Understanding area
Length squared, in two systems.
Whatever held for length applies twice over.
The metric ladder, squared.
Each metric length step multiplies by ten; each metric area step therefore multiplies by a hundred. A square metre is ten thousand square centimetres because a metre is a hundred centimetres on a side, and a hundred squared is ten thousand.
1 m² = 10 000 cm² · 1 km² = 1 000 000 m² · 1 ha = 10 000 m²
Acres, hectares, and other land units.
Land tends to get its own units. The hectare is metric — a square hectometre, exactly ten thousand square metres — and is the working unit for farms and forests outside the United States. The acre is older and more idiosyncratic: originally the area an ox team could plough in a day, now defined by treaty.
1 acre ≡ 4046.8564224 m² · 1 hectare ≡ 10 000 m²
Imperial bridges (squared from length)
- 1 in² = 6.4516 cm²
- 1 ft² = 929.0304 cm²
- 1 yd² = 0.83612736 m²
- 1 mi² ≈ 2.59 km²
Three worked conversions.
500 square feet to square metres
1 ft² = 0.092903 m²
A square foot is smaller than a square metre, so the count shrinks — multiply by the small factor.
500 × 0.092903 ≈ 46.4515
= 46.4515 m²
1 acre to hectares
1 acre = 4046.8564224 m² · 1 ha = 10 000 m²
Convert through the metre as a common base.
4046.8564224 ÷ 10 000 ≈ 0.40469
= 0.40469 ha
2 km² to square miles
1 mi² ≈ 2.589988 km²
A square mile is bigger than a square kilometre — divide.
2 ÷ 2.589988 ≈ 0.7722
= 0.7722 mi²
A note on precision.
Areas computed from squared length factors carry the same double-precision accuracy — fifteen significant digits, plenty for surveying and farming. For deeds and registered plots, the authoritative figure is whatever the registry recorded, not the calculator.
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