Area Converter
An acre was a day's ploughing, and it stuck.
Convert Area. An acre was a day's ploughing, and it stuck. Shows the working, not just the answer.
Converted
1 acres
40,468,564.224 square centimetres · 4,046.8564 square metres
An acre was originally the area a yoke of oxen could plough in a day, standardised as one chain by one furlong — 4,840 square yards. That it converts to exactly 4,046.8564224 square metres is a consequence of the yard being exactly 0.9144 m, not a coincidence. Every factor in this family is exact by international agreement rather than measured, so the only rounding is in the display.
How the Area Converter works
Area between metric and imperial units, including acres and hectares. The acre's odd value in square metres follows exactly from the yard's definition rather than being an approximation.
Also known as: square feet to square metres · acres to hectares converter · how big is an acre · land area unit converter
Square the linear factor, always
A foot is 0.3048 metres, so a square foot is 0.3048² = 0.09290304 square metres. Using the linear factor for an area conversion is a common error and it is wrong by a factor of about three.
The same applies to volume, where the factor is cubed. A cubic foot is 0.3048³ = 0.0283 cubic metres, which is roughly a thirty-fifth rather than a third.
It is why a 10% linear increase adds 21% to an area and 33% to a volume. The dimensional exponent is what turns a modest linear change into a large one in area or volume.
Where the acre comes from
An acre was originally the area a yoke of oxen could plough in a day — standardised as one chain by one furlong, which is 22 by 220 yards, or 4,840 square yards.
The long thin shape reflects that turning a plough team was slow, so long furrows were efficient. The unit encodes a piece of agricultural practice that vanished centuries ago.
That it converts to exactly 4,046.8564224 square metres is a consequence of the yard being defined as exactly 0.9144 metres. The awkward decimal is exact rather than approximate.
Hectares, sections and how land is actually measured
A hectare is exactly 10,000 square metres — a square 100 metres on a side — which makes it a far tidier unit than the acre at about 2.471 to the hectare.
A square mile is exactly 640 acres, which is why the American public land survey divides land into sections of that size and quarter-sections of 160 acres. The homestead grants were built on that arithmetic.
Which unit is used for farmland splits by country, and agricultural yield figures follow the same split. Comparing yields internationally is therefore a conversion exercise before it is a comparison.
Where to go next
The Area Converter question rarely arrives on its own. These are the ones that usually come with it:
- Length Converter — An inch has been exactly 25.4 mm since 1959.
- Rectangle Area Calculator — Same perimeter, wildly different areas.
- Polygon Area Calculator — Exterior angles always sum to 360°, whatever the shape.
- Ring Size Calculator — Finger measurement to US, UK, EU and Japanese sizes.
Frequently asked questions
How many square metres in an acre?
Exactly 4,046.8564224. It looks arbitrary and it follows precisely from the yard being defined as exactly 0.9144 metres.
How many acres in a hectare?
About 2.471. A hectare is exactly 10,000 square metres — a square 100 m on a side — which makes it a much tidier unit to work with.
Where does the acre come from?
Originally the area a yoke of oxen could plough in a day, standardised as one chain by one furlong. That is 4,840 square yards, and the shape reflects that ploughing long furrows was efficient.
How do I convert square feet to square metres?
Multiply by 0.09290304. Note that the area factor is the length factor squared — 0.3048² — which is why area conversions cannot use the linear number.
What is a square kilometre in acres?
About 247.1. A square mile is 640 acres exactly, which is why land in the American survey system is divided into sections of that size.
How do I calculate the area of an irregular plot?
Break it into triangles and rectangles, or use the shoelace formula from surveyed coordinates. There is no shortcut for a genuinely irregular boundary.
What is a rood?
A quarter of an acre, forty perches. It appears in old deeds and land records and it is entirely obsolete in modern use.
How large is a football pitch?
It varies within permitted ranges, but roughly 0.7 hectares or 1.75 acres for a typical professional pitch. That is why it is such an unreliable unit of comparison.
What is a square used for in construction?
One hundred square feet, used in roofing. A roof is quoted in squares, so a 2,000 square foot roof is twenty squares.
How do I convert between area units correctly?
Square the linear factor. A foot is 0.3048 m, so a square foot is 0.3048² = 0.09290304 m². Using the linear factor for area is a common and large error.
What is a hectare in football pitches?
About one and a half. It is a square 100 m on a side, which is the useful mental image rather than the sporting comparison.
How is farmland measured?
Hectares in most of the world, acres in the US, UK and a few others. Yield figures follow the same split, which makes agricultural comparisons a conversion exercise.
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