How to calculate area
Area is the amount of flat space inside a two-dimensional shape, measured in square units such as square feet (ft²) or square meters (m²). To calculate area, measure the lengths the area formula for your shape needs, convert them to the same unit, and multiply as the formula says. This area calculator converts for you, so each length can be entered in a different unit.
When you mix units, the result is shown in every unit you used, with the conversion steps. For example, a rectangle 12 ft long and 3 yd wide is 12 × 9 = 108 ft², which is the same as 4 × 3 = 12 yd².
Area formulas
Here l is a length, w a width, r a radius, b a base, h a height measured at a right angle to the base, and a, b, c are sides or semi-axes.
| Shape | Area formula |
|---|---|
| Rectangle | A = l × w |
| Circle | A = πr² |
| Triangle | A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ⁄ 2 |
| Trapezoid | A = (b₁ + b₂) ⁄ 2 × h |
| Parallelogram | A = b × h |
| Sector | A = r²θ ⁄ 2 (θ in radians) |
| Ellipse | A = πab |
Area of a circle
Square the radius and multiply by π (about 3.14159). A circle with a 10 ft radius covers π × 10² ≈ 314.16 ft². If you measured the diameter, halve it first. A sector, or pie slice, is the same circle scaled by its angle: a 60° slice of a 12 ft circle is 12² × (π ⁄ 3) ⁄ 2 ≈ 75.40 ft².
Area of a triangle
With a base and a height, the area is half of base × height. When you only know the three side lengths, this calculator uses Heron's formula: find the semiperimeter s = (a + b + c) ⁄ 2, then A = √(s(s − a)(s − b)(s − c)). A triangle with sides 13, 14, and 15 ft has s = 21 and A = √(21 × 8 × 7 × 6) = 84 ft². The three sides only form a triangle when each one is shorter than the other two added together.
Area of a trapezoid
Average the two parallel sides and multiply by the height between them. A trapezoid with bases of 12 and 20 ft and a height of 8 ft is (12 + 20) ⁄ 2 × 8 = 128 ft². A parallelogram is simpler, base × height, as long as the height is measured straight across rather than along the slanted side.
What the result includes
- The area in the square version of each length unit you entered, with the steps.
- The same area in common units: square feet, square yards, square inches, acres, square miles, square meters, hectares, square kilometers, and square centimeters.
| Unit | Equals |
|---|---|
| 1 square foot | 144 square inches ≈ 0.0929 square meters |
| 1 square yard | 9 square feet ≈ 0.836 square meters |
| 1 acre | 43,560 square feet ≈ 4,047 square meters |
| 1 square mile | 640 acres ≈ 2.59 square kilometers |
| 1 hectare | 10,000 square meters ≈ 2.471 acres |
Frequently asked questions
How do I convert square feet to acres?
Divide square feet by 43,560. A lot 150 ft wide and 290.4 ft deep is 43,560 ft², exactly one acre. Enter a rectangle in feet and read the acres row under the result.
What is the area of a rectangle?
Area = length × width. A 24 ft by 15 ft room is 360 square feet. For an L-shaped room, split it into two rectangles and add their areas.
How do I find the area of an irregular shape?
Break it into rectangles, triangles, circles, or sectors, find each area separately, and add them together. Subtract the area of any cut-out, such as a round pool inside a rectangular yard.
Why is area in square units?
Area multiplies two lengths, so the unit is multiplied too: feet × feet = square feet. That is also why 1 yd² is 9 ft², not 3 ft²: a yard is 3 feet in both directions.
Limitations
The formulas assume ideal flat shapes with straight sides, true circles, and heights measured at right angles. Real land or floor plans are rarely perfect, and land area on a large scale also follows the curve of the earth. Results are rounded to 10 significant digits, or 8 when shown in scientific notation.
What's changed
- Launched.
References
- Wolfram MathWorld, Heron's Formula
triangle area from three sides
- Wolfram MathWorld, Trapezoid
trapezoid area formula
- Wolfram MathWorld, Circular Sector
sector area, r²θ ⁄ 2
- Wolfram MathWorld, Ellipse
ellipse area, πab
- NIST, U.S. Survey Foot
the foot is exactly 0.3048 m, and the acre is now defined from this international foot