See the difference on one rectangle
For a 12 ft × 10 ft rectangle, multiply the two sides to calculate 120 ft² of area. Add all four sides to calculate 44 ft of perimeter. The numbers are not interchangeable.
Formula comparison
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle (l,w) | lw | 2(l+w) |
| Square (s) | s² | 4s |
| Circle (r) | πr² | 2πr (circumference) |
| Triangle (b,h; sides a,b,c) | bh/2 | a+b+c |
A triangle's base and height determine its area, but do not necessarily determine its perimeter. Finding the perimeter requires its three side lengths.
An important surprise: the same perimeter can mean different area
Compare a square 10 ft × 10 ft and a rectangle 15 ft × 5 ft:
10 × 10: P = 40 ft, A = 100 ft²
15 × 5: P = 40 ft, A = 75 ft²
Both need the same boundary length, but the square encloses 25 more square feet. For a given perimeter, a square has the greatest area among rectangles. That is why knowing the fence length alone does not determine how much land it encloses.
Which one does your project need?
Choose area for…
Flooring, paintable surfaces, grass coverage, rugs, panels and the space inside a boundary.
Choose perimeter for…
Fencing, trim, edging, framing and the total length around an outline.
Errors to catch before you buy materials
If you multiplied the sides but wrote “feet,” your unit is wrong: the result is square feet. If you added sides but wrote “square feet,” you calculated boundary length and labeled it as area. Complex shapes may need their areas split into pieces, while the perimeter must follow the exterior border only.
To compute area for common shapes, use our Area Calculator. For a real room example, continue to how to measure square footage.