Area Calculator
Area is length × width for a rectangle, π × r^2 for a circle and base × height ÷ 2 for a triangle, so a 12 × 10 ft room is 120 sq ft and a circle with a 5 ft radius is about 78.54 sq ft. Pick a shape to see the formula and working, plus metric and acre conversions.
By the Calculators With Steps team · Updated November 10, 2026 · How we check our math
- Perimeter
- 44 ft
- Diagonal
- 15.6205 ft√(l² + w²)
- Square metres
- 11.1484 m²
Step-by-step working
- Formula: A = length × width
- A = l × w = 12 × 10 = 120 ft²
- Perimeter = 2 × (l + w) = 2 × (12 + 10) = 44 ft
- In square metres: 120 ft² × 0.09290304 = 11.1484 m²
Area in other units
| Unit | Area |
|---|---|
| Square millimetres (mm²) | 11,148,364.8 |
| Square centimetres (cm²) | 111,483.65 |
| Square metres (m²) | 11.1484 |
| Hectares (ha) | 0.001115 |
| Square kilometres (km²) | 0.000011 |
| Square inches (in²) | 17,280 |
| Square feet (ft²) | 120 |
| Square yards (yd²) | 13.3333 |
| Acres | 0.002755 |
| Square miles (mi²) | 0.000004 |
How to use the area calculator
- Choose the shape from the list. There are 12 options, including two ways to measure a triangle and a circle.
- Choose the length unit you measured in: mm, cm, m, km, inches, feet, yards or miles.
- Enter the measurements. Keep every length in the same unit.
You get the area in that unit squared (ft², m² and so on), the formula, the working, the perimeter where it can be found, and a table converting the area to every common unit, including acres and hectares.
Area formulas for common shapes
| Shape | Area formula | Example | Area |
|---|---|---|---|
| Square | A = s² | s = 10 | 100 |
| Rectangle | A = length × width | 12 × 10 | 120 |
| Triangle | A = ½ × base × height | b = 10, h = 6 | 30 |
| Triangle (3 sides) | A = √(s(s − a)(s − b)(s − c)) | 13, 14, 15 | 84 |
| Circle | A = πr² | r = 5 | 78.5398 |
| Ellipse | A = πab | a = 6, b = 4 | 75.3982 |
| Trapezoid | A = ½(a + b)h | 8, 12, h = 5 | 50 |
| Parallelogram | A = base × height | 10 × 6 | 60 |
| Rhombus | A = (p × q) ÷ 2 | diagonals 8 and 6 | 24 |
| Sector | A = (θ ÷ 360°) × πr² | r = 10, θ = 60° | 52.3599 |
| Regular polygon | A = ns² ÷ (4 tan(180° ÷ n)) | hexagon, s = 4 | 41.5692 |
In Heron’s formula, s is the semi-perimeter, (a + b + c) ÷ 2. For the 13-14-15 triangle, s = 21 and the area is √(21 × 8 × 7 × 6) = √7,056 = 84.
The height of a triangle, parallelogram or trapezoid is always measured at right angles to the base, not along a slanted side. If you only know a slanted side and part of the base, the Pythagorean theorem calculator can find the height.
Worked examples
A bedroom floor. A room measures 12 ft by 10 ft. Area = 12 × 10 = 120 ft², which is about 11.1484 m². The perimeter, useful for skirting boards, is 2 × (12 + 10) = 44 ft.
A round patio. A circular patio has a radius of 5 m. Area = π × 5² ≈ 78.5398 m², or about 845.3955 square feet, and the circumference is about 31.4159 m.
A building plot. A rectangular lot is 100 ft by 200 ft. Area = 20,000 ft², which is about 1,858.0608 m², 0.459137 acres or 0.185806 hectares.
A hexagonal table top. A regular hexagon with 4 m sides has an area of about 41.5692 m² and a perimeter of 24 m.
Converting square units
Squaring the unit squares the conversion factor too. One foot is 0.3048 m, but one square foot is 0.3048² = 0.09290304 m², not 0.3048 m².
| Unit | In square metres |
|---|---|
| 1 square inch | 0.00064516 m² |
| 1 square foot | 0.09290304 m² |
| 1 square yard | 0.83612736 m² |
| 1 acre (43,560 ft²) | 4,046.8564224 m² |
| 1 hectare | 10,000 m² |
| 1 square mile (640 acres) | 2,589,988.110336 m² |
These factors follow the international yard and pound definitions used by NIST, where 1 inch is exactly 2.54 cm. Convert any lengths to a single unit before you start, because mixing feet and inches is the most common source of wrong answers.
Irregular shapes and practical tips
- Split complex shapes. An L-shaped room is two rectangles. A room with a bay window is a rectangle plus a trapezoid. Work out each part and add them.
- Subtract cut-outs. For a lawn with a round flower bed, find the rectangle’s area and subtract the circle.
- Buy a little extra. Flooring, tiles and turf are usually bought with 5 to 10% extra for cutting and waste. The square footage calculator adds that allowance and works out cost.
- Need depth as well? If you are pouring a slab or filling a bed, area alone is not enough. Use the volume calculator or the concrete calculator.
- Measure twice. A 1-inch error on each side of a 12 × 10 ft room changes the area by almost 2 square feet.
Area Calculator: frequently asked questions
How do you calculate area in square feet?
Measure the length and width in feet and multiply them. A room 12 ft long and 10 ft wide is 12 × 10 = 120 square feet. If you measured in inches, multiply and then divide by 144, because one square foot is 144 square inches.
How do you calculate the area of a circle?
Use A = πr², where r is the radius. A circle with a radius of 5 m has an area of π × 25 ≈ 78.5398 m². If you know the diameter, halve it first: a 10 m diameter gives the same 5 m radius.
How do you find the area of a triangle?
With the base and the perpendicular height, A = ½ × base × height, so a base of 10 and a height of 6 give 30. With only the three sides, use Heron's formula: sides 13, 14 and 15 give an area of 84.
How do I calculate the area of a trapezoid?
Average the two parallel sides and multiply by the height: A = ½ × (a + b) × h. With parallel sides of 8 and 12 and a height of 5, the area is 10 × 5 = 50.
How many square feet are in an acre?
One acre is exactly 43,560 square feet, or about 4,046.86 m². A 100 ft × 200 ft lot is 20,000 square feet, which is about 0.459137 acres or 0.185806 hectares.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and circles, find each area and add them. An L-shaped room made of a 12 × 10 ft section and a 6 × 4 ft section has an area of 120 + 24 = 144 square feet.
How do you convert square metres to square feet?
Multiply by about 10.7639, because one foot is exactly 0.3048 m and one square foot is 0.09290304 m². For example, 50 m² is about 538.1955 square feet.
What is the difference between area and perimeter?
Area measures the surface inside a shape in square units. Perimeter measures the distance around it in ordinary units. A 12 × 10 ft room has an area of 120 square feet and a perimeter of 44 feet.
How we checked this page: every figure in the examples and FAQs above is produced by this calculator and verified by automated tests against known answers, and the rules and rates come from the sources below. Last updated . Spotted a problem? Tell us.
Sources and further reading