Area Calculator

Area = length × width. A room 5 m long and 4 m wide has area 5 × 4 = 20 m². For a square, area = side². Always use the same units for both dimensions. The result is always in square units: feet gives ft², meters gives m². For rooms with irregular shapes, divide into rectangles, calculate each, then add.

Area = π × r², where r is the radius (half the diameter) and π ≈ 3.14159. Example: circle with radius 7 cm. Area = π × 49 ≈ 153.94 cm². The circumference (perimeter) is 2πr. If you know the diameter: radius = diameter / 2. If you know the circumference: radius = C / (2π).

Most common: Area = ½ × base × height, where height is the perpendicular distance from base to opposite vertex. Example: base 10 cm, height 6 cm = ½ × 10 × 6 = 30 cm². If you only know three sides, use Heron's Formula: s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c)). For a right triangle, the two legs serve directly as base and height.

Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the perpendicular height between them. Example: parallel sides 8 cm and 12 cm, height 5 cm. Area = ½ × (8 + 12) × 5 = 50 cm². This works because a trapezoid is the average width of the two parallel sides multiplied by the height. The formula derives from decomposing the trapezoid into a parallelogram and a triangle.

Square the linear conversion factor. Since 1 m = 100 cm, then 1 m² = 100² = 10,000 cm². Key conversions: 1 ft² = 144 in². 1 yd² = 9 ft². 1 m² = 10.764 ft². 1 acre = 43,560 ft² = 4,047 m². 1 hectare = 10,000 m² = 2.471 acres. A common error is using the linear factor (1 m = 100 cm) instead of squaring it for area conversions.

Calculate room area (length × width) then add 10–15% for waste from cuts, pattern matching, and future repairs. For diagonal installation, add 15%. For irregular rooms, divide into rectangles, calculate each, then sum. Example: a 12 × 15 ft room = 180 ft². Adding 10% = 198 ft², so order 200 ft². Always buy slightly more — matching batches later can be difficult if the product is discontinued.

Area = base × height, where height is the perpendicular distance between parallel sides (NOT the slant side length). Example: base 10 cm, perpendicular height 6 cm. Area = 60 cm². A parallelogram can be rearranged into a rectangle of the same base and height, which is why the formula is identical. Using the slant side instead of perpendicular height is a common error that gives an inflated result.

Area = π × a × b, where a is the semi-major axis (half the longer diameter) and b is the semi-minor axis (half the shorter diameter). Example: semi-axes 6 cm and 4 cm. Area = π × 6 × 4 ≈ 75.40 cm². When a = b = r, this becomes πr² (a circle). The ellipse perimeter has no simple exact formula and requires an approximation (Ramanujan's formula is commonly used).

Area refers to the 2D space of a flat shape. Surface area is the total area of all faces of a 3D object. A rectangle has area = length × width. A rectangular box has surface area = sum of all six face areas = 2(lw + lh + wh). This calculator computes 2D area for flat shapes. For 3D surfaces like spheres (4πr²), cylinders, or cubes, use a dedicated surface area or volume calculator.

Four approaches: (1) Decomposition: divide into known shapes (rectangles, triangles), calculate each area, add them. (2) Grid counting: draw on graph paper, count full and partial squares. (3) Shoelace Formula: if you know all vertex coordinates (x,y), Area = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|. (4) Digital tools: GIS software, CAD programs, or Google Maps can measure irregular areas from satellite images directly.