How to Calculate Area and Perimeter of Shapes

Area and perimeter are fundamental geometric measurements used in construction, interior design, land surveying, and everyday practical tasks. Area measures the space enclosed within a shape (in square units), while perimeter measures the total length of the boundary. Different shapes require different formulas, though the underlying logic is consistent.

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Formula

$$Circle:\ A = \pi r^2 \quad Rectangle:\ A = l \times w \quad Square:\ A = s^2$$

Area & Perimeter Calculator

Calculate area and perimeter for circle, rectangle, triangle, or square.

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Worked Example

Given:

Shape = RectangleLength (l) = 8 mWidth (w) = 5 m

ResultArea: 40 m² — Perimeter: 26 m

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FAQs

Why is π used in circle area calculations?

π (pi) is the ratio of a circle's circumference to its diameter — approximately 3.14159. It appears in circle formulas because circles are defined by their relationship to π. The area formula A = πr² can be understood by imagining the circle rearranged into a near-rectangle of height r and width πr.

How do I calculate the area of an irregular shape?

Break the irregular shape into regular sub-shapes (rectangles, triangles, circles) whose areas you can calculate separately, then add them together. Alternatively, the surveyor's formula or integration can handle complex irregular shapes. For land areas, GPS and GIS tools provide direct measurements.

What is the difference between area and surface area?

Area measures the 2D space enclosed by a flat shape. Surface area measures the total area of all faces of a 3D object — the amount of material needed to cover it. For example, the surface area of a cube with side s is 6s², while its volume is s³.