Area Calculator

• Circle: π × r² (where r is radius)
• Rectangle: length × width
• Triangle: (base × height) / 2
• Square: side² (side length squared)
• Ellipse: π × a × b (where a and b are semi-major and semi-minor axes)
• Trapezoid: ((a + c) × h) / 2 (where a and c are parallel sides, h is height)
• Parallelogram: base × height

• 1 square meter (m²) = 10.7639 square feet (ft²)
• 1 hectare (ha) = 10,000 square meters (m²)
• 1 acre = 43,560 square feet (ft²)
• 1 square kilometer (km²) = 247.105 acres
• 1 square mile = 640 acres
• 1 square yard (yd²) = 9 square feet (ft²)
• 1 square inch (in²) = 6.4516 square centimeters (cm²)

For irregular or complex shapes, several methods can be used:

• Decomposition: Breaking down into simpler shapes and adding their areas
• Grid Method: Counting squares on grid paper that the shape covers
• Coordinate Geometry: Using the Shoelace formula for polygons with known vertices
• Calculus: Using integrals for curved boundaries
• Heron's Formula: For triangles when only side lengths are known: √(s(s-a)(s-b)(s-c)) where s=(a+b+c)/2

For 3D objects, surface area calculations include:

• Cube: 6 × side²
• Rectangular Prism: 2(length × width + length × height + width × height)
• Sphere: 4π × radius²
• Cylinder: 2π × radius × height + 2π × radius²
• Cone: π × radius × slant height + π × radius²
• Pyramid: Base area + sum of triangular face areas

• Flooring: Calculating material needs for tiles, carpet, or hardwood
• Painting: Determining paint quantity for walls and ceilings
• Roofing: Estimating shingles or other roofing materials
• Land Development: Planning building footprints and zoning requirements
• Cost Estimation: Calculating material and labor costs based on area

• Crop Planning: Calculating seed quantities and yield estimates
• Irrigation: Determining water requirements based on field area
• Fertilization: Calculating application rates per unit area
• Land Valuation: Assessing property value based on usable area
• Garden Design: Planning plant spacing and layout
• Lawn Care: Determining fertilizer, seed, and treatment quantities

• Physics: Calculating pressure (force per unit area)
• Fluid Dynamics: Determining flow rates through openings
• Heat Transfer: Calculating thermal conductivity across surfaces
• Solar Energy: Sizing solar panel installations
• Aerodynamics: Calculating drag and lift based on surface area
• Material Science: Determining material properties per unit area

Example 1: Painting a Room

To calculate paint needed for a room with dimensions 4m × 5m with 2.5m height:

1. Wall area: 2 × (4m + 5m) × 2.5m = 45m²
2. Subtract for windows/doors (approx. 5m²): 45m² - 5m² = 40m²
3. With paint coverage of 10m²/liter: 40m² ÷ 10m²/liter = 4 liters needed

Example 2: Flooring Installation

For a rectangular living room measuring 6m × 4m:

1. Floor area: 6m × 4m = 24m²
2. Add 10% for waste: 24m² × 1.1 = 26.4m²
3. With flooring sold in 2m² boxes: 26.4m² ÷ 2m² = 13.2 boxes (round up to 14)

Example 1: Agricultural Planning

For a triangular field with base 200m and height 150m:

1. Field area: (200m × 150m) ÷ 2 = 15,000m²
2. Convert to hectares: 15,000m² ÷ 10,000 = 1.5 hectares
3. Seed requirement at 25kg/hectare: 1.5ha × 25kg/ha = 37.5kg seed needed

Example 2: Commercial Roofing

For a gabled roof with two rectangular sections each 12m × 8m:

1. Each section area: 12m × 8m = 96m²
2. Total roof area: 2 × 96m² = 192m²
3. With shingles covering 0.5m² each: 192m² ÷ 0.5m² = 384 shingles
4. Add 15% for waste and overlaps: 384 × 1.15 = 442 shingles needed