Area Calculator – Common Shapes
Calculate the area of common shapes: rectangle, circle, triangle, and trapezoid.
Common Area Formulas
Area measures the two-dimensional space inside a shape. Essential formulas:
- Rectangle: A = length × width
- Triangle: A = ½ × base × height
- Circle: A = pi × r²
- Trapezoid: A = ½ × (base1 + base2) × height
- Parallelogram: A = base × height
- Ellipse: A = pi × a × b (where a and b are semi-axes)
Area is always expressed in square units (cm², m², ft², acres, hectares).
Converting Area Units
Key conversions: 1 m² = 10.764 ft². 1 acre = 43,560 ft² = 4,047 m². 1 hectare = 10,000 m² = 2.471 acres. 1 km² = 100 hectares = 247.1 acres. 1 square mile = 640 acres = 2.59 km².
For context: a tennis court is about 260 m² (2,800 ft²). A football (soccer) pitch is about 7,000 m² (1.7 acres). A typical US home lot is 0.15–0.25 acres.
Real-World Area Calculations
Flooring: Measure room dimensions, add 10% for waste and cuts. Painting: Calculate wall area minus windows and doors. Landscaping: Measure lawn area for seed, fertilizer, or sod quantities. Roofing: Account for pitch — a steeper roof has more surface area than its footprint. Land: Irregular plots can be divided into triangles and rectangles, calculated individually, then summed.
Frequently Asked Questions
How do I measure the area of an irregular shape?
Break it into regular shapes (rectangles, triangles), calculate each, and sum them. For very irregular shapes, use the grid method: overlay a grid and count full and partial squares. Digital tools can trace outlines on maps for land area.
What is the difference between square feet and linear feet?
Linear feet measures length in one dimension. Square feet measures area in two dimensions. A 10 ft × 12 ft room is 120 square feet but has a 44 linear foot perimeter. Flooring is sold by square feet; baseboards by linear feet.
How do I calculate the area of a circle from diameter?
A = pi × (d/2)² = pi × d²/4. For a 10-foot diameter circle: A = 3.14159 × 25 = 78.5 square feet.