Area Calculator
12 shapes · Formulas and steps · Square feet · m² · Acres
⬛ Pick a shape and enter its dimensions to see the area, perimeter, formula steps, and unit conversions.
What Is Area?
Area is the amount of flat surface inside a closed shape. It is measured in square units: a square that is 1 foot on each side covers 1 square foot (ft²), and a square 1 meter on each side covers 1 square meter (m²). This area calculator finds the area of 12 common shapes, shows the formula with your numbers substituted, and converts the answer to square feet, square meters, acres, hectares, and other units.
Area and perimeter are different measurements. Perimeter is the distance around the edge, in plain length units, while area is the surface inside, in square units. A 12 ft by 10 ft room has a perimeter of 44 ft (for baseboard) and an area of 120 ft² (for flooring). The calculator reports both, where the inputs allow it.
People use area to estimate flooring, tile, carpet, paint, sod, mulch, roofing, land size, and fabric, and to solve geometry homework. Each shape tab uses the standard geometry formula listed in the table below.
How to Use the Area Calculator
- Choose a shape. The tabs cover rectangle, square, triangle by base and height, triangle by three sides, circle, ellipse, trapezoid, parallelogram, rhombus, circular sector, regular polygon, and ring (annulus).
- Pick a length unit. Enter every length in that unit. Angles are in degrees, and the polygon side count is a whole number.
- Enter the dimensions. The result updates as you type. Heights must be perpendicular to the base, not the slanted side.
- Read the results. The hero shows the area in your unit squared. Below it are the perimeter, conversions, the substituted formula, and a chart that compares your shape with a square and a circle that have the same perimeter.
Conversions use exact factors: 1 inch = 2.54 cm and 1 foot = 0.3048 m. Results are rounded for display only; calculations keep full precision.
Area Formulas for Every Shape
| Shape | Area formula | Example |
|---|---|---|
| Rectangle | l × w | 12 × 10 = 120 |
| Square | a² | 10² = 100 |
| Triangle | ½ × b × h | ½ × 8 × 5 = 20 |
| Circle | πr² | π × 3² = 28.27 |
| Ellipse | πab | π × 5 × 3 = 47.12 |
| Trapezoid | ½ × (a + b) × h | ½ × 16 × 4 = 32 |
| Parallelogram | b × h | 10 × 6 = 60 |
| Rhombus | (p × q) ÷ 2 | 8 × 6 ÷ 2 = 24 |
| Sector | (θ ÷ 360) × πr² | 60° of r 6 = 18.85 |
| Regular polygon | n s² ÷ (4 tan(180°/n)) | hexagon, s 4 = 41.57 |
| Ring | π(R² − r²) | π(25 − 9) = 50.27 |
The ellipse perimeter has no exact elementary formula, so the calculator uses Ramanujan's approximation P ≈ π[3(a + b) − √((3a + b)(a + 3b))], which gives 25.53 for a = 5, b = 3.
How to Calculate Area Manually: Worked Examples
Every example uses the same steps: write the formula, substitute the measurements in one unit, compute, and label the answer in square units.
Square Unit Conversions
An area factor is the length factor squared. Because 1 ft = 0.3048 m exactly, 1 ft² = 0.3048² = 0.09290304 m².
| Unit | Equals |
|---|---|
| 1 ft² | 144 in² = 0.09290304 m² |
| 1 m² | 10.7639 ft² = 10,000 cm² |
| 1 yd² | 9 ft² = 0.83613 m² |
| 1 acre | 43,560 ft² = 4,046.8564224 m² |
| 1 hectare | 10,000 m² = 2.4711 acres |
| 1 mi² | 640 acres = 2.59 km² |
Area of Irregular Shapes
An irregular shape has no single formula, but most can be split into rectangles, triangles, and circle parts. Find each piece and add them, or subtract a cutout from a larger shape.
A running track with semicircle ends is a rectangle plus one full circle. A ring is a large circle minus a small one, which is what the ring tab computes. For a curved garden bed, measure several widths at equal spacing along its length and multiply the average width by the length to estimate the area.
Using Your Area Result: Flooring, Paint, Land, and the Chart
Flooring and tile. Divide the area by the coverage of one box. A 120 ft² floor with boxes that cover 20 ft² needs 6 boxes, or 7 after adding about 10% for cuts. For an open plan, measure each section separately and add the areas.
Paint. Wall area is the room perimeter times the wall height, minus doors and windows. A 12 by 10 ft room with 8 ft walls has 44 × 8 = 352 ft² of wall before openings. Compare that with the coverage printed on the paint can.
Land. Lots and fields are often quoted in acres or hectares. Divide square feet by 43,560 for acres, or square meters by 10,000 for hectares.
Reading the chart. For a fixed perimeter, a circle encloses more area than any other shape. The chart and verdict compare your shape with that circle: a square reaches 78.5%, a regular hexagon 90.7%, and a long thin rectangle far less. Put the other way, a round shape needs the shortest boundary for a given area.
Common Mistakes When Calculating Area
- Diameter instead of radius. πr² needs the radius. Using a 6 inch diameter as r gives 113.10 in² instead of 28.27 in², four times too large.
- Slanted side instead of height. Triangles, parallelograms, and trapezoids need the perpendicular height. The parallelogram tab asks for both and checks that the height is not longer than the side.
- Mixing units. 12 ft by 30 inches must become 12 ft × 2.5 ft = 30 ft², not 12 × 30 = 360.
- Converting square units with the length factor. 1 yd = 3 ft, but 1 yd² = 9 ft². Divide square feet by 9 for square yards of carpet.
- Triangle sides that do not close. Sides 2, 3, and 6 cannot form a triangle because 2 + 3 is less than 6. The calculator flags this instead of returning a false area.
- Buying exactly the floor area. Flooring and tile need extra for cuts and waste; installers often add 5% to 15%, depending on the layout.
Frequently Asked Questions
Sources & References
- NIST. U.S. Survey Foot: Revised Unit Conversion Factors (acre = 43,560 ft² = 4,046.8564224 m²). nist.gov
- NIST. Putting the Best Foot Forward: Ending the Era of the U.S. Survey Foot (1 ft = 0.3048 m exactly from 2023). nist.gov
- OpenStax. Prealgebra 2e, 9.4 Use Properties of Rectangles, Triangles, and Trapezoids. openstax.org
- OpenStax. Prealgebra 2e, 9.5 Solve Geometry Applications: Circles and Irregular Figures. openstax.org
- Weisstein EW. Heron's Formula, Ellipse, and Regular Polygon. Wolfram MathWorld. Heron · Ellipse · Polygon
Results are for educational and estimating purposes. Confirm measurements on site before ordering materials. Methodology reviewed: 2026.