Area & Perimeter Calculator with Shapes
Select a shape, enter its dimensions, and instantly see the calculated area and perimeter along with a scaled SVG drawing of the shape with labeled measurements. Supports rectangles, squares, circles, triangles, trapezoids, parallelograms, and ellipses.
Area and Perimeter Formulas for Common Shapes
Area measures the space inside a shape, while perimeter (or circumference for circles) measures the total length around the outside. These are two of the most fundamental measurements in geometry, used in construction, landscaping, interior design, manufacturing, and everyday problem-solving.
Rectangle
Area = length x width. Perimeter = 2(length + width). The diagonal can be found using the Pythagorean theorem: d = sqrt(length^2 + width^2). Rectangles are the most common shape in architecture and design.
Circle
Area = pi x radius^2. Circumference = 2 x pi x radius. Given the diameter, radius = diameter/2. Circles maximize the area enclosed for a given perimeter, which is why bubbles and planets tend toward spherical shapes.
Triangle
Area = 1/2 x base x height. Perimeter = sum of all three sides. For a right triangle, the hypotenuse can be found with the Pythagorean theorem. Heron's formula allows calculating area from three side lengths: Area = sqrt(s(s-a)(s-b)(s-c)) where s is the semi-perimeter.
Trapezoid
Area = 1/2 x (base1 + base2) x height. The perimeter is the sum of all four sides. Trapezoids appear in roof cross-sections, bridge supports, and table designs.
Real-World Applications
Calculating area helps you determine how much paint covers a wall, how much carpet fills a room, how much soil fills a garden bed, or how much fabric covers a cushion. Perimeter calculations tell you how much fencing surrounds a yard, how much trim goes around a window, or how much edging borders a path. These formulas save time, money, and material.