How it works
Most solids grow in proportion to their length and to the temperature rise. The constant of proportionality is the linear expansion coefficient, in inches of growth per inch of length per degree Fahrenheit. Multiply the coefficient, the length, and the temperature change.
The result is the free change in length. If the part is restrained, it develops force instead of moving, which is why long runs of pipe or rail need expansion joints or loops.
Worked example
100 ft of mild steel warmed by 100°F:
- Coefficient = 5.9 × 10⁻⁶ per °F (Mild steel)
- Length change = 5.9×10⁻⁶ × 100 ft × 12 in/ft × 100 °F = 0.708 in
| Input | Value |
|---|---|
| Material | Mild steel |
| Own coefficient (per °F, in millionths) | 30 ×10⁻⁶/°F |
| Original length | 100 ft |
| Temperature change | 100 °F |
| Result | Value |
|---|---|
| Length change | 0.708 in |
| Change per 100 ft per 100°F | 0.708 in |
| Coefficient used | 5.9 ×10⁻⁶/°F |
Linear expansion coefficients used
| Material | ×10⁻⁶ per °F |
|---|---|
| Mild steel | 5.9 |
| Stainless steel 304 | 9.6 |
| Aluminum | 13.1 |
| Copper | 9.8 |
| Yellow brass | 11.3 |
| Gray cast iron | 5.8 |
| My own coefficient | your input |
Show the linear expansion coefficients used table
| Material | ×10⁻⁶ per °F |
|---|---|
| Mild steel | 5.9 |
| Stainless steel 304 | 9.6 |
| Aluminum | 13.1 |
| Copper | 9.8 |
| Yellow brass | 11.3 |
| Gray cast iron | 5.8 |
| My own coefficient | your input |
Values from the Engineering ToolBox; they vary with temperature range and alloy.
Assumptions and limits
- The coefficient is treated as constant across the temperature range; it changes somewhat with temperature.
- Free expansion of a straight, unrestrained length. Restrained parts are stressed, and this tool does not calculate that stress.
- Plastic pipe coefficients are not built in because published values differ between sources; use your manufacturer’s figure in the “own coefficient” field.
Common questions
How much does steel expand per 100 feet?
About 0.7 inch for a 100°F rise (0.708 in with a coefficient of 5.9×10⁻⁶ per °F).
Does aluminum expand more than steel?
Yes, more than twice as much: 13.1 versus 5.9 (×10⁻⁶ per °F).
How do I convert to Celsius?
Switch to Metric. Coefficients per °C are 1.8 times the per °F values.
What about plastic pipe?
Plastics expand several times more than metals and published values vary; use the pipe manufacturer’s coefficient with the own-coefficient option.
Sources
- Engineering ToolBox: metals temperature expansion coefficients (aluminum 13.1, copper 9.8, yellow brass 11.3, mild steel 5.9, stainless 304 9.6, gray cast iron 5.8, in 10⁻⁶ in/in·°F).
- Linear thermal expansion: ΔL = α × L₀ × ΔT.
- Read them: Engineering ToolBox: Metals, temperature expansion coefficients
Updated 2026-09-30