Area Converter
Understanding Area and This Converter
Area measures how much two-dimensional space a surface covers. Whether you are comparing property plots, planning a garden, or checking room sizes on a floor plan, you are working with area. Because different regions of the world use different units, quickly converting between them is essential for clear planning and communication.
This area converter lets you convert between common metric and imperial (US customary) units in one step. Supported units include square millimeters, square centimeters, square meters, hectares, square kilometers, square inches, square feet, square yards, acres, and square miles. Enter a value, pick the starting unit, and the tool returns the equivalent area in all other supported units.
Core Area Formulas
Area itself comes from basic geometric formulas. Two of the most common shapes in everyday use are rectangles and circles.
- Rectangle with length l and width w: A = l × w
- Circle with radius r: A = π × r²
In MathML, the area of a circle can be written as:
These formulas explain why area conversions scale with the square of length. If one meter is 100 centimeters, then one square meter is 10,000 square centimeters, because both the length and width scale by 100 (and 100 × 100 = 10,000).
Metric Area Units
The metric system is built on the meter as the base unit of length, and the square meter (m²) as the base unit of area. Larger and smaller metric area units are powers of ten, which makes conversions straightforward.
- Square millimeter (mm²) – very small surfaces, such as component footprints or small hardware.
- Square centimeter (cm²) – paper sizes, labels, and small craft projects.
- Square meter (m²) – room sizes, apartment areas, smaller yards, and construction surfaces.
- Are (a) and hectare (ha) – land areas. One are is 100 m², and one hectare is 10,000 m².
- Square kilometer (km²) – large regions, cities, and map areas.
Because metric units are powers of ten, you can convert between them mentally:
- 1 m² = 10,000 cm²
- 1 m² = 1,000,000 mm²
- 1 ha = 10,000 m²
- 1 km² = 1,000,000 m²
Imperial and US Customary Area Units
Imperial and US customary systems use units based on feet and yards. These units are common in real estate listings, building plans, and land descriptions in the United States and some other countries.
- Square inch (in²) – very small surfaces, such as electronic screens or small components.
- Square foot (ft²) – room sizes, apartment floor areas, and many building specifications.
- Square yard (yd²) – some flooring, landscaping, and fabric measurements.
- Acre (ac) – common for land and property, especially in agriculture and real estate.
- Square mile (mi²) – very large regions, counties, and geographic areas on maps.
Unlike metric units, the relationships between these units are not powers of ten, so conversion factors are especially important. For example:
- 1 ft² = 144 in²
- 1 yd² = 9 ft²
- 1 acre = 43,560 ft²
- 1 mi² = 640 acres
How Area Conversions Work
This converter uses square meters as an internal reference unit. Every supported unit has a fixed factor tying it to the square meter. Conversions follow two basic steps:
- Convert the original area into square meters.
- Convert from square meters into the target unit.
For example, if Am² is an area in square meters and Aft² is the same area in square feet, then:
Aft² = Am² × 10.7639
The reverse conversion uses the reciprocal factor:
Am² = Aft² × 0.092903
You do not need to remember these constants to use the tool, but seeing how they work can help you sanity-check results.
Reference Conversion Factors
The table below shows how much area one unit represents in square meters. To convert from any unit to square meters, multiply your value by the factor in the second column. To go from square meters to that unit, divide by the same factor.
| Unit | Symbol | Square meters per unit |
|---|---|---|
| Square millimeter | mm² | 0.000001 |
| Square centimeter | cm² | 0.0001 |
| Square meter | m² | 1 |
| Hectare | ha | 10,000 |
| Square kilometer | km² | 1,000,000 |
| Square inch | in² | 0.00064516 |
| Square foot | ft² | 0.092903 |
| Square yard | yd² | 0.836127 |
| Acre | ac | 4,046.8564224 |
| Square mile | mi² | 2,589,988.110336 |
Worked Example: Square Feet to Acres
Imagine you are looking at a listing for a rectangular field that measures 300 ft by 600 ft and want to know its size in acres.
- Compute the area in square feet:
- A = 300 ft × 600 ft = 180,000 ft²
- Use the fact that 1 acre = 43,560 ft². Divide the square feet by this factor:
- Area in acres = 180,000 ÷ 43,560 ≈ 4.13 acres
Using the converter, you could simply enter 180,000 as the value, choose square feet as the unit, and read the result directly in acres, hectares, square meters, or any other unit you need.
Interpreting Conversion Results
When you convert between units that differ by orders of magnitude, the numbers can change dramatically even though the actual area remains the same. For example, a modest city park may be:
- 20,000 m²
- 2 ha
- about 4.94 acres
To make sense of results, it can help to compare them to familiar references:
- Room or apartment sizes: Often measured in m² or ft². Values between about 10 m² and 200 m² (roughly 100–2,000 ft²) are typical for rooms and homes.
- Residential lots: Commonly described in m² or acres. Many suburban lots fall between 400 m² and 1,500 m² (0.1–0.4 acres), though this varies widely.
- Fields and farms: More often in hectares or acres. A small farm might be 5–20 ha (about 12–50 acres).
- Cities and regions: Typically in km² or mi².
Comparison of Units and Typical Uses
The table below compares key units, approximate size ranges you might see in practice, and typical use cases.
| Unit | Symbol | Typical scale | Common uses |
|---|---|---|---|
| Square millimeter | mm² | fractions of a cm² | small components, fasteners, tiny contact areas |
| Square centimeter | cm² | 1–1,000 cm² | labels, screens, small craft projects |
| Square meter | m² | 1–1,000 m² | rooms, apartments, offices, small yards |
| Square foot | ft² | 10–10,000 ft² | rooms, homes, decks, offices |
| Square yard | yd² | 1–1,000 yd² | flooring, carpets, landscaping, fabric |
| Are | a | 100 m² per are | small land plots in some metric contexts |
| Hectare | ha | 0.5–1,000 ha | farms, forests, large properties |
| Acre | ac | 0.1–1,000+ ac | land parcels, agricultural fields, rural property |
| Square kilometer | km² | 1–10,000+ km² | cities, regions, watersheds |
| Square mile | mi² | 1–10,000+ mi² | counties, states, large geographic areas |
Limitations and Assumptions
This converter uses standard, widely accepted definitions for all units and fixed conversion factors between them. Calculations assume flat, two-dimensional surfaces and do not adjust for real-world effects such as terrain, curvature of the Earth, or survey projection methods.
The tool is intended for general planning, education, and everyday decision-making. For legal property descriptions, land surveys, engineering work with strict tolerances, or jurisdiction-specific definitions, you should confirm requirements and conversion factors with local regulations or a qualified professional.
Very large or very small inputs may be rounded for display. If you are working with extreme values, treat results as approximate and verify any critical figures independently.
Related Calculations and Next Steps
Area often appears alongside other measurements. After converting an area, you may want to compute the area of a particular shape from its dimensions, convert lengths, or estimate volumes. If your project involves building, mapping, or engineering, consider pairing this converter with length, volume, or geometry tools to keep all units consistent.