Ten Metres of Copper Pipe Grows Eight Millimetres

The units are the easiest thing to get wrong

Coefficients are almost always published as a number of millionths per degree — 17 for copper, 12 for steel, 23 for aluminium — and the exponent is left implicit in the table heading. Entering 17 where the calculation wants 0.000017, or the reverse, is a factor of a million in either direction, and it produces an answer so absurd that it is usually caught. The dangerous error is subtler: mixing a coefficient quoted per degree Celsius with a temperature change measured in degrees Fahrenheit. The sizes of the two degrees differ by a factor of 1.8, so that mistake gives an answer that is wrong by 80 % and still looks plausible.

Blocked expansion becomes force instead of movement

The millimetres in this calculation are what happens when the material is free to move. Clamp both ends and the material still tries to grow by the same amount, and the stress that results does not depend on the length at all — a two-metre bar and a twenty-metre bar restrained at both ends develop the same stress for the same temperature change, because the strain is a proportion. That is why long runs are not more at risk than short ones for stress and are much more at risk for movement, and why the fix is a fixed point plus somewhere for the growth to go, rather than more clamps.

Frequently asked questions

Does this apply to area and volume too?

Yes, with the coefficient multiplied. For small changes the area coefficient is about twice the linear one and the volume coefficient about three times it, which follows from expanding each dimension independently. A steel plate warming by 50 degrees therefore grows about 0.12 % in area, and a steel block about 0.18 % in volume. The same reasoning explains a fact that surprises people: a hole in a heated plate gets larger, not smaller, because the metal around it expands outwards along with everything else.

Why do laminate floors need a gap if wood barely expands with heat?

Because the movement there is caused by humidity rather than temperature, and it is far larger. Wood-based boards take up and give off moisture with the air around them, swelling across the grain by an amount that dwarfs anything thermal expansion produces at room temperatures. This calculation does not model that at all, and applying it to a floor would suggest a gap of a millimetre or two where manufacturers specify ten or more. Use the thermal formula for metals, glass and plastics; for anything wooden, follow the moisture-movement figure the maker publishes.