Find the area of any shape.
Pick a shape, type its dimensions, and see the area, the perimeter, and a labeled diagram update as you go. Every formula is spelled out with your own numbers.
Your shape
What the numbers mean
The same area in other units
Your dimensions are treated as generic lengths in the unit you picked. Here is that area expressed in other square units.
Result scorecard
How area grows when you scale the shape
Multiply every length by a factor and the area changes by the factor squared. Double the size and the area is 4 times as large.
| Scale | Longest side | Area | Perimeter | Area vs now |
|---|
Area, explained
Area Formulas for Common Shapes
Rectangle: A = length × width. Circle: A = πr². Triangle: A = ½ × base × height. Trapezoid: A = ½ × (base₁ + base₂) × height. Ellipse: A = π × a × b (where a and b are semi-major and semi-minor axes). These formulas cover the most common shapes encountered in everyday calculations.
Understanding Area Units
Area is measured in square units, square feet (ft²), square meters (m²), acres, hectares, etc. When converting, remember that 1 m² = 10.764 ft², 1 acre = 43,560 ft², and 1 hectare = 10,000 m². Always ensure all dimensions are in the same unit before calculating.
Irregular Shapes
For irregular shapes, divide them into recognizable shapes, calculate each area separately, and sum them. Alternatively, use the grid method (counting squares) or calculus for complex curves. Many real-world areas (rooms, lots) can be broken into rectangles and triangles.
Practical Applications
Area calculations are essential for home improvement (paint, flooring, tiling), landscaping (sod, mulch), construction (roofing, concrete), real estate (lot size), agriculture (crop planning), and manufacturing (material estimation). Accurate area measurements save time and money.
Common questions
How do I calculate the area of an irregular shape?
Break it into regular shapes (rectangles, triangles, circles), calculate each area, then add them up. Subtract areas for cutouts. For very complex shapes, use coordinate geometry or graphing tools.
What is the area of a circle with diameter 10?
The radius is 5 (half the diameter). Area = π × 5² = 25π ≈ 78.54 square units.
How do I convert between area units?
Square the linear conversion factor. Since 1 foot = 12 inches, 1 ft² = 144 in². Since 1 meter ≈ 3.281 feet, 1 m² ≈ 10.764 ft².
What is pi (π)?
Pi (π) is the ratio of a circle's circumference to its diameter, approximately 3.14159265. It is an irrational number that appears in all circle-related formulas.
Results are geometric estimates based on the dimensions you enter. Measure carefully and keep every length in the same unit before you calculate.