Thermal Expansion Calculator
How much a length or a diameter grows or shrinks with temperature, from the coefficient of thermal expansion (CTE), in inch and °F or millimeter and °C. Presets cover common machining metals and plastics, and the shrink-fit helper tells you how hot to heat a hub to get it over its shaft.
Thermal expansion
Aluminum 6061-T6: 13.11 µin/in·°F. Leave blank to use it.
Enter a length or diameter and the final temperature. A bore grows by the same rule as a solid diameter.
Shrink fit: how hot to heat the bore
The bore has to grow by the diametral interference plus enough clearance to slide over the shaft before the heat soaks into it.
Leave blank to use the material value.
Enter the bore diameter and the interference to get a heating temperature.
Keep the hub below its tempering or aging temperature (heat-treated steel, aluminum and PH stainless all soften if overheated), heat evenly, and follow the bearing maker's limit when the hub is a bearing ring.
Tight-tolerance parts or press-fit assemblies? , or browse CNC machining shops.
Coefficients of thermal expansion
Typical mean values from about 20 to 100 °C (68 to 212 °F). The inch column is the metric value divided by 1.8. CTE rises with temperature and moves a few percent with heat and temper; plastics also vary with grade, moisture and filler. Use the data sheet for the exact material when the tolerance is tight.
| Material | µm/m·°C | µin/in·°F | Note |
|---|---|---|---|
| Aluminum 6061-T6 | 23.6 | 13.1 | |
| Aluminum 7075-T6 | 23.4 | 13.0 | |
| Stainless 304 | 17.3 | 9.6 | |
| Stainless 316 | 16.0 | 8.9 | |
| 17-4 PH stainless | 10.8 | 6.0 | |
| Steel 1018 | 11.7 | 6.5 | |
| Steel 4140 | 12.2 | 6.8 | |
| Titanium Ti-6Al-4V | 8.6 | 4.8 | |
| Inconel 718 | 13.0 | 7.2 | |
| Brass C360 | 20.5 | 11.4 | |
| Copper C110 | 17.0 | 9.4 | |
| Gray cast iron | 10.8 | 6.0 | Varies with class; roughly 10 to 12. |
| Delrin (acetal homopolymer) | 110.0 | 61.1 | Grade dependent; roughly 85 to 120. |
| PEEK, unfilled | 47.0 | 26.1 | Below the 143 °C glass transition; it rises sharply above it. |
| Nylon 6/6, unfilled | 80.0 | 44.4 | Dry as molded; moisture swells nylon as well. |
| Nylon 6/6, 30% glass filled | 23.0 | 12.8 | Along the flow direction. Across the flow it is several times higher. |
The formulas
- Change in length: ΔL = α x L x ΔT
- Change in diameter (shaft or bore): ΔD = α x D x ΔT
- Shrink-fit temperature rise: ΔT = (interference + clearance) / (α x D)
- Units: α in µm/m·°C = α in µin/in·°F x 1.8; a temperature change of 1 °C = 1.8 °F
Worked example: 1 m of 6061 aluminum at 23.6 µm/m·°C heated from 20 °C to 120 °C grows 23.6 x 10^-6 x 1000 x 100 = 2.36 mm. The same bar in inch units is 39.37" at 13.1 µin/in·°F over 180 °F, which is 0.093".
Where it bites in the shop
- Measuring warm parts: a part fresh off the machine or out of the wash reads large. Drawing sizes apply at 20 °C (68 °F).
- Mixed materials: an aluminum part clamped in a steel fixture grows about twice as fast as the fixture, roughly 0.06 mm over 500 mm for a 10 °C swing.
- Plastics: unfilled acetal and nylon move several times more than aluminum. Leave clearance in metal housings and hold tight tolerances only at a stated temperature.
- Long travel: a 2 m (79") steel rail changes about 0.23 mm (0.009") over a 10 °C (18 °F) swing.
Frequently asked questions
- How do you calculate thermal expansion?
- Change in length = CTE x length x temperature change. One meter of 6061 aluminum (23.6 µm/m·°C) heated 100 °C grows 23.6 x 10^-6 x 1000 mm x 100 = 2.36 mm. In inch units, 10" of the same aluminum (13.1 µin/in·°F) heated 50 °F grows about 0.0066".
- How do I convert CTE between µm/m·°C and in/in·°F?
- Divide by 1.8 to go from per °C to per °F, because one degree Fahrenheit is 5/9 of a degree Celsius. 23.6 µm/m·°C is 13.1 x 10^-6 in/in·°F, and 11.7 µm/m·°C (1018 steel) is 6.5 x 10^-6 in/in·°F. The length units cancel, so µm/m is the same ratio as µin/in.
- Does a hole get bigger or smaller when a part is heated?
- Bigger. A bore grows exactly as a solid disk of the same material would, by CTE x diameter x temperature change. That is why heating a hub or a bearing ring opens its bore enough to slide over a shaft for a shrink fit.
- How hot do I need to heat a hub for a shrink fit?
- Temperature rise = (diametral interference + assembly clearance) / (CTE x bore diameter). A 2.000" bore in 1018 steel with 0.002" interference and 0.001" clearance needs about a 231 °F rise, so roughly 300 °F from a 68 °F shop. You can cool the shaft instead with dry ice (about -78 °C, -109 °F) or liquid nitrogen (about -196 °C, -320 °F), but CTE falls at low temperature, so the shaft shrinks less than the room-temperature value predicts.
- Why do inspection reports mention 20 °C?
- ISO 1 sets 20 °C (68 °F) as the reference temperature for dimensional measurement, so a drawing dimension means the size at 20 °C. A 100 mm aluminum part measured 5 °C warm reads about 0.012 mm (0.0005") long. Let parts soak to room temperature before final inspection, especially aluminum and plastics.
