How this instrument works
A statute mile has measured 1609.344 metres exactly since six national standards bodies signed the international yard and pound agreement in 1959, fixing an inch at 25.4 millimetres. Multiply that length by itself and you get 2 589 988.110336 m², or 2.589988110336 km². That figure is definitional rather than measured, so moving between these two units introduces no experimental uncertainty at all.
Squaring is where most mistakes begin. Length converts by 1.609344; area converts by its square, 2.589988110336. Reach for 1.609 out of habit and your answer lands nearly 38 percent low. Matching trouble waits on the metric side, because one km² is 1 000 000 m² and not 1 000 — any prefix sitting inside a squared unit gets squared along with it.
Both units still earn their keep. American land from Ohio westward is platted on Jefferson's rectangular survey, begun in 1785, where one section equals one mi² — 640 acres — and 36 sections make a township, which is why county lines and USGS drainage basins so often come out in whole mi². Census density tables likewise count residents per mi². Almost everywhere else, and in every scientific paper, ground is reported in km²: Manhattan covers roughly 22.8 mi² or 59 km², Greater London about 607 mi² or 1,572 km².
- Type an area into Square miles (mi2). A value of 10 sits there to start with, which is ten survey sections.
- Read Square kilometres (km2) directly beneath it; that line recalculates on every keystroke.
- Working backwards from metric? Divide your km² by 2.58998811034 to recover mi².
- Need hectares? Multiply Square kilometres (km2) by 100. Need acres? Multiply your Square miles (mi2) entry by 640.
- Negative entries are refused — ground area cannot run below zero, so that field asks for zero or more.
Worked example — ten sections of a township
A ranch listing covers ten contiguous sections of a Wyoming township, and the buyer's agronomist works in metric. Enter 10 into Square miles (mi2). Square kilometres (km2) returns 25.8998811034 — call it 25.9 km² in an offer letter, and keep every digit for a deed schedule.
Two cross-checks confirm it. Ten sections come to 6,400 acres, or 2,589.988110336 hectares; multiplying 25.8998811034 km² by 100 gives 2,589.98811034 — agreement through eleven digits, with the twelfth surrendered to this sheet's rounded factor. Had anyone grabbed 1.609344 instead, they would have written 16.09 km² and undersold 9.8 km² of grazing.
Questions
Why can I not just multiply by 1.609?
Because that number converts length, not ground. A square mile is a mile along each side, so both sides scale: 1.609344 × 1.609344 = 2.589988110336. Using a linear factor on an area leaves you roughly 38 percent short — ten mi² would read 16.09 km² instead of 25.90 km². Cubic units follow an identical rule, needing 1.609344³ for a mile cubed.
Is 2.589988110336 exact, or has it been rounded?
Exact at source, trimmed on screen. That 1959 agreement fixed one yard at 0.9144 m and therefore one statute mile at 1609.344 m, both without uncertainty, so squaring gives 2.589988110336 km² precisely. This sheet carries 2.58998811034 — that same value at twelve significant figures — which is why 10 mi² shows as 25.8998811034 rather than 25.89988110336. Discrepancy introduced: four square millimetres per section.
Do imperial and US customary square miles differ?
No. Britain and America have shared one statute mile of 1609.344 m since 1959, so a mi² means an identical patch of ground on either side of the Atlantic. What did differ was America's survey mile, built on a foot of 1200⁄3937 m. Squared, it ran about four parts per million larger — roughly ten m² per section, enough to shift a state plane grid. NIST and NOAA retired it on 31 December 2022, so new work uses one mile only.
How many acres or hectares are in a square mile?
Exactly 640 acres, and 258.9988110336 hectares. That 640 is no approximation: an acre is defined as 4,840 square yards, and 640 of them tile a section perfectly, which is why homestead claims arrived as quarter-sections of 160 acres. Starting from metric instead, one km² holds 100 hectares and about 247.105 acres.
How do I convert a population density?
Divide rather than multiply. Residents per mi² ÷ 2.58998811034 = residents per km², because you are spreading a fixed headcount across a wider patch of ground. A tract listed at 5,000 people per mi² houses about 1,931 per km². US Census tables publish density per mi² while Eurostat and most national statistics agencies publish per km², so two sources get compared wrongly more often than you might expect.
Does this handle square nautical miles?
It does not. A nautical mile is exactly 1852 m, so a nautical mi² works out at 3.429904 km² — about 32 percent bigger than its statute cousin. Marine charts, exclusive economic zones and search-and-rescue grids all quote it, so check which mile a source means before converting anything at sea.