Area Calculator with Perimeter and Unit Conversion
Choose a plane shape, enter only the dimensions that define it, and calculate area plus perimeter or circumference where possible. The calculator converts every measurement through a single base unit and displays the exact shape formula and substitution.
Shape and dimensions
Area and perimeter results
Area formulas and measurement rules
This area calculator provides a dedicated calculation workflow rather than a generic converter. Area describes the amount of a plane enclosed by a boundary. Perimeter measures the boundary length, so area and perimeter must never be reported in the same type of unit.
Rectangles, squares and parallelograms
Rectangle area is length × width. A square uses side². A parallelogram uses base × perpendicular height; its slanted side is needed only for perimeter.
Triangles and trapezoids
Triangle area is one half of base × perpendicular height. A trapezoid averages the two parallel bases and multiplies by height. Additional side lengths are used for perimeter.
Circles, annuli and ellipses
Circle area is πr² and circumference is 2πr. An annulus subtracts the inner circle from the outer circle. Ellipse area is πab; its perimeter is approximated with Ramanujan’s accurate formula.
Rhombi and regular polygons
A rhombus area can be computed as half the product of its diagonals. A regular polygon with n sides of length s has area ns² ÷ [4 tan(π/n)] and perimeter ns.
Converting square units correctly
One foot is 12 inches, but one square foot is 144 square inches. The calculator squares the length conversion factor instead of applying a linear conversion to the final area.
Why does triangle height need to be perpendicular?
The area formula uses the shortest perpendicular distance from the base line to the opposite vertex.
Can the calculator find an irregular shape area?
No. Divide an irregular outline into supported shapes or use coordinate-survey methods.
Why is ellipse perimeter approximate?
Unlike circle circumference, ellipse perimeter has no simple elementary closed form; the calculator uses a high-accuracy approximation.