Area

Area factors are the squares of length factors, and that single fact causes most of the mistakes people make with them. A foot is 0.3048 m, so a square foot is 0.3048² = 0.09290304 m². Nobody converts area by 0.3048 on purpose, but plenty of drawings have been scaled that way.

The squaring has a second consequence that surprises people looking at floor plans: a 10% error in a linear dimension becomes a 21% error in the area, because 1.1² is 1.21. Halve both sides of a room and the floor area drops to a quarter.

Eight units are covered, opening on one acre. Two of them — the acre and the hectare — are land units with no dimensions attached, which is why they need the historical explanation below rather than just a factor.

The factors, all referenced to the square metre

• 1 cm² = 0.0001 m², 1 km² = 1,000,000 m²
• 1 ft² = 0.09290304 m² (exact)
• 1 yd² = 0.83612736 m² (exact, and nine square feet)
• 1 acre = 4,046.8564224 m² (exact, and 43,560 ft²)
• 1 hectare = 10,000 m² (exact, a 100 m square)
• 1 mi² = 2,589,988.110336 m² (exact, and 640 acres)

The two land units convert to each other as 1 ha = 2.471054 acres and 1 acre = 0.404686 ha. A quick field estimate: a hectare is about two and a half acres, and an acre is about 40% of a hectare.

Note the yard: nine square feet, not three. Carpet and turf are sold by the square yard in the US, and ordering by a factor of three instead of nine is the classic way to end up with a third of a floor covered.

Land areas, and the American survey grid

The last three rows are the Public Land Survey System, the grid that was laid across most of the United States west of the original colonies from 1785 onward. A township is six miles square and holds 36 numbered sections; a section is one square mile, or 640 acres; and dividing a section twice gives the 40-acre "quarter-quarter" that homestead law made famous as the back forty. It is also why so much of the American Midwest is a visible chequerboard from the air, and why rural road spacing there is so often exactly one mile.

Where 43,560 comes from

The acre is not a square. It is one chain by one furlong: a surveyor’s chain of 66 feet multiplied by a furlong of 660 feet gives 43,560 square feet. The shape reflects its origin as roughly the land a team of oxen could plough in a day — a long, thin strip, because turning the team was the slow part.

That 66-foot chain propagates through the whole system: eighty chains make a mile (80 × 66 = 5,280 feet), ten chains make a furlong, and ten square chains make an acre. The Length Converter covers the linear side of the same family.

The hectare was built the other way round, from the metric system outward: a square 100 m on a side, 10,000 m², defined for convenience rather than inherited from ploughing. It is the unit of EU agricultural policy, most national land registries and international forestry statistics, and it is what almost every country outside the US and UK uses for land.

Flooring, a lot listing, and a farm

Ordering flooring from a metric supplier. A room measuring 12 ft 6 in by 14 ft 3 in is 12.5 × 14.25 = 178.125 ft², which converts to 16.55 m². Laminate sold in boxes covering 2.2 m² means 16.55 ÷ 2.2 = 7.5 boxes for bare coverage. Add the standard 10% for cuts and waste and you need 18.2 m², or 9 boxes. Ordering 8 leaves you short by less than half a box, which is the single most common way a floor ends up with a mismatched dye lot.

Reading a US lot listing. A 0.28-acre lot is 0.28 × 43,560 = 12,196.8 ft², or 1,133 m². For a buyer used to European listings that is a plot roughly 34 m square.

Farmland across systems. A 40-hectare holding is 98.84 acres. A 100-acre American farm is 40.47 ha. Neither converts to a round number in the other system, which is why agricultural statistics comparing countries always quote one unit and convert everything into it.

What "square feet" actually includes

The number is only as good as its definition, and property markets do not share one. US residential listings usually quote gross living area measured to the outside of exterior walls, so interior usable space is smaller. Commercial leases quote rentable square feet, which add a pro-rata share of lobbies, corridors and restrooms through a load factor typically running 10–20%: 1,000 rentable square feet can be 850 usable. Converting that to 92.9 m² carries the load factor along with it.

Other markets have their own units entirely. Japanese listings quote tsubo, equal to two tatami mats, 3.30578 m² or 35.58 ft². Thai land is sold by the rai of 1,600 m². Indian land documents use bigha, which varies by state and has no single value at all. Convert the number, then check what the number was measuring.

For paint, tiling and material estimates, remember that area alone does not tell you quantity — coverage rates, waste allowance and the shape of the offcuts all intervene.

Rounding, irregular shapes, and legal descriptions

This converter carries the acre as 4,046.86 m² against an exact 4,046.8564224, and the square mile as 2.59 × 10^6 m² against an exact 2,589,988.110336. The relative errors are about nine parts in ten million and five parts in a million respectively — on a 100-acre parcel the acre rounding is under 0.4 m², which is a rounding error on a rounding error.

What it cannot do is deal with shape. Real parcels are rarely rectangles, and a legal description works from bearings and distances around a boundary, not from a single area figure. If the area on a listing disagrees with the area on the plat, the plat governs, and the difference is usually an easement, a right of way or a sliver excluded from the deed rather than an arithmetic error.

Land areas also change with how they are projected. Measured on a map, an area depends on the map projection; a Mercator-projected polygon far from the equator can overstate true ground area substantially. Survey and cadastral figures use projections chosen to preserve area or minimise local distortion, which is another reason to trust the recorded document over a measurement taken off a web map.

Frequently asked questions

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