Calculate the area, perimeter, circumference, and arc length for Rectangles, Triangles (Heron's Formula), Trapezoids, Circles, Sectors, Ellipses, and Parallelograms with complete multi-unit conversions.
• Select a 2D shape tab above, customize linear dimensions and units, then click Calculate.
• Results are automatically converted into metric units ($m^2, cm^2, km^2$), imperial units ($ft^2, in^2, yd^2, mi^2$), Acres, and Hectares.
Calculate the surface area of a rectangle or square.
Formulas, proofs, real-world surface coverage metaphors, and polygon decomposition strategies.
Area is the quantity that expresses the extent of a two-dimensional region or shape in the planar surface. An intuitive way to understand area is the amount of paint required to cover the surface without overlapping, or the number of unit squares (such as 1 m × 1 m) that fit completely inside the boundary.
Standard international measurement units include square meters (m²), square centimeters (cm²), square feet (ft²), acres, and hectares (1 ha = 10,000 m²).
Perimeter: P = 2(l + w). For a square where l = w = s, Area = s².
Where semi-perimeter s = (a + b + c) / 2. Alternatively, standard Area = (1/2) · Base · Height.
The average length of the parallel bases multiplied by the perpendicular height h.
Circumference C = 2πr, Diameter d = 2r.
Arc length L = r · θ_rad.
Semi-major axis a, semi-minor axis b.
Real-world floorplans, land parcels, and architectural elevations are rarely single perfect rectangles. To calculate the total area of any irregular polygon:
One international acre is exactly equal to 43,560 square feet (or approximately 4,046.86 square meters). One hectare equals 10,000 square meters (approx. 2.471 acres).
The Triangle Inequality Theorem states that the sum of any two side lengths must be strictly greater than the third side (a + b > c, a + c > b, b + c > a). If this condition fails, the three sides cannot connect in 2D space to form a closed triangle, and Heron's formula would yield an imaginary or zero area.
First convert all linear measurements into a single unified unit before multiplying. In our calculator, each input has an independent unit dropdown that automatically normalizes dimensions into standard meters before evaluating.
A circle represents the complete 360° disk (Area = πr²). A sector represents a fractional wedge of that circle defined by central angle θ (Area = (θ/360°) · πr²).