Steel moves 6 mm per 10 m per 50 K and PVC moves 40 mm. Get the change for fifteen solids and four liquids, in Celsius or Fahrenheit, as a length, an area or a volume.
How much does 20 ft of PVC expand over a 100 degree swing?
Steel moves 6 mm per 10 m per 50 K and PVC moves 40 mm. Get the change for fifteen solids and four liquids, in Celsius or Fahrenheit, as a length, an area or a volume.
Rigid PVC moves about 80 millionths of its own length per kelvin, which is nearly seven times what steel does and the reason plastic waste systems are built with slip couplings instead of being solvent welded end to end. Over a 20 ft run taken from 40 to 140 degrees Fahrenheit, a range an unvented attic reaches without trying, that coefficient turns into a movement you can measure with a tape.
The number below is the free movement, the distance the pipe would travel if nothing held it. Clamp it at both ends and the same temperature rise turns into force instead, which is what bows a run between two tight brackets and what eventually cracks a fitting. The gap or the slip joint has to give back at least the figure shown, and it has to do it in the direction the run actually grows.
Fitting temperature decides where that gap sits. Install on a cold morning and almost the whole allowance has to be on the hot side; install at the top of the range and it goes the other way. Halfway through the span the movement splits both ways, which is why the sensible advice is to set expansion joints at a middling temperature rather than on the hottest or coldest day of the job.
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Everything a temperature change does to a solid, in one place
A 500 m steel bridge deck that spends winter at -20 °C and summer at +40 °C is 360 mm longer in August than in January. Nothing about the steel changed. The same span of aluminum would move 693 mm, the same span of invar 36 mm. That spread, a factor of nineteen between those two, is what this page is about: one coefficient per material, one formula, and the gap someone has to leave for the difference.
The calculator takes a size, two temperatures and a material, and returns the change in the unit you typed plus the same change in millimeters and inches for a length, or in the matching units for an area or a volume. It covers a length, an area or a volume, it accepts Celsius or Fahrenheit, and it carries four liquids with a measured volumetric coefficient rather than pretending a liquid has a length.
Four fields, and what each one is asking for
- What changes - a length, an area or a volume. A rail, a pipe run or a beam is a length. A pane, a facade panel or a tabletop is an area. A block, a tank or anything liquid is a volume. The choice sets whether the coefficient is used once, twice or three times.
- Starting size and its unit - the size measured at the starting temperature, in meters, centimeters, millimeters, feet or inches. For area and volume the unit is squared or cubed automatically, so a 2.5 entered with meters means 2.5 square meters in area mode.
- Both temperatures and the scale - the temperature the size was measured at, and the one it ends up at. Celsius and Fahrenheit both work, and the second one is not a relabeling: a span of 90 °F is a span of 50 K, and the calculator converts the span, not the reading.
- Material - fifteen solids and four liquids from the table below, or the last entry, which lets you type a coefficient off a datasheet. If your figure is quoted per degree Fahrenheit, say so; the two forms differ by a factor of 1.8 and mixing them up is a 44 percent error in the wrong direction.
- Read the change at the top, the size it ends at next to it, and the material comparison at the bottom, which repeats your own numbers for every other material on the list.
One coefficient, three geometries, and the two factors nobody explains
The linear coefficient, written alpha, is the fraction of its own length a material gains for every kelvin it warms. Carbon steel sits at 12 x 10-6, which reads as twelve millionths per degree: a meter of it gains twelve micrometers per kelvin, and a kilometer gains twelve millimeters. That is the whole quantity. Everything else on this page is that number multiplied by a size and a temperature span.
Areas and volumes do not get their own coefficient. A square that grows by a factor of (1 + alpha x dT) on each side grows by that factor squared in area, and expanding the bracket gives 1 + 2 alpha dT + alpha squared dT squared. The last term, for a metal over a hundred kelvin, is about one part in ten thousand of the change itself, which is far below the precision of any published coefficient. So area uses 2 alpha and volume uses 3 alpha, and the approximation costs nothing you could measure.
Liquids are the exception, and it is the reason the material list is split. A liquid takes the shape of its container, so it has no length of its own and no alpha to publish. What gets measured instead is beta, the volumetric coefficient, directly. Water at room temperature sits at 207 x 10-6 per kelvin, gasoline at 950, which is why a tanker loaded cold and delivered warm arrives with more liters than it left with and exactly the same mass. Picking a liquid in length mode here returns a refusal rather than a number, because three times an alpha nobody measured is not an answer.
One more thing the formula assumes: the object is free to move. A steel rail that is clamped down cannot get longer, so the same temperature rise turns into stress instead, on the order of 2.4 MPa per kelvin for steel, which is why continuously welded track is laid pre-tensioned at a chosen neutral temperature. The calculator gives the movement a free object would make. If yours is restrained, that movement is the thing your fixings have to fight.
Table 1: coefficients for fifteen solids and four liquids
Solids carry a linear alpha, liquids a volumetric beta, and the third column is the same figure expressed per degree Fahrenheit for anyone reading an American datasheet. Published values vary by a few percent with alloy, mix and moisture, so treat them as good to two figures rather than four.
| Material | 10-6 per °C | 10-6 per °F | Where the figure bites |
|---|---|---|---|
| Invar 36 | 1.2 | 0.67 | Gauge blocks, clock pendulums, surveying tape |
| Glass, borosilicate | 3.3 | 1.83 | Ovenware and lab glass, the reason it survives a hot plate |
| Wood, along the grain | 5.0 | 2.78 | Joists and studs, where thermal movement is the small problem |
| Brick masonry | 5.5 | 3.06 | Long facade runs and the movement joints in them |
| Titanium | 8.6 | 4.78 | Aerospace fits, where it is paired with aluminum at 23.1, nearly three times as much |
| Glass, soda-lime | 9.0 | 5.00 | Window panes, and thermal shock cracks in them |
| Cast iron | 10.5 | 5.83 | Engine blocks, radiators, old drain stacks |
| Carbon steel | 12.0 | 6.67 | Rails, beams, reinforcement, the default of the whole trade |
| Concrete | 12.0 | 6.67 | Slabs and control joints; matching steel is why rebar works |
| Copper | 16.6 | 9.22 | Hot water lines, roof flashing, bus bars |
| Stainless steel 304 | 17.3 | 9.61 | Flues and food plant, half again the movement of carbon steel |
| Brass | 19.0 | 10.56 | Fittings and bearings, and the classic bimetallic strip |
| Aluminum | 23.1 | 12.83 | Window frames, curtain walling, patio doors that stick |
| Wood, across the grain | 50.0 | 27.78 | Board widths, though moisture moves them much further |
| PVC, rigid | 80.0 | 44.44 | Drain and vent runs, siding, the biggest gaps on any site |
| Mercury (volumetric beta) | 181 | 100.56 | The thermometer that made the whole idea visible |
| Water at 20 °C (beta) | 207 | 115.00 | Why a sealed heating loop needs an expansion vessel |
| Ethanol (beta) | 750 | 416.67 | Distilling and lab work, three and a half times water |
| Gasoline (beta) | 950 | 527.78 | Tank ullage, and why fuel is sold corrected to a reference temperature |
Seven runs, from a gauge block to a tanker
That is 54.19 mm, or 2.13 in, on one run. It is also why plastic waste systems are built with slip or expansion couplings rather than solvent-welded end to end.
That is 15.18 mm, or 0.6 in. Enough to make a clipped pipe tick against a joist every time the cylinder reheats, which is what most people are actually hearing.
That is 2.82 mm, or 0.111 in. Small until you remember the clearance around a sliding leaf is often a couple of millimeters, which is the whole explanation for a door that runs beautifully in April and binds in July.
Concrete and steel share almost the same coefficient, and that coincidence is the reason reinforced concrete works at all: the two do not tear each other apart on the first hot day.
The identical pane in borosilicate gains 9.9 cm2, a third as much. Thermal shock cracking is not about the heat, it is about one part of the pane wanting to be a different size from the part next to it.
The fuel did not multiply. The same mass now occupies more space, which is exactly why a brim-full tank left in the sun pushes into the vapor line, and why wholesale fuel is invoiced corrected to a reference temperature.
Metrology labs hold 20 °C to a fraction of a degree for this reason alone, and it is why invar was invented rather than discovered.
Table 2: what 10 meters and 100 feet actually move
The same two runs through the same 50 K, which is a 90 °F swing, material by material. Read the last column as the gap a joint has to give back before anything starts pushing.
| Material | 10 m over 50 K | 100 ft over 90 °F | What that means on site |
|---|---|---|---|
| Invar 36 | 0.60 mm | 0.072 in | Below the tolerance of most things you would build with it |
| Glass, borosilicate | 1.65 mm | 0.198 in | Survives a temperature gradient that shatters window glass |
| Brick masonry | 2.75 mm | 0.330 in | A long unjointed run cracks at its weakest course, not evenly |
| Titanium | 4.30 mm | 0.516 in | A bit over a third of aluminum, which matters where the two are bolted together |
| Carbon steel and concrete | 6.00 mm | 0.720 in | The pair that shares a coefficient, and the reason rebar holds |
| Copper | 8.30 mm | 0.996 in | One clip too tight and the run creaks every heating cycle |
| Stainless steel 304 | 8.65 mm | 1.038 in | Flues and chimney liners need a sliding joint, not a fixed one |
| Aluminum | 11.55 mm | 1.386 in | Curtain walling is designed around this figure, not despite it |
| Wood, across the grain | 25.00 mm | 3.000 in | Real boards move further still, and mostly from moisture |
| PVC, rigid | 40.00 mm | 4.800 in | Nearly seven times steel; siding and drainage are fitted loose for this |
Where the coefficient stops being a constant
Eight questions that decide the size of a gap
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See also
Calculator verified by the LiczGrupa.pl team
Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.
Reviewed by: Krystian Szyszka