Area Calculator
How do you calculate the area of different shapes?
| Shape | Formula | Example |
|---|---|---|
| Rectangle / Square | Area = length × width | 12m × 8m = 96 m² |
| Circle | Area = π × r² | r=5m: π × 25 = 78.54 m² |
| Triangle (base × height) | Area = 0.5 × b × h | 0.5 × 10 × 6 = 30 m² |
| Trapezoid | Area = 0.5 × (a+b) × h | 0.5 × (6+10) × 4 = 32 m² |
| Ellipse | Area = π × a × b | π × 5 × 3 = 47.12 m² |
| Parallelogram | Area = base × height | 8 × 5 = 40 m² |
| Sector (of circle) | Area = (θ/360) × π × r² | 90° sector, r=4: 12.57 m² |
What is the area of common real-world objects?
| Object | Area | Formula Used |
|---|---|---|
| Standard A4 sheet of paper | 623.7 cm² | 29.7 × 21 cm (rectangle) |
| Football pitch (FIFA standard) | 7,140 m² | 105 × 68 m (rectangle) |
| Tennis court (singles) | 195.7 m² | 23.77 × 8.23 m |
| Pizza (30cm diameter) | 706.9 cm² | π × 15² (circle) |
| Standard door | 1.68 m² | 0.8 × 2.1 m (rectangle) |
Area vs perimeter: what is the difference?
Area measures the surface enclosed by a shape — the amount of paint needed to cover a wall, or carpet needed for a floor. Perimeter measures the total length of the boundary — the amount of fencing needed around a garden, or skirting board around a room. Both use the same dimensions but are used for completely different purposes. Continue your calculation with the Circumference Calculator, or check the Volume Calculator.
Converting area units
1 m² = 10.764 sq ft = 10,000 cm². 1 acre = 4,047 m² = 43,560 sq ft. 1 hectare = 10,000 m² = 2.471 acres. Use the area converter for all unit conversions. — see also: circumference calculator
Frequently asked questions
How do you calculate the area of a circle?
Area of a circle = π × r² where r is the radius (half the diameter). For a circle with diameter 10m: radius = 5m, area = π × 25 = 78.54 m². Using diameter directly: Area = π × (d/2)² = π × d² / 4.
How do you find the area of an irregular shape?
Divide the irregular shape into simpler shapes (rectangles, triangles, circles) whose areas you can calculate. Calculate each part separately, then add them together. For very irregular shapes, the grid method works: overlay a grid, count complete squares, estimate partial squares.
What is the difference between area and surface area?
Area applies to flat 2D shapes. Surface area is the total area of all surfaces of a 3D object — like the area of all six faces of a box. For a cube with side 3m: area of one face = 9 m², total surface area = 6 × 9 = 54 m².
How do you calculate square footage for flooring?
Measure room length × width in feet. Add 10% for waste (cuts and offcuts). For L-shaped rooms: divide into two rectangles, calculate each, add totals. 1 sq ft = 0.0929 m². Use the square footage calculator for multi-room projects.
What is Heron's formula for the area of a triangle?
When you know all three sides (a, b, c) but not the height: s = (a+b+c)/2 (semi-perimeter). Area = √(s × (s-a) × (s-b) × (s-c)). For a triangle with sides 5, 6, 7: s=9; Area = √(9 × 4 × 3 × 2) = √216 = 14.7 m².
Sources & References
Sources: Euclid, Elements Books I-VI; NIST Digital Library of Mathematical Functions — area formulas; ISO 80000-3 (Quantities and units — Space and time).
How do you measure a room for flooring or carpet?
Measuring an irregular room for flooring requires dividing it into simple rectangles. Step-by-step guide:
- Sketch the room and divide it into rectangles (most rooms are L-shaped or have alcoves).
- Measure each rectangle: length × width in metres or feet.
- Add all rectangle areas together for the total floor area.
- Add 10% for cutting waste on tiles and straight-lay carpet. Add 15% for diagonal installation.
- Convert to the unit your supplier uses: 1 m² = 10.764 sq ft.
| Flooring Type | Typical Waste Factor | Notes |
|---|---|---|
| Ceramic / porcelain tile (straight lay) | 10% | More waste for small tiles |
| Tile (diagonal lay) | 15% | More cuts needed |
| Hardwood / laminate | 10% | Plus 5% for acclimation wastage |
| Carpet (broadloom) | 10–15% | Depends on room shape and seam placement |
| Vinyl / LVP planks | 10% | Less waste than tile |
Indian land area units: bigha, gunta, cent, marla
India uses regional land measurement units that vary significantly by state. The area calculator works in standard units — use this conversion table to convert Indian units to square metres or square feet:
| Unit | State / Region | Square Feet | Square Metres |
|---|---|---|---|
| Bigha (Punjab, UP) | Punjab, UP, Bihar | 27,225 sq ft | 2,529 m² |
| Bigha (West Bengal) | West Bengal | 14,400 sq ft | 1,338 m² |
| Gunta / Guntha | Maharashtra, Karnataka | 1,089 sq ft | 101.2 m² |
| Cent | Tamil Nadu, Kerala, AP | 435.6 sq ft | 40.47 m² |
| Marla | Punjab, Haryana, Pakistan | 272.25 sq ft | 25.29 m² |
| Ground | Tamil Nadu | 2,400 sq ft | 222.97 m² |
| Acre | All India | 43,560 sq ft | 4,047 m² |
| Hectare | All India (official) | 107,639 sq ft | 10,000 m² |
Area in agriculture: hectares, acres, and football fields
Agricultural land is measured in hectares (global standard) or acres (US, UK, older Indian records). 1 hectare = 2.471 acres = 10,000 m². For intuitive scale: 1 football pitch (FIFA standard) = 0.714 hectares. An average Indian farm: 1.08 hectares (2.67 acres). A 40×40 ft house plot = 1,600 sq ft = 148.6 m² = 0.015 hectares. Paint coverage reference: 1 litre of standard exterior paint covers approximately 10 m² — divide your wall area by 10 to estimate litres needed. See also: paint calculator.
Irregular polygon area: the Shoelace formula
For any polygon with known vertex coordinates, the Shoelace (or Surveyor's) formula calculates exact area without decomposing into triangles. List vertices in order (x₁,y₁), (x₂,y₂)... (xₙ,yₙ). Area = |Σ(xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)| ÷ 2. Example: quadrilateral with vertices (0,0), (4,0), (4,3), (0,3): Area = |(0×0−4×0) + (4×3−4×0) + (4×3−0×3) + (0×0−0×3)| ÷ 2 = |0+12+12+0| ÷ 2 = 12 m². This is the same as 4×3=12 m² (a rectangle), verifying the formula. Surveyors use this formula to calculate land areas from GPS coordinates.
Paint coverage from wall area
Calculate wall area first, then convert to litres of paint needed. Standard interior wall: width × height, minus door (0.8m × 2.1m = 1.68 m²) and window (1.2m × 1.0m = 1.2 m²) areas.
| Paint Type | Coverage (m²/litre) | Coats Needed | Litres for 20 m² wall |
|---|---|---|---|
| Standard emulsion (interior) | 12–14 | 2 | ~3.2 litres |
| Premium emulsion | 14–16 | 2 | ~2.7 litres |
| Exterior masonry paint | 5–8 | 2 | ~5.7 litres |
| Gloss (woodwork) | 17 | 2 | ~2.4 litres |
| Primer | 10–12 | 1 | ~1.8 litres |
Always add 10% for waste and touch-ups. See the paint calculator for a full room-by-room calculation.