Area Calculator

Our Area Calculator simplifies the computation of area and perimeter for common geometric shapes: rectangles, circles, triangles, trapezoids, and ellipses. This tool is invaluable for students, engineers, and DIY enthusiasts who need quick and accurate measurements for projects ranging from home renovations to complex design work.

For rectangles, area is length * width and perimeter is 2 * (length + width). Circles use π * radius² for area and 2 * π * radius for perimeter. Triangles use 0.5 * base * height for area. Because only the base and height are entered, the perimeter assumes an isosceles triangle with two equal sides of √((base/2)² + height²); a triangle with unequal sides has the same area but a different perimeter. Trapezoids calculate area as 0.5 * (side a + side b) * height, and the perimeter likewise assumes two equal legs of √(((b − a)/2)² + height²). Ellipses use π * semi-major axis * semi-minor axis for area. Their exact perimeter is an elliptic integral with no simple closed form, so the calculator uses Ramanujan's approximation, π * [3(a + b) − √((3a + b)(a + 3b))].

Ensure you use consistent units for all measurements (e.g., all meters or all feet) to avoid incorrect results. For triangles, always use the perpendicular height to the base, not a slanted side. When dealing with ellipses, be mindful that the perimeter calculation is an approximation unless using advanced methods, so understand the limitations of the formula provided.