Convert in² to mm² square inches ↔ square millimetres Free Online Secure
Type a value in square inches and read it in square millimetres at once. The factor is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
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Common values — Convert in² to mm² (square inches ↔ square millimetres)
| in² | mm² |
|---|---|
| 1 | 645.16 |
| 2 | 1290.32 |
| 3 | 1935.48 |
| 5 | 3225.8 |
| 10 | 6451.6 |
| 20 | 12903.2 |
| 50 | 32258 |
| 100 | 64516 |
Where these units come from
Square units need no definition of their own: a square metre is a metre by a metre, and everything follows from the length. The land measures are older and stranger. The acre began as the land a yoke of oxen could plough in a day, which is why it was long and thin rather than square — one chain by one furlong, 4840 square yards. The hectare and the are came out of the French Revolution, when land had to be measured in something decimal; neither belongs to the International System, but both were kept for land because a hectare is a comfortable size to picture and a square metre is not. Since the 1959 agreement on the yard, the acre is exactly 4046.8564224 square metres, so the conversions on this page are exact rather than approximate.
Where you meet them
Square metres price flats, size carpets and decide how much paint a wall needs; square feet do the same work in the United States and in much of the property market worldwide. Hectares belong to farmland, forests and planning permissions; acres to land deeds in the English-speaking world. Square kilometres and square miles are for countries, lakes and fires. Square centimetres and square millimetres live in workshops, on datasheets and anywhere a cross-section matters.
Questions people ask
How many square millimetres is a square inch?
Exactly 645.16, or 6.4516 square centimetres. The figure follows from the inch being exactly 25.4 millimetres: squaring 25.4 gives 645.16. Square inches turn up in the pressure unit psi, in the sizes of screens and prints, and in small component specifications.
Why is a square metre a million square millimetres and not a thousand?
Because area is length multiplied by length. A metre is 1000 millimetres, so a square metre is 1000 × 1000, which is 1,000,000 square millimetres. The same trap catches people with every squared unit: the conversion factor of the length is squared along with the unit.
Is the answer exact?
Where both units are defined in terms of one another by whole numbers, yes — the page says so above the figure, and the only rounding is in how many digits are shown. Where the ratio has no finite decimal, the page shows twelve significant digits and says the relation is approximate rather than pretending otherwise.
Does anything I type leave my device?
No. The arithmetic runs in your browser; nothing is uploaded and there is no server to upload it to. Load the page once and it keeps working with the network switched off.
When American cross sections meet metric drawings
The gauge of a wire, the thread of a bolt, the pad of a circuit board: engineers in North America describe these tiny areas in square inches or fractions of them, while the rest of the world writes square millimetres. To convert in² to mm² you multiply by 645.16, which is the square of the 25.4 millimetres in an inch. So 0.01 in² is 6.45 mm² and 0.1 in² is 64.5 mm². The number is easy to get wrong because small values like 0.0032 look unfamiliar, and a slip of a decimal place changes a wire into a bus bar. This page multiplies as you type, and the text below shows where the conversion appears, from AWG wires to bolt threads.
You will find the rule with worked examples, short profiles of both units, a comparison, a long tour of real situations and a list of the mistakes people make most often. The calculation runs in your browser and nothing you type leaves your device.
How to convert in² to mm²: multiply by 645.16
The rule
One square inch equals exactly 645.16 square millimetres. To convert in² to mm², multiply the number of square inches by 645.16. So 0.001 in² is 0.645 mm², 0.01 in² is 6.45 mm², 0.1 in² is 64.5 mm² and 1 in² is 645.16 mm². In the other direction, divide by 645.16 or multiply by 0.00155.
Worked examples
A wire with a cross section of 0.00324 in² is 2.09 mm². A bolt with a stress area of 0.0318 in² is 20.5 mm². A pad of 0.1 by 0.1 inch is 0.01 in², 6.45 mm². For a quick estimate, multiply by 650 and take off a little: 0.01 in² gives 6.5, against 6.45 exactly.
The square of 25.4
An inch is 25.4 millimetres, so a square inch is 25.4 times 25.4, which is 645.16. The factor for an area is therefore never 25.4. Using 25.4 gives a number 25 times too small, and the error is most likely when the square symbol is lost in copying.
A quick check
The square millimetre is tiny, so the number must grow by about 650 times. If your “convert in² to mm²” calculation gave you a number only 25 times bigger, you used the linear factor.
The square inch
One inch squared
The square inch is 6.4516 square centimetres, 645.16 square millimetres or 1/144 of a square foot. It is the unit behind pounds per square inch and a standard for small parts in the United States.
Where it appears
Wire data, bolt tables, hydraulic and pneumatic components, heat sinks and printed circuit boards in American catalogues.
The square millimetre
A millimetre by a millimetre
The square millimetre is a millionth of a square metre and a hundredth of a square centimetre. It is the standard unit for the cross sections of wires, bolts and rods in the metric world, and for the pressure unit megapascal, since 1 MPa is 1 N per mm².
Where it appears
European cable standards, mechanical drawings, steel tables, chip data sheets and optical components use square millimetres.
Square inch and square millimetre compared
A square inch holds 645.16 square millimetres, so the two units differ by nearly three orders of magnitude. A wire described as 0.0033 in² and one described as 2.1 mm² are the same wire, but few people recognise that without the arithmetic.
For stress and pressure, a similar contrast arises: 100 psi is 0.69 MPa, and 1 MPa is 145 psi. Since stress is force over area, converting the area correctly decides whether a part is safe.
Where the conversion appears
Wire gauges
The American Wire Gauge describes conductors by number. AWG 18 has a cross section of 0.00127 in², 0.82 mm². AWG 14 has 0.00324 in², 2.08 mm², AWG 12 has 0.00513 in², 3.31 mm², and AWG 10 has 0.00815 in², 5.26 mm². A European buyer who wants a metric cable of 2.5 mm² chooses AWG 13 or 14 after a “convert in² to mm²” calculation.
Bolts and screws
A 1/4-20 bolt has a tensile stress area of 0.0318 in², 20.5 mm². A 3/8-16 bolt has 0.0775 in², 50 mm², and a 1/2-13 bolt 0.1419 in², 91.5 mm². Engineers multiply the stress area by the allowable stress to obtain the load a bolt can carry.
Circuit board pads
A through hole pad of 0.06 inch diameter has an area of 0.0028 in², 1.82 mm². A surface mount pad of 0.04 by 0.06 inch is 0.0024 in², 1.55 mm². Boards are designed in thousandths of an inch in many American shops and in millimetres in others, so conversions are routine.
Pressure and stress
A pound per square inch is 0.00689 megapascals. A load of 1,000 pounds on a bar of 0.2 in², 129 mm², gives 5,000 psi, 34.5 MPa. If the bar area is given in square millimetres, divide the load in newtons by the area to obtain MPa directly. Most mistakes in this calculation come from mixing units, not from the formula.
Rope, cable and wire rope
A steel wire rope of 1/2 inch diameter has a metallic area of about 0.1 in², 64.5 mm². A 1 inch rope has 0.4 in², 258 mm². The breaking load depends on the metallic area and on the steel grade, so rope tables in the United States give areas in square inches.
Chip packages
A typical small integrated circuit package of 0.15 by 0.2 inches occupies 0.03 in², 19.4 mm². A larger package of 0.5 by 0.5 inch has 0.25 in², 161 mm². American data sheets give package sizes in inches, European ones in millimetres, and a “convert in² to mm²” calculation helps match footprints.
Glue lines and adhesive joints
A glue joint of 1 by 0.5 inch has an area of 0.5 in², 323 mm². At a shear strength of 2,000 psi, 13.8 MPa, the joint carries 1,000 pounds, 4.4 kN. Adhesive data sheets use the unit of their country, and a designer comparing two products must convert both strength and area.
Rubber seals and gaskets
An O ring with a 0.07 inch cross section has a section area of 0.00385 in², 2.48 mm². A seal strip of 0.25 by 0.5 inch has 0.125 in², 80.6 mm². Compression force is estimated from the seal area and the hardness, so the area in the metric unit is needed for European design rules.
Rounding and significant figures
The factor 645.16 is exact. For wire sizes, keep three significant figures: 0.00324 in² is 2.09 mm². For machine parts, keep four. Do not round the factor to 650 in engineering work, since the error is 0.7 per cent.
Spreadsheet use
Write square inches in column A and =A2*645.16 in column B. For the reverse, use =B2/645.16. Use scientific format for very small numbers, so 0.00127 does not disappear into zeros. A third column with =A2*6.4516 gives square centimetres.
Teaching the idea
Draw a square of one inch on millimetre graph paper, 25.4 mm on each side, and count the squares: about 645. Students who count see that the area factor is 25.4 squared, and understand why the linear factor does not apply.
Micro and nano scales
Some American components are specified in circular mils, where 1 circular mil is 0.000000785 in², 0.000507 mm². A wire of 1,000 circular mils has 0.507 mm². This old unit survives in the wire trade, so conversions to square millimetres appear in cable catalogues.
Contact area of coins and buttons
A US quarter has a face of 0.716 in², 462 mm². A 5 euro cent coin, 21.25 mm diameter, has 355 mm², 0.55 in². The contact area decides how well a coin is read by a vending machine, and designers compare sizes in both systems.
Heat sinks, fins and thermal pads
A thermal pad for a processor of 1.5 by 1.5 inches has an area of 2.25 in², 1,452 mm². A small power transistor tab of 0.4 by 0.5 inch has 0.2 in², 129 mm². Thermal resistance is stated per unit area, in degrees per watt per square inch in American sheets and per square millimetre in metric ones, so a “convert in² to mm²” calculation lets you compare them fairly.
Pipes and tubing
A 1/4 inch tube with a 0.18 inch inner diameter has a bore area of 0.0254 in², 16.4 mm². A 1/2 inch tube with 0.43 inch bore has 0.145 in², 93.7 mm². Flow depends on the bore area, and pump data sheets from American makers list flow areas in square inches while European ones use square millimetres.
Machine screws and the thread stress area
A number 10 screw has a stress area of 0.0175 in², 11.3 mm², and a number 6 screw 0.0090 in², 5.8 mm². A metric M5 has 14.2 mm² and an M4 8.78 mm². Comparing the strength of American and metric screws means comparing their stress areas and materials, and the factor 645.16 is the bridge between the two systems.
Clamps, brackets and structural sections
A steel angle of 1 by 1 by 1/8 inch has a section of 0.234 in², 151 mm². A flat bar of 2 by 1/4 inch has 0.5 in², 323 mm². Structural tables in the United States give areas in square inches, and European tables in square centimetres or square millimetres, so a designer comparing a bracket from one catalogue with another must convert the section carefully.
Ear tags, labels and tiny parts
An ear tag of 1 by 2 inches has 2 in², 1,290 mm², and a small part label of 0.5 by 1 inch 0.5 in², 323 mm². Livestock and parts catalogues use inches in North America. A European importer who needs the same part cut from a sheet of metric stock should convert the area before ordering material.
Keyholes, slots and openings
A slot of 0.25 by 1 inch has an area of 0.25 in², 161 mm². A ventilation hole of 0.5 inch diameter has 0.196 in², 127 mm². In an electrical enclosure, openings are limited by area so that sparks cannot escape, and codes in the United States list limits in square inches while European standards use square millimetres. A “convert in² to mm²” calculation translates one rule into the other.
Reading a datasheet in two languages
When a manufacturer prints a cross section as 0.0123 in² in one table and 7.94 mm² in another, check that both belong to the same part and that nobody rounded the first. A “convert in² to mm²” calculation with the exact factor gives 7.935 mm², so a printed 7.94 is consistent. If the numbers disagree by more than one per cent, one of them describes a different size, and you should ask the supplier before you order anything.
Scales of small things
A square millimetre is about the area of a pinhead, and a square inch holds roughly 645 of them. A grain of rice is about 12 mm², a lentil 30. In the same unit, a postage stamp is about 450 mm² and a credit card 4,600. These comparisons give you a feel for whether a number from a conversion is plausible before you rely on it in a design.
Fuses and conductors
A 15 ampere household circuit uses AWG 14 wire, 2.08 mm². A 20 ampere circuit uses AWG 12, 3.31 mm². European installations use 1.5 and 2.5 mm² for similar loads. The cross section limits the current the wire can carry without overheating, so a conversion reveals which wire matches which fuse.
Welding and cutting
A weld bead with a throat of 0.25 inch and a length of 4 inches has a section of 1 in², 645 mm². A cut through a 0.5 inch plate 2 inches wide removes 1 in² of metal, 645 mm². The strength of welds is calculated from the area, so welding codes list sections in square inches in the United States and square millimetres in Europe.
Springs, rods and shafts
A rod of 0.5 inch diameter has a cross section of 0.196 in², 126.7 mm². A shaft of 1 inch has 0.785 in², 506.7 mm². Tensile strength tables give force per area, and converting the area tells you the load a rod can take. A “convert in² to mm²” calculation is the first line of such a calculation.
Hydraulic seals and pistons
A hydraulic piston of 0.75 inch diameter has an area of 0.442 in², 285 mm². At 3,000 psi it pushes with 1,325 pounds, 5.9 kN. Small pistons in valves and actuators are described in square inches in American catalogues, but in mm² in German ones.
Printed circuit traces
A trace 0.01 inch wide and 0.0014 inch thick, a one ounce copper layer, has a section of 0.000014 in², 0.009 mm². A power trace of 0.1 inch width has 0.09 mm², and carries about 3 amperes. Designers use the cross section to estimate current capacity and temperature rise.
Needles, pins and small tools
A sewing pin of 0.03 inch diameter has a section of 0.0007 in², 0.456 mm². A drill bit of 1/8 inch has 0.0123 in², 7.92 mm². Tool makers use these small areas to estimate cutting forces, and convert them when moving between American and metric catalogues.
Contacts and connectors
A plug pin of 0.08 inch diameter has a contact area of 0.005 in², 3.24 mm². A battery terminal of 0.5 by 0.25 inch is 0.125 in², 80.6 mm². The resistance of a contact depends on the area, so connector data sheets give it in the local unit, and engineers must convert when mixing parts.
More values for convert in² to mm²
A longer list of conversions
If the value you need is not in the first list, these further conversions may be close enough to read off directly:
- 0.1 in² = 64.516 mm²
- 0.5 in² = 322.58 mm²
- 3 in² = 1,935.48 mm²
- 4 in² = 2,580.64 mm²
- 7 in² = 4,516.12 mm²
- 15 in² = 9,677.4 mm²
- 20 in² = 12,903.2 mm²
- 75 in² = 48,387 mm²
- 200 in² = 129,032 mm²
- 500 in² = 322,580 mm²
- 2,000 in² = 1,290,320 mm²
- 10,000 in² = 6,451,600 mm²
Mistakes when you convert in² to mm²
Using 25.4
That is the length factor. For area, multiply by 645.16.
Dividing instead of multiplying
The square millimetre is far smaller, so the number grows. If 0.01 in² became 0.0000155, you divided.
Losing the square
in and in² differ. Check the exponent on every number you copy.
Quick answers
How many square millimetres in a square inch?
645.16.
How do I convert in² to mm²?
Multiply by 645.16.
What is 0.01 in² in mm²?
6.45 mm².
How many square inches in a square millimetre?
0.00155.
Does my number leave my device?
No. The calculation runs in your browser.
Related pages and a last word
If you work with small areas, these conversions are close at hand: Convert in² to cm², Convert in² to ft², Convert m² to mm², Convert cm² to mm², Convert mm² to m², Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. The reverse of this page is Convert mm² to in².
In short, to convert in² to mm² multiply by 645.16, remember that the factor is the square of 25.4, and keep the digits your measurement supports. Your number stays on your device: nothing is uploaded and no account is needed.