By Josh Infiesto • Updated Aug 30, 2022
Image: Kwanchai_Khammuean/iStock/GettyImages
The perimeter of a shape is the total length around its outer boundary, while the area measures the two‑dimensional space it occupies. The ratio of perimeter to area is simply the perimeter divided by the area. This metric is useful in engineering, design, and geometry to compare the compactness of different shapes.
Measure the distance from the center to the circumference; this value is the radius r.
The perimeter of a circle is calculated with C = 2πr.
The area is given by A = πr².
Divide the perimeter by the area: R = C ÷ A. For a circle, this simplifies to R = 2/r, indicating that smaller radii yield larger ratios.
Identify the rectangle’s base b (longer side) and width w (shorter side).
The perimeter is P = 2(b + w).
The area is A = b × w.
Divide the perimeter by the area: R = P ÷ A = 2(b + w)/(b × w). This ratio decreases as the rectangle becomes more proportionate.
For any shape, find its perimeter and area, then compute the ratio by dividing the perimeter by the area. If you encounter a complex shape, decompose it into rectangles or other basic shapes to apply these formulas.
