How to use
- Choose a shape and a length unit.
- Enter the dimensions — area and perimeter appear instantly. Area is shown in the square of your unit (for example ft²), with conversions to square meters or square feet.
- The formula used is shown under the result, along with extras such as the diagonal, diameter, arc length or interior angle.
Area and perimeter formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | width × height | 2 × (width + height) |
| Triangle (base & height) | base × height ÷ 2 | needs all three sides |
| Triangle (three sides) | √(s(s−a)(s−b)(s−c)), s = (a+b+c)÷2 | a + b + c |
| Circle | πr² | 2πr |
| Trapezoid | (top + bottom) × height ÷ 2 | sum of four sides |
| Parallelogram | base × height | 2 × (base + side) |
| Ellipse | π × a × b | Ramanujan: π(a+b)(1 + 3h÷(10+√(4−3h))) |
| Sector | πr² × θ ÷ 360° | 2r + arc (arc = 2πr × θ ÷ 360°) |
| Regular n-gon | n × s² ÷ (4 tan(180°÷n)) | n × s |
An ellipse’s perimeter has no simple exact formula, so the tool uses Ramanujan’s second approximation (with h = ((a−b)÷(a+b))²), which is accurate to a tiny fraction for everyday shapes.
Examples
- Triangle with sides 3, 4 and 5 ft: s = 6, area = √(6×3×2×1) = 6 ft² (a right triangle, so it equals 3 × 4 ÷ 2).
- Circle with radius 5 ft: area = π × 25 ≈ 78.54 ft², circumference ≈ 31.42 ft.
- Trapezoid with bases 4 and 8 ft and height 3 ft: (4 + 8) × 3 ÷ 2 = 18 ft².
- Regular hexagon with 2 ft sides: 6 × 4 ÷ (4 × tan 30°) ≈ 10.39 ft².
Things to watch
- Height means the perpendicular height. For triangles, parallelograms and trapezoids, using a slanted side as the height overstates the area.
- For three sides to form a triangle, the longest side must be shorter than the other two combined.
- Area units are squared length units: 1 ft² = 144 in², and 1 m² = 10,000 cm². The conversions below the result help when mixing units.
FAQ
How do I find the square footage of a room?
Measure length and width in feet and use the rectangle. For L-shaped rooms, split the floor into rectangles and add the areas. To convert between area units, see the area converter.
Can I estimate materials from the area?
Yes — the tile calculator and paint calculator turn an area into tile counts or gallons, including waste.