Area Calculator: Find the Area of Any Shape Online
Result Summary
Area = length × width10 m × 6 m = 60 m²
Regional Land Units: Ropani · Bigha · KatthaNepal / South Asia ▾
Traditional land measurement units used in Nepal and parts of South Asia. Use the Nepal Land Converter for a full multi-tier breakdown.
How to Calculate Area for Common Shapes
Area represents the extent of a two-dimensional surface enclosed by a perimeter boundary. Depending on the geometric characteristics of the shape, use the following standard equations:
How to use
- Select the shape from the top grid (Square, Rectangle, Circle, Triangle, Trapezoid, Parallelogram, Rhombus, or Ellipse).
- Choose your measurement unit (meters, feet, centimeters, inches, yards, kilometers, or miles).
- Enter known dimensions in the input fields. For circles, toggle between radius and diameter.
- Check the primary area result card, applied formula, and step-by-step arithmetic.
- Review the live multi-unit conversion table to see equivalents in square feet, square meters, acres, hectares, and square miles.
- For land plots, check the multi-unit table for acres, hectares, and square miles. Expand the Regional Land Units section for Ropani, Aana, and Bigha measurements (Nepal / South Asia).
Standard 2D Geometric Area Formulas
Standard mathematical formulas for calculating two-dimensional surface areas.
1. Mathematical Formulas for 2D Geometric Shapes
Square & Rectangle
The most common quadrilaterals where opposite sides are parallel and all interior angles are right angles (90°).
Rectangle: A = Length × Width
Example: A room measuring 14 ft by 12 ft has an area of 14 × 12 = 168 sq ft (15.61 m²).
Circle & Ellipse
Curved 2D figures defined by radius from a focal center or semi-major and semi-minor axes.
Ellipse: A = π × a × b
Example: A circular round table of diameter 6 ft (radius 3 ft) has an area of π × 3² ≈ 28.27 sq ft.
Triangle (Base-Height & Heron's)
When base and perpendicular height are known, use the standard formula. When all 3 side lengths (a, b, c) are known, use Heron's formula.
Heron's: A = √[s(s - a)(s - b)(s - c)]
where semi-perimeter s = (a + b + c) / 2
Essential for calculating irregular land plots by triangulation.
Trapezoid, Parallelogram & Rhombus
Slanted quadrilaterals frequently encountered in property boundaries, roof profiles, and mechanical components.
Parallelogram: A = Base × Perpendicular Height
Rhombus: A = ½ × Diagonal₁ × Diagonal₂
Example: A trapezoidal plot with parallel sides of 40 ft and 60 ft, spaced 30 ft apart: ½ × (40 + 60) × 30 = 1,500 sq ft.
2. Area Unit Conversion Reference Table
Area scales quadratically compared to linear lengths. For example, 1 meter equals 3.28084 feet, so 1 square meter equals 10.7639 square feet (3.28084²). Here is a quick reference conversion table:
| Unit | Equivalent in Sq Meters (m²) | Equivalent in Sq Feet (ft²) | Typical Application |
|---|---|---|---|
| 1 Square Meter (m²) | 1 m² | 10.7639 sq ft | International standard, architectural drawings |
| 1 Square Foot (sq ft) | 0.0929 m² | 1 sq ft (144 sq in) | Room flooring, apartment floorplans |
| 1 Square Yard (sq yd) | 0.8361 m² | 9 sq ft | Carpet rolls, turf, landscaping |
| 1 Acre (ac) | 4,046.86 m² | 43,560 sq ft | Farmland, agricultural estates, subdivisions |
| 1 Hectare (ha) | 10,000 m² | 107,639 sq ft (2.471 acres) | Large-scale agriculture, forest surveys |
| 1 Square Mile (sq mi) | 2,589,988 m² (2.59 km²) | 27,878,400 sq ft (640 acres) | Municipalities, regional planning, districts |
3. Land Area Units: Acres, Hectares & Regional Systems
When measuring land (whether a garden plot, agricultural field, housing estate, or national park), two units dominate internationally: the acre (standard in the US, UK, Canada, and parts of South Asia) and the hectare (the SI standard used throughout Europe, Australia, and most of Asia). Regional systems remain common across South and East Asia. Use the area calculator above to compute any shape; acres and hectares appear automatically in the results table.
| Unit | Equivalent | Common Use Region |
|---|---|---|
| 1 Acre (ac) | 43,560 sq ft · 4,046.86 m² · 0.4047 ha | USA, UK, Canada, India, Nepal |
| 1 Hectare (ha) | 10,000 m² · 107,639 sq ft · 2.471 acres | Europe, Australia, China, International |
| 1 Are | 100 m² · 1,076 sq ft (= 0.01 ha) | Continental Europe (plot subdivisions) |
| 1 Dunam | 1,000 m² · 10,764 sq ft (≈ 0.247 acres) | Turkey, Israel, Jordan, Iraq, Cyprus |
| 1 Cent | 435.6 sq ft · 40.47 m² (= 0.01 acres) | South India: Tamil Nadu, Kerala, Karnataka |
| 1 Guntha | 1,089 sq ft · 101.2 m² (= 0.025 acres) | Maharashtra, Andhra Pradesh, Goa |
| 1 Tsubo | 3.306 m² · 35.58 sq ft | Japan (residential property) |
Nepal: Ropani & Bigha Systems
- 1 Ropani = 16 Aana = 5,476 sq ft (508.74 m²)
- 1 Aana = 342.25 sq ft (31.80 m²)
- 1 Bigha = 72,900 sq ft (6,772 m² ≈ 1.68 acres)
- 1 Kattha = 3,645 sq ft (338.63 m²)
- Nepal Land Converter →
India: Bigha & Regional Units
- 1 Bigha varies by state, typically 1,333–4,356 m²
- 1 Katha (Bengal) = 720 sq ft (66.89 m²)
- 1 Cent (South India) = 435.6 sq ft (0.01 acres)
- 1 Guntha = 1,089 sq ft (0.025 acres)
Acres and hectares appear automatically in every area calculator result. For Nepal-specific Ropani, Aana, Bigha, and Kattha, expand the Regional Land Units section in the calculator results panel.
4. Gross vs. Net Area: Practical Area Calculations for Flooring, Paint & Tiling
Accurate area computation is essential when estimating materials. The total area of a surface is the gross geometric measurement; subtract openings like doors and windows to get the net usable area, the actual quantity to order:
Net Wall Paintable Area
When estimating paint, find the total wall surface area and subtract openings:
Tile Flooring with Waste Allowance
Ceramic or porcelain tiles require cutting along perimeters and diagonal corners. Add a standard 10% buffer: