Area Calculator
Professional area calculator for various geometric shapes. Calculate area and perimeter of squares, rectangles, triangles, circles, trapezoids, parallelograms, and ellipses with step-by-step solutions.
Square Area Calculator
Rectangle Area Calculator
Triangle Area Calculator
Circle Area Calculator
Trapezoid Area Calculator
Parallelogram Area Calculator
Ellipse Area Calculator
Understanding Area
Area is the measure of the space inside a two-dimensional shape. It's expressed in square units and is fundamental in geometry, engineering, and many practical applications.
Area Formulas
| Shape | Formula | Description |
|---|---|---|
| Square | A = s² | Side length squared |
| Rectangle | A = l × w | Length times width |
| Triangle | A = ½ × b × h | Half base times height |
| Circle | A = πr² | Pi times radius squared |
| Trapezoid | A = ½ × (b₁ + b₂) × h | Half sum of bases times height |
| Parallelogram | A = b × h | Base times height |
| Ellipse | A = π × a × b | Pi times major axis times minor axis |
Perimeter/Circumference Formulas
- Square: P = 4s (4 times side length)
- Rectangle: P = 2(l + w) (2 times sum of length and width)
- Circle: C = 2πr (2 times pi times radius)
- Triangle: Sum of all three sides
Applications
- Construction: Flooring, painting, landscaping
- Architecture: Room design, building planning
- Engineering: Material calculations, structural design
- Agriculture: Field measurements, crop planning
- Real Estate: Property valuation, lot sizing
- Manufacturing: Material usage, cost estimation
Units of Measurement
- Metric: Square meters (m²), square centimeters (cm²)
- Imperial: Square feet (ft²), square inches (in²)
- Conversion: 1 m² = 10.764 ft², 1 ft² = 0.093 m²
Special Cases
- Right Triangle: Area = ½ × base × height
- Equilateral Triangle: Area = (√3/4) × side²
- Regular Polygon: Area = ½ × perimeter × apothem
- Composite Shapes: Break into simple shapes and add areas
Note
This calculator provides accurate area calculations for basic geometric shapes. For complex shapes or 3D volumes, consider using specialized geometric software.