Area Calculator (All Shapes)

Basic Shape Formulas

Rectangle: Area = length × width. Perimeter = 2(l + w). Square: Area = side². Triangle: Area = ½ × base × height. For a triangle with sides a, b, c, use Heron's formula: s = (a+b+c)/2; Area = √(s(s-a)(s-b)(s-c)). Circle: Area = πr². Circumference = 2πr. Parallelogram: Area = base × height. Trapezoid: Area = ½(a + b) × h where a and b are parallel sides.

Circle and Ellipse

Circle area = πr², where r is radius. Circumference = 2πr = πd. For a sector (pizza slice): Area = ½r²θ where θ is the angle in radians (degrees × π/180). Arc length = rθ. Ellipse area = πab where a is the semi-major axis and b is the semi-minor axis. Unlike a circle, an ellipse does not have a simple perimeter formula — Ramanujan's approximation is used: P ≈ π(3(a+b) − √((3a+b)(a+3b))).

Units and Conversion

Area units: 1 m² = 10,000 cm² = 1,000,000 mm². 1 km² = 1,000,000 m². 1 hectare = 10,000 m² = 0.01 km². 1 acre = 4,047 m² ≈ 0.4 hectares. 1 square foot = 0.0929 m². 1 square yard = 0.836 m². For land measurement: 1 acre ≈ 0.405 hectares; 1 football pitch ≈ 0.64 hectares (105×68m). Always note what units your dimensions are in before calculating — mixing metres and centimetres is the most common error.

Real-World Applications

Area calculations are used for: flooring and carpeting (room area + 10% waste), paint coverage (wall area ÷ coverage rate), turf and grass seed (garden area), solar panels (roof area for system sizing), land valuation (property and agricultural land), and fabric cutting (pattern layout). For irregular shapes, divide them into regular sub-shapes and sum the areas. For very irregular shapes, use the surveyor's formula (shoelace formula) with coordinate pairs.