Area Calculator — Rectangle, Circle, Triangle & More

The area calculator computes the area and perimeter of six common geometric shapes — rectangle, square, circle, triangle, trapezoid, and ellipse — using the standard mathematical formulas for each shape. Select your shape, enter the required dimensions, and instantly receive both the enclosed area (in square units) and the boundary perimeter (in linear units).

Area and perimeter calculations are among the most universally applicable geometric computations in everyday life. Every home improvement project — flooring, tiling, painting, fencing, gardening — requires knowing the area of a surface or the perimeter of a boundary. Architects and interior designers calculate room areas to determine material quantities. Real estate listings specify floor areas in square feet or square meters as the primary measurement of home size. Agricultural land is measured in acres or hectares — both derived from area calculations. Engineers calculate cross-sectional areas of structural members to determine load-bearing capacity.

This calculator covers the six most commonly needed geometric shapes, providing both the formula and the numerical result for each. Understanding the underlying formulas — not just the results — allows you to decompose more complex irregular shapes into these basic building blocks and sum the components. A floor plan that is L-shaped is two rectangles; a circular garden pond is a circle subtracted from a square; a trapezoidal room is exactly what the trapezoid formula handles directly.

Example 1 — Room flooring (rectangle): Room: 5.2 m × 4.8 m Area = 5.2 × 4.8 = 24.96 m² → need 24.96 m² of flooring Perimeter = 2 × (5.2 + 4.8) = 20 m → need 20 m of baseboard

Example 2 — Garden pond (circle): Pond radius: 2.5 m Area = π × 2.5² = π × 6.25 ≈ 19.63 m² Circumference = 2π × 2.5 ≈ 15.71 m → edging needed

Example 3 — Triangular plot: Base: 12 m, perpendicular height: 9 m Area = 0.5 × 12 × 9 = 54 m²

Example 4 — Oval flowerbed (ellipse): Semi-major axis: 4 m, semi-minor axis: 2.5 m Area = π × 4 × 2.5 ≈ 31.42 m² Perimeter ≈ π × [3(6.5) − √(14.5 × 6.5)] ≈ 21.4 m

Example 5 — Trapezoid driveway: Parallel sides: 6 m and 9 m, height: 12 m Area = 0.5 × (6 + 9) × 12 = 90 m²

Area calculation is the bridge between geometric theory and practical decision-making in construction, real estate, agriculture, and manufacturing. In home improvement alone, accurate area calculation prevents both expensive material waste and embarrassing shortfalls. Overestimating by 20% means buying and paying for €400 of unnecessary flooring. Underestimating by 10% means a second store trip mid-project and potentially mismatched dye lots. The few minutes spent accurately calculating room area pays back immediately in material cost savings.

In real estate, floor area is the primary metric used to value, compare, and regulate residential and commercial property. A miscalculation of 5 m² in a property listing can misrepresent a home's value by tens of thousands of dollars in high-value markets. Many countries regulate how floor area is measured for legal purposes — whether to include hallways, closets, stairwells, or external walls — making precise area calculation a legally relevant calculation in property transactions.

In agriculture, area calculation is directly tied to resource planning and financial projection. A 10-hectare field requires specific quantities of seed, fertilizer, and pesticide per hectare — errors in area estimation translate directly into over- or under-application of inputs, affecting yield and profitability. Land valuation for purchase or lease is denominated in price per acre or hectare, making area the fundamental metric for agricultural land economics. GPS-based field measurement tools are widely used precisely because area miscalculation at field scale is financially consequential.

This calculator computes area and perimeter using exact or well-established approximate formulas for six standard shapes. It does not handle irregular shapes with non-standard boundaries — L-shapes, U-shapes, polygons with more than four sides, or curved boundaries other than circles and ellipses. For these, decompose the shape into standard components calculated separately, then sum the areas.

For triangle calculations, this calculator uses the base and perpendicular height formula (Area = 0.5 × base × height). If you know only the three side lengths but not the height, use Heron's formula: s = (a+b+c)/2; Area = √(s × (s-a) × (s-b) × (s-c)). If you know two sides and the included angle, Area = 0.5 × a × b × sin(C). These alternative triangle formulas are not implemented in this calculator but can be computed with a scientific calculator.

The perimeter formula for the triangle shown here assumes a right triangle (using the Pythagorean theorem for the hypotenuse). For non-right triangles where you know base, height, but not all three side lengths, the perimeter cannot be calculated from just two inputs. In that case, the perimeter output may not apply to your specific triangle geometry. For accurate non-right triangle perimeter, you need all three side lengths.