Area Calculator
Pick a shape, type its measurements and get the area, perimeter, a to-scale diagram and the working. Ten flat shapes, any unit, conversions to square feet, square meters and acres.
A = l × w
Perimeter: P = 2(l + w)
- Perimeter
- 40 ft
- A = l × w = 12 × 8 = 96 ft²
- P = 2(12 + 8) = 40 ft
Area in other units
| m² | 8.9187 |
| cm² | 89,186.9 |
| ft² | 96 |
| in² | 13,824 |
| yd² | 10.6667 |
| acres | 0.002204 |
| hectares | 0.000892 |
Area formulas at a glance
| Shape | Area | Perimeter |
|---|---|---|
| Square | A = s² | P = 4s |
| Rectangle | A = l × w | P = 2(l + w) |
| Triangle | A = ½ × b × h | see page |
| Trapezoid | A = ½ (a + b) × h | Add the two bases and both slanted legs |
| Parallelogram | A = b × h | P = 2(b + s) |
| Rhombus | A = (p × q) / 2 | P = 4 × √((p/2)² + (q/2)²) |
| Circle | A = πr² | C = 2πr |
| Semicircle | A = πr² / 2 | P = πr + 2r |
| Ellipse | A = π × a × b | see page |
| Regular polygon | A = n × s² / (4 × tan(π/n)) | P = n × s |
What area actually measures
Area counts how many unit squares fit inside a shape. A 12 ft × 8 ft floor holds 96 squares that are one foot on each side, so it has 96 ft². That's why area units are always "squared", and why doubling every length of a shape multiplies its area by four, not two.
Irregular shapes, such as an L-shaped room, can be split into rectangles and triangles; work each one out and add them. The square footage calculator does this for a list of areas.
Why a triangle is half of b × h
Slide the top corner sideways. The triangle leans, but its base and height stay the same, so its area never changes. Switch on the copy: two identical triangles always make a parallelogram of area b × h, so one triangle is half.
Area = ½ × 10 × 6 = 30 square units
Questions people ask
How do I calculate area?
Choose the formula for the shape: length × width for a rectangle, ½ × base × height for a triangle, πr² for a circle. Measure in one unit and the result is in that unit squared.
How do I find the area of an irregular shape?
Break it into simple shapes (rectangles, triangles, circle parts), compute each area and add them. Subtract any cut-outs such as a fireplace hearth.
What is the difference between area and perimeter?
Area is the surface inside the outline (square units). Perimeter is the length of the outline itself (plain units). A 4 × 4 square and a 2 × 8 rectangle have the same area, 16, but perimeters of 16 and 20.
How do I convert square feet to square meters?
Multiply by 0.092903. 100 ft² ≈ 9.29 m². To go the other way multiply by 10.7639.
Stuck on a word problem?
Paste a homework question or describe your project. The AI tutor names the formula and works it through step by step. Always check the result with the calculator above.