Area Formulas for Common 2D Shapes
Area is the amount of two-dimensional space enclosed by a flat shape. It is measured in square units, such as square metres (m²), square centimetres (cm²), or square feet (ft²). Each shape has a specific formula derived from its geometry.
| Shape | Formula | Variables |
|---|
| Rectangle | A = l x w | l = length, w = width |
| Circle | A = pi x r² | r = radius |
| Triangle | A = (1/2) x b x h | b = base, h = perpendicular height |
| Trapezoid (Trapezium) | A = ((a + b) / 2) x h | a, b = parallel sides, h = height |
| Parallelogram | A = b x h | b = base, h = perpendicular height |
| Ellipse | A = pi x a x b | a = semi-major axis, b = semi-minor axis |
| Circular Sector | A = (theta / 360) x pi x r² | theta = angle in degrees, r = radius |
| Rhombus | A = (d1 x d2) / 2 | d1, d2 = diagonals |
How to Use This Calculator
Select your shape from the dropdown, then choose your preferred unit of measurement (metres, centimetres, feet, or other). Enter the required dimensions for the selected shape. The area and a worked formula update instantly as you type. All inputs must be positive numbers. The unit selector affects only the label on the result, not the calculation itself, so make sure all your dimensions are in the same unit before entering them.
Rectangle and Square
The area of a rectangle is simply its length multiplied by its width: A = l x w. A square is a special case where length and width are equal, giving A = s² where s is the side length. For example, an 8 m x 5 m rectangle has an area of 40 m².
Circle
The area of a circle uses the constant pi (approximately 3.14159). The formula is A = pi x r². The radius is half the diameter. If you know the diameter, divide it by 2 before entering it. A circle with radius 5 m has an area of 3.14159 x 25 = 78.5398 m².
Triangle
The area of a triangle is half the base multiplied by the perpendicular height: A = (1/2) x b x h. The height must be the vertical distance from the base to the apex, measured at a right angle to the base, not the slant side. If you know all three side lengths instead, use Heron's formula via the triangle area calculator.
Trapezoid (Trapezium)
A trapezoid has one pair of parallel sides. The area formula averages the two parallel sides and multiplies by the perpendicular height: A = ((a + b) / 2) x h. For parallel sides of 6 m and 10 m with a height of 4 m, the area is ((6 + 10) / 2) x 4 = 8 x 4 = 32 m².
Ellipse
An ellipse is a stretched circle. Its area is A = pi x a x b, where a is the semi-major axis (half the longer diameter) and b is the semi-minor axis (half the shorter diameter). When a equals b, the shape is a circle and the formula reduces to A = pi x r².
Circular Sector
A sector is a "pizza slice" of a circle. Its area is the fraction of the full circle corresponding to the central angle: A = (theta / 360) x pi x r². A quarter-circle (90 degrees) with radius 5 m has an area of (90 / 360) x pi x 25 = 0.25 x 78.5398 = 19.635 m².
Rhombus
A rhombus is a quadrilateral with four equal sides. Its area is most easily calculated from its diagonals: A = (d1 x d2) / 2, where d1 and d2 are the lengths of the two diagonals. For diagonals of 8 m and 6 m, the area is (8 x 6) / 2 = 24 m². A square is a special case of a rhombus where both diagonals are equal.
Related Calculators
Sources and method: Standard geometric area formulas as found in NZQA mathematics curriculum resources and general reference texts. Pi is taken as Math.PI in JavaScript (IEEE 754 double precision, approximately 3.141592653589793). All calculations are exact closed-form results with no rounding until display (4 decimal places).
This calculator applies standard area formulas and returns a mathematically exact result for the inputs provided. Ensure all dimensions are in the same unit before entering them. The unit selector is a display label only and does not perform any unit conversion.
