How this instrument works
Centi- and milli- are two of the original metric prefixes, written into French law in 1795, meaning one hundredth and one thousandth ever since. One centimetre is ten millimetres. Square both sides and that ratio squares with them: 1 cm² = (10 mm)² = 100 mm². Prefixes are not separate multipliers bolted onto symbols — each fuses to its symbol, so any exponent then acts on both together. That single rule, spelled out in NIST Special Publication 811, is this whole conversion.
Square millimetres own cross-sections. Electrical conductors outside North America are specified by area in mm² — 1.5 mm² lighting circuits, 2.5 mm² socket rings, 95 mm² service cable — because current rating tracks how much copper carries that current; IEC 60228 sets conductor classes on exactly that basis. Structural work leans on this same unit for another reason: one newton per square millimetre is precisely one megapascal, so European concrete and steel strengths quoted as N/mm² need no conversion whatsoever.
Square centimetres survive wherever an object fits in your hand. Cell-culture flasks sell by growth area — T-25, T-75, T-175 — and dose per unit area governs transdermal patches, burn charts, wound notes and solar coupons rated in milliwatts per square centimetre. That unit survives from centimetre-gram-second physics, which ran on it before SI arrived, persisting because human-scale things land in tidy ranges: a thumbnail is roughly 1 cm², a postage stamp about 5 cm², a credit card 46.2 cm². Multiply any of those by 100 to speak in millimetres.
- Type your area into Square centimetres (cm2). It starts at 10, which happens to be a copper bar 100 mm wide by 10 mm thick.
- Read Square millimetres (mm2) below your entry — that output redraws while you type, with nothing to submit.
- Sanity-check magnitude before trusting any result: your answer is always one hundred times bigger, so 7.5 cm² becomes 750 mm², never 75.
- Going backwards from millimetres, divide by 100 — shift your decimal point two places left and you are done.
Worked example — a 10 cm² copper busbar
A panel builder receives a drawing dimensioned in centimetres: a copper bar 10 cm wide and 1 cm thick, giving 10 cm² of cross-section. Every current-rating table on his bench is written in square millimetres. He enters 10 into Square centimetres (cm2), and Square millimetres (mm2) returns 1000.0 — one bar, redescribed as 100 mm × 10 mm.
Redoing that multiplication in smaller units confirms it: 100 × 10 = 1000, matching digit for digit. Had he squared by 10 instead of 100, his bar would read 100 mm², roughly a 10 mm square rod carrying a tenth of that metal. Errors of exactly this shape are what melt terminations, and they are why area factors deserve a second look.
Questions
Why multiply by 100 and not by 10?
Because area carries its length factor twice over. One centimetre is ten millimetres, so any one-centimetre square measures ten millimetres along each edge and holds 10 × 10 = 100 little squares of one square millimetre apiece. Sketch that grid once on paper and this mistake stops recurring. Volume follows identical logic with a third power: one cubic centimetre is 1000 cubic millimetres.
Is 1 cm² = 100 mm² exact, or has something been rounded?
Exact, and permanently so. This relationship rests only on SI prefixes centi- and milli-, defined as 10⁻² and 10⁻³ by decree rather than by measurement. It stays independent of how metres themselves are defined — that 1983 redefinition tying metres to light-speed changed nothing here. Any digits past your decimal point come from what you typed, never from this factor.
What does cm2 mean where a superscript is missing?
Square centimetres. Plain-text output, spreadsheet exports and older databases strip that raised 2, leaving cm2 and mm2 — which is how fields on this sheet are labelled. Read it as (cm)², a whole symbol squared. Never read it as centi-(m²), which comes to 10⁻² m² instead of 10⁻⁴ m² — that misreading misses by exactly the hundred this page exists to apply. So 5 cm2 means five square centimetres, or 500 mm².
How do square inches fit alongside these two?
Through one exact definition. Six standards bodies pinned the inch at 25.4 mm precisely in 1959, making one square inch 645.16 mm² or 6.4516 cm² — exact figures, rounded nowhere. Imperial usage and US customary usage share that inch, so their square inches match digit for digit. Only the deprecated US survey foot ever differed, by roughly four parts per million in area, and NIST retired it at the end of 2022.
How many decimal places should I keep in an answer?
Multiplying by 100 shifts your decimal point two places and adds no precision at all, so carry only what you actually measured. Caliper readings of 2.05 cm by 1.30 cm give 2.665 cm², honestly 2.66 or 2.67, which lands between 266 and 267 mm². Reporting 266.5 mm² claims tenth-of-a-millimetre certainty your measurement never had.
Are both units really part of SI?
Yes. Coherent SI measures area in square metres; these two are decimal submultiples of it, 10⁻⁴ m² and 10⁻⁶ m² respectively. Style guidance prefers prefixes stepping in thousands, which quietly favours mm² over cm², yet centimetres are grandfathered in, while medicine, biology and everyday trade show no sign of dropping them.