Thermal Expansion Calculator
Length growth from material, length, and temperature change.
What it does
Heat stretches solids in strict proportion. A 30 meter steel bar across plus 40 C grows 14.4 mm, and a 100 foot rail across the same shift in Fahrenheit grows 0.576 inches. Small per meter, bridge scale over long runs.
The tool above runs both unit systems with four materials. Enter length and temperature shift, and it prints growth, new length, and percent. Metric defaults show the steel bar; imperial mirrors at 100 ft with plus 72 F for the identical physics.
References bracket the coefficients. HyperPhysics derives growth as length times alpha times delta-T with a full coefficient table, and NIST publishes thermal expansion compilations for technical solids. Nominal values here sit inside published ranges for common alloys and mixes.
Joints exist because of this math. Rails, decks, and pipe runs leave calculated gaps so summer steel has somewhere to go. Cooling reverses the sign: winter contraction pulls with the same force per degree.
How to use
- Pick metric (m, C) or imperial (ft, F).
- Pick the material for its coefficient.
- Enter the starting length.
- Enter the temperature shift.
- Read growth first, then new length.
- Leave gaps for the growth on long runs.
Formula
- alpha
- Material coefficient per C, x1e-6.
- L0
- Starting length: m or ft by system.
- delta-T
- Temperature shift: C or F degrees.
Nominal coefficients within published ranges (HyperPhysics lists steel 13, aluminum 24, copper 17, iron 12 x1e-6). Delta-F converts x5/9 inside.
Worked example
Example: 30 m steel, plus 40 C
Metric defaults: 30 m steel at plus 40 C. Imperial mirrors at 100 ft, plus 72 F.
- Inputs: 30 m steel bar, plus 40 C.
- Coefficient: steel 12e-6 per C.
- Growth: 30 x 0.000012 x 40 = 0.0144 m.
- Millimeters: 0.0144 x 1,000 = 14.4 mm.
- Tool shows 14.4 mm, 30.0144 m, 0.048%.
Reference table
| Case | Growth | Percent |
|---|---|---|
| 30 m steel, +40 C | 14.4 mm | 0.048 % |
| 10 m aluminum, +50 C | 11.5 mm | 0.115 % |
| 5 m copper, +60 C | 5.1 mm | 0.102 % |
| 100 m concrete, +30 C | 30.0 mm | 0.030 % |
Limits
- Nominal coefficients only. Alloys and mixes vary.
- Small range linear rule; extremes deviate.
- One dimension only. Area and volume scale differ.
- Restraint forces need stress math beyond growth.
Common mistakes
- Using Fahrenheit shifts as Celsius.
- Forgetting concrete moves too.
- Sizing gaps from nominal without margin.
- Mixing coefficient units across tables.
- Ignoring contraction on the cold side.
Try it yourself
Quick checks. Answers sit tucked under each question.
10 m aluminum, plus 50 C?
10 x 23e-6 x 50 = 0.0115 m = 11.5 mm. New 10.0115 m, 0.115 %.
5 m copper, plus 60 C?
5 x 17e-6 x 60 = 0.0051 m = 5.1 mm. New 5.0051 m, 0.102 %.
Questions
How is growth figured?
Coefficient times length times temperature shift. Steel: 30 x 12e-6 x 40 = 14.4 mm.
What are the coefficients?
Steel 12, aluminum 23, copper 17, concrete about 10, all x1e-6 per C. Alloys vary a little around these.
How do Fahrenheit shifts work?
Enter the shift in F; the tool converts (x5/9) inside. Plus 72 F equals plus 40 C.
Where does expansion matter?
Bridges, rails, and pipe runs leave gaps for it. A 100 m concrete deck at plus 30 C grows 30 mm.
Does cooling shrink?
Yes, with a minus sign. Cooling shrinks lengths by the same rule; contraction joints handle both.
What percent is that?
About 0.048 % here (0.0144/30). Small per meter, serious over long runs.
Sources
- Georgia State HyperPhysics: Thermal Expansion
- Georgia State HyperPhysics: Expansion Coefficients Table
- NIST: Thermal Expansion of Technical Solids (compilation)