Area Calculator
Calculate the area of common 2D shapes. Select your shape and enter the required dimensions to find area, perimeter, and conversions to different units.
For rectangle, parallelogram, or one side of trapezoid
For rectangle or second side of trapezoid
For square
For triangle or parallelogram
Perpendicular height for triangle, trapezoid, or parallelogram
For circle
For ellipse - longer radius
For ellipse - shorter radius
What is area and how is it measured?
Area is the amount of space inside a 2D shape, measured in square units (sq ft, sq m, acres, etc.). It tells you how much surface the shape covers. Common formulas: Rectangle = length × width, Square = side², Triangle = ½ × base × height, Circle = π × radius². Always square your units: 5 ft × 4 ft = 20 ft². Used in: Real estate (house size), flooring, painting (wall coverage), landscaping, farming (field size). Larger units: 1 acre = 43,560 sq ft, 1 hectare = 10,000 sq m = 2.47 acres.
How do I calculate the area of irregular shapes?
Method 1: Break into smaller regular shapes. Example: L-shaped room = two rectangles. Method 2: Grid method - overlay grid, count squares, multiply by scale. Method 3: Shoelace formula for polygon with coordinates. Method 4: Approximate with circles/rectangles. For land: Use surveying tools or GPS coordinates. Online: Google Earth can measure areas. Practical: For rooms with alcoves, measure main rectangle then add/subtract smaller sections. Always draw a sketch and label dimensions clearly.
What are the most common area formulas I should know?
Rectangle/Square: A = length × width (or side²). Triangle: A = ½bh (half base times height). Circle: A = πr² (pi times radius squared, ~3.14r²). Trapezoid: A = ½(b₁ + b₂)h (average of parallel sides times height). Parallelogram: A = base × height. Ellipse: A = πab (pi times both radii). Regular polygon: A = ½ × perimeter × apothem. Sector (pizza slice): A = ½r²θ (theta in radians). Remember: Height must be perpendicular to base. Use consistent units throughout.
How do I convert between different area units?
Common conversions: 1 sq ft = 144 sq in, 1 sq yd = 9 sq ft, 1 acre = 43,560 sq ft = 4,840 sq yd. Metric: 1 sq m = 10,000 sq cm, 1 hectare = 10,000 sq m. Cross-system: 1 sq m = 10.764 sq ft, 1 acre = 0.405 hectares. Important: When converting length, square the conversion factor. Example: 1 ft = 12 in, so 1 sq ft = 12² = 144 sq in. To convert: 500 sq ft to sq m: 500 ÷ 10.764 = 46.45 sq m. For land: acres or hectares. For flooring/rooms: sq ft or sq m.
How much area do I need for common projects?
Flooring: Measure room length × width, add 10% for waste/cuts. Paint: Wall area = (length × height) × number of walls, subtract doors/windows. 1 gallon covers ~400 sq ft. Carpet: Usually priced per sq yd (divide sq ft by 9). Tile: Calculate area, divide by tile size, add 10-15% waste. Landscaping: Grass seed = sq ft ÷ 1,000 × lbs per 1,000 sq ft (label specs). Mulch: sq ft × depth (in) ÷ 324 = cubic yards needed. Roofing: Roof area ÷ 100 = squares (1 square = 100 sq ft). Always buy 10-15% extra for irregular cuts and mistakes.