Calculate the area of 2D shapes including rectangle, triangle, circle, trapezoid, ellipse, parallelogram, and more. Get instant results with step-by-step calculations and area formulas.
Area is the measure of the extent of a two-dimensional surface within a boundary. It quantifies the amount of space inside a 2D shape and is fundamental in mathematics, engineering, architecture, agriculture, and countless practical applications where surface measurement is required.
Understanding area calculations is essential for material estimation, space planning, land measurement, construction projects, and any situation where you need to determine how much surface area is available or required.
Where length and width are the dimensions of the rectangle
Where base and height are perpendicular measurements
Where r is the radius of the circle
Where a and b are parallel sides, h is height
| Shape | Formula | Required Measurements | Real-World Examples |
|---|---|---|---|
| Rectangle | A = l × w | Length, Width | Floors, walls, screens |
| Square | A = s² | Side length | Tiles, squares, plots |
| Triangle | A = ½bh | Base, Height | Roofs, sails, signs |
| Circle | A = πr² | Radius | Plates, wheels, pools |
| Trapezoid | A = ½(a+b)h | Two bases, Height | Tables, bridges, land plots |
| Parallelogram | A = bh | Base, Height | Slanted shapes, logos |
| Ellipse | A = πab | Semi-major, Semi-minor axis | Ovals, egg shapes |
| Rhombus | A = ½d₁d₂ | Diagonal lengths | Diamond shapes |
| Unit | Symbol | Square Meters | Common Usage |
|---|---|---|---|
| Square Meter | m² | 1 | Rooms, land, construction |
| Square Centimeter | cm² | 0.0001 | Small surfaces, paper |
| Square Millimeter | mm² | 0.000001 | Very small objects |
| Square Kilometer | km² | 1,000,000 | Cities, countries, large areas |
| Square Foot | ft² | 0.0929 | Rooms, houses (US) |
| Square Inch | in² | 0.000645 | Small items (US) |
| Acre | ac | 4,047 | Land, farming, real estate |
| Hectare | ha | 10,000 | Large land areas |
Construction and Architecture: Calculating floor space, wall area for painting, roofing materials, window and door openings, and overall building footprints for planning and material estimation.
Agriculture and Landscaping: Determining field sizes for crop planning, calculating lawn areas for seeding or fertilizing, designing garden plots, and planning irrigation coverage areas.
Manufacturing and Design: Material usage calculations for cutting, fabric requirements for clothing, packaging design, surface treatments, and quality control measurements.
Real Estate and Property: Property size determination, usable space calculations, zoning compliance, property valuation based on area, and space planning for commercial use.
Composite Shapes: Complex shapes can be broken down into simpler components. Calculate each part separately and add areas together, or subtract areas for hollow sections.
Irregular Shapes: Use approximation methods like grid counting, triangulation, or coordinate geometry. For very irregular shapes, digital measurement tools or calculus integration may be required.
Curved Boundaries: Shapes with curved edges often require integration calculus or approximation using many small rectangles or triangles to achieve accurate area calculations.
Coordinate Geometry: For shapes defined by coordinates, use the shoelace formula or break the shape into triangles using the cross product method.
Unit Consistency: Always ensure all measurements use the same units before calculating. Mixed units will give incorrect results and the area unit will be the square of the linear unit.
Precision Requirements: Consider the precision needed for your application. Construction typically requires more precision than general estimates.
Measurement Accuracy: The accuracy of your area calculation is limited by the precision of your measurements. Small measurement errors can compound in area calculations.
Practical Factors: In real applications, consider waste factors, overlap requirements, and practical constraints that might affect the actual usable area.
Double-Check Measurements: Verify that all measurements are correct and properly labeled before calculating area.
Use Appropriate Formulas: Ensure you're using the correct formula for your specific shape. Different triangle area formulas exist for different known measurements.
Consider Scale: When working with drawings or maps, account for scale factors to get real-world areas.
Validate Results: Check if your calculated area makes sense in the context of the problem and compare with known reference areas when possible.