Area Calculator
Calculate the area and perimeter of common 2D shapes: square, rectangle, triangle, circle, trapezoid, parallelogram, and ellipse.
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How to use this calculator
Square: A=s². Rectangle: A=lw. Triangle: A=½bh. Circle: A=πr². Trapezoid: A=½(a+b)h. Parallelogram: A=bh. Ellipse: A=πab.
- 1
Select the shape from the dropdown menu.
- 2
Enter the required dimensions (length, width, radius, base, height, etc.).
- 3
The area and perimeter (or circumference) are calculated immediately.
- 4
For trapezoids and parallelograms, the third field is the height — enter it too.
Frequently asked questions
Why does the triangle calculator need base and height, not all three sides?
Area = ½ × base × height only requires those two values. If you have three sides instead, use Heron's formula: s = (a+b+c)/2, Area = √[s(s−a)(s−b)(s−c)]. The perimeter of a triangle also requires all three sides.
What units does the area use?
Area is always in squared units of whatever unit you enter. If you enter centimeters, the area is in cm². If meters, then m². The calculator does not assume any unit — it works with any consistent unit system.
How is the trapezoid perimeter estimated?
The perimeter formula shown assumes the trapezoid is isosceles (both legs equal). The two legs are calculated as √[((b−a)/2)² + h²] each. For a non-isosceles trapezoid, you would need the actual leg lengths rather than deriving them from a symmetry assumption.
Why is the ellipse perimeter an approximation?
The exact perimeter of an ellipse requires an infinite series (elliptic integrals) and has no simple closed form. Ramanujan's approximation π[3(a+b) − √((3a+b)(a+3b))] is accurate to within 0.005% for most practical ellipses and is far simpler to compute.
Area calculator for all common 2D shapes
Why area formulas differ by shape
Each shape's area formula is derived from first principles. Rectangle area is straightforward — length times width counts unit squares. Triangle area is half of its enclosing rectangle (½bh) because a diagonal cut always splits a rectangle in half. Circle area πr² is derived by integrating thin rings from center to edge, or by "unrolling" the circle into a triangle of base 2πr and height r, giving ½ × 2πr × r = πr².
Converting between area units
Area scales as the square of the linear unit. 1 meter = 100 cm, so 1 m² = 10,000 cm². 1 foot = 12 inches, so 1 ft² = 144 in². This squared relationship catches people out: a room that is twice as long and twice as wide has four times the floor area, not twice. Always square the conversion factor when converting area — never apply a linear conversion factor directly to an area value.
Area in architecture and land measurement
Architects calculate floor areas in m² or ft² to estimate material costs (flooring, paint, carpet). Land area is measured in acres (1 acre = 4,047 m²), hectares (10,000 m²), or square miles. A football field is about 0.53 acres. The shapes most commonly needed in construction are rectangles (rooms, plots), triangles (roofs, gables), circles (columns, wells), and trapezoids (irregular plots with one pair of parallel sides).
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