 = 64 m²

Triangle Example (Roof)

Formula: Area = ½ × base × height

Example: If base = 10 m and height = 6 m, then Area = ½ × 10 × 6 = 30 m²

Circle Example (Tank)

Formula: Area = π × radius²

Example: If radius = 7 m, then Area = π × 7² ≈ 153.94 m²

Ellipse Example (Track)

Formula: Area = π × a × b

Example: If a = 6 m and b = 4 m, then Area = π × 6 × 4 ≈ 75.40 m²

Trapezoid Example (Ramp)

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

Example: If base₁ = 10 m, base₂ = 6 m, height = 4 m, then Area = ½ × (10 + 6) × 4 = 32 m²

Parallelogram Example (Shed)

Formula: Area = base × height

Example: If base = 9 m and height = 5 m, then Area = 9 × 5 = 45 m²

Rhombus Example (Tile)

Formula: Area = ½ × diagonal₁ × diagonal₂

Example: If d₁ = 10 m and d₂ = 6 m, then Area = ½ × 10 × 6 = 30 m²

Sector Example (Pizza)

Formula: Area = (θ/360) × π × radius²

Example: If radius = 5 m and angle θ = 90°, then Area = (90/360) × π × 5² ≈ 19.63 m²

Rectangle

A rectangle is a four-sided polygon with four right angles and opposite sides of equal length. It’s one of the most commonly encountered shapes in construction, design, and planning. Its area is determined by multiplying the length by the width — a simple yet powerful formula that applies across countless real-world applications.

Rectangles are used every day, from designing buildings and furniture to planning floor layouts and calculating packaging space. A square is a special case of a rectangle where all sides are equal in length.

A set designer working for a television studio needed to prepare the layout for an indoor living room scene. The director had strict requirements: the walls had to be removable, lighting should fall evenly, and props needed to be placed symmetrically. The main floor section was a rectangle measuring 36 feet in length and 24 feet in width, so its area was 36 × 24 = 864 sq ft.

This 864 square foot space gave the crew exact boundaries to arrange furniture, wire in lighting, and design overhead scaffolding. Knowing the area also helped the lighting engineer calculate lumens per square foot, ensuring uniform brightness across the entire rectangular set. With precise measurements in hand, the team was able to finish the setup ahead of schedule — all beginning with one fundamental rectangle calculation.

Square

A square is a special type of rectangle in which all four sides are equal in length and all angles are right angles. Because of this uniformity, calculating the area of a square is even simpler than a general rectangle. The only measurement needed is the side length, and the area is found by multiplying the side by itself.

Squares are frequently used in architecture, floor planning, artwork layouts, and digital interfaces. Their symmetry makes them ideal for creating balance and consistency in both physical and visual design.

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

Knowing the area of each square display helped the team space the artwork precisely and balance the wall visually. It also allowed them to determine how many paintings could fit across the available wall area without overcrowding. The square’s consistent dimensions made the design grid clean, repeatable, and easy to plan — proving the usefulness of a basic area calculation.

Triangle

A triangle is a three-sided polygon where the sum of the interior angles equals 180 degrees. There are different types of triangles—equilateral, isosceles, and scalene—and multiple methods to calculate their area depending on the available measurements. One common method, especially for general triangles, is Heron’s formula, which uses all three side lengths.

Triangles are essential in structural design, land measurement, and construction because they provide stability and can form complex shapes when combined.

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 area helped the team install the correct number of panels and ensure even weight distribution across the triangular section. It also prevented overspending on excess materials, showing how simple geometry supports sustainable building practices.

Parallelogram

A parallelogram is a four-sided polygon with opposite sides that are both parallel and equal in length. Its area is determined by multiplying the base by the perpendicular height. Unlike a rectangle, the angles in a parallelogram aren't necessarily right angles, but the sides still maintain symmetry.

Parallelograms are often used in architecture, fabric design, land surveying, and mechanical structures, especially when working with angled loads or sloped surfaces.

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

This 150 square feet measurement guided the printing of the banner, cutting of the vinyl sheet, and installation layout. Using the parallelogram’s angled design not only improved wind resistance but also maintained visual appeal — all enabled by a precise area calculation.

Circle

A circle is a perfectly round, two-dimensional shape where every point on its boundary is equidistant from a central point. The distance from the center to the edge is called the radius. The area of a circle is calculated using the radius and the mathematical constant π (pi), which approximates to 3.1416.

Circles are used in engineering, landscaping, mechanical design, and everyday objects like clocks, wheels, and fountains — wherever symmetry and rotation matter.

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

This value helped the team reserve sufficient space, allocate water flow systems, and plan the surrounding tile layout. The circular design created a symmetrical focal point that attracted visitors and added aesthetic harmony to the entire square — all starting from one clean area calculation.

Ellipse

An ellipse is a two-dimensional shape that looks like a flattened circle. It has two axes: a major axis (the longest diameter) and a minor axis (the shortest diameter). The area of an ellipse is calculated by multiplying π with the product of its semi-major and semi-minor axes.

Ellipses often appear in architecture, orbital paths, racetracks, and garden layouts — especially when soft curves are preferred over sharp corners.

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, so the area was calculated as π × 25 × 15 = π × 375 ≈ 1,178.1 sq ft.

The result helped the team order the correct quantity of paving tiles and estimate costs. The elliptical design allowed for natural flow and visual elegance — blending functionality and aesthetics in a way only geometry can deliver.

Trapezoid

A trapezoid is a four-sided polygon with at least one pair of parallel sides, known as the bases. The perpendicular distance between these bases is called the height. The area of a trapezoid is calculated by averaging the lengths of the two bases and multiplying by the height.

Trapezoids are used in bridge supports, ramps, roof designs, and landscaping borders where sloped geometry is needed.

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 precise material planning and helped ensure the wall’s stability. The trapezoidal structure was chosen for both functional integrity and aesthetic appeal — demonstrating how geometry aids real-world problem-solving.

Rhombus

A rhombus is a quadrilateral where all four sides are equal in length, and opposite angles are equal. Its area can be found using either the base and height or the lengths of its diagonals. The diagonal-based method is especially useful when the rhombus is tilted or set into irregular layouts.

Rhombuses are used in tiling, textiles, logo design, and land measurement where symmetry and diagonal orientation are important.

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 tile area helped the designer calculate the number of tiles needed and avoid material waste. The rhombus shape added a geometric flair to the courtyard — balancing both form and function through precise measurement.

Sector

A sector is a portion of a circle enclosed by two radii and the connecting arc. It resembles a slice of pie or pizza. To calculate its area, you need the radius and the angle of the sector. The result is a fraction of the full circle’s area, based on the angle.

Sectors are common in pie charts, clock faces, garden layouts, and any circular design where only part of the area is involved.

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 use of packaging material and proper fit. By modeling the pizza slice as a geometric sector, the team optimized both design and logistics in a single equation.

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.

Common Area Units and Conversion to Square Meters