Area Calculator Guide: Calculate Area of Rectangles, Circles & Complex Shapes
An area calculator computes how much surface a shape covers and converts between square units. It’s useful for planning materials (tile, paint, concrete), landscaping, or checking geometry homework. This guide covers formulas for common shapes and the quickest way to handle irregular rooms.
What is Area Calculator?
The area calculator lets you enter dimensions for shapes—rectangles, circles, triangles, trapezoids, ellipses, and more—and returns area (and often perimeter). Contractors, DIYers, and students use it to size projects and verify answers.
How to Use the Area Calculator
- Choose a shape that matches your project (rectangle, circle, triangle, etc.).
- Enter dimensions in your preferred units (ft, m, in, cm). Use decimals for precision.
- Compute area and optionally perimeter; switch units as needed.
- For complex rooms, break into simpler shapes, sum their areas, and subtract voids.
- Add waste if you’re ordering materials (often 5–15%).
Formulas & Methods
- Rectangle:
A = L × W - Triangle:
A = ½ × b × h(right triangle:A = ½ × a × b) - Circle:
A = πr² - Trapezoid:
A = ½ × (b₁ + b₂) × h - Ellipse:
A = πab(a, b are semi‑axes) - Sector:
A = ½ × r² × θ(θ in radians) orA = (θ/360) × πr²
Assumptions & limitations
- Inputs are interior dimensions; measure carefully.
- Keep units consistent; convert before calculating to avoid mistakes.
- For irregular polygons, split into known shapes or use coordinate methods (shoelace formula).
Examples
Example A — Room area for flooring
Room 1: 14 ft × 11 ft → 154 ft²
Alcove: 5 ft × 3 ft → 15 ft²
Total = 154 + 15 = 169 ft². Add 10% waste → ~186 ft² of material.
Example B — Circular garden bed
Radius r = 6 ft. Area = π × 6² = 113.10 ft² (approx). For a 90° quarter‑circle, use (θ/360) × πr² = 0.25 × π × 36 ≈ 28.27 ft².
| Shape | Formula | Inputs → Area |
|---|---|---|
| Rectangle | A = L × W | 12 m × 3 m → 36 m² |
| Triangle | A = ½ × b × h | 10 cm × 8 cm → 40 cm² |
| Circle | A = πr² | r = 2.8 m → 24.63 m² |
Pro Tips & Best Practices
- Measure twice with the same tape; small errors scale up on large areas.
- Convert units once (e.g., all to meters) to avoid mixing systems.
- Mark obstacles (columns, hearths) and subtract their area.
- Use graph paper to decompose irregular rooms into rectangles and triangles.
- Keep formulas handy; sectors and ellipses are common in landscaping.
Related Calculators
FAQ
Q: What is an area calculator?
A: A tool that computes the size of a surface for shapes like rectangles, circles, triangles, and more.
Q: Which units can I use?
A: Enter any supported length units; the tool returns area in square units (e.g., ft², m²) and can convert between systems.
Q: How do I find the area of a room with alcoves?
A: Break it into rectangles, compute each area, and sum the results. Subtract the area of voids like chimneys or stairs.
Q: What about circles and sectors?
A: Use A=πr² for full circles; sectors use A=½·r²·θ with θ in radians (or A=(θ/360)·πr² if θ is degrees).
Q: Do I need to include waste in material estimates?
A: For flooring/paint/tile, add 5–15% for cuts and waste depending on layout complexity.
Call to Action
Enter your dimensions above and get area instantly. Then explore the related calculators for precise material and cost planning.