Convert coefficients of thermal expansion between metric and US units.
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By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.
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The coefficient of thermal expansion says how much a material grows per degree. Data sheets write the same number in many ways: 1.2 × 10⁻⁵ /°C, 12 ppm/°C, 12 µm/m·°C and 6.67 µin/in·°F all describe ordinary steel. Enter your value and pick the units. For the length change itself, use the calculator linked below.
ppm/°C = ppm/°F × 1.8 exactly (1 °C = 1.8 °F). 10⁻⁶/K = ppm/°C.
| ppm/°C (µm/m·°C) | ppm/°F (µin/in·°F) |
|---|---|
| 1 | 0.5556 |
| 5 | 2.7778 |
| 10 | 5.5556 |
| 12 | 6.6667 |
| 17 | 9.4444 |
| 23 | 12.7778 |
| 30 | 16.6667 |
| 50 | 27.7778 |
| 100 | 55.5556 |
112 ppm/°C → ppm/°F
12 µm/m·°C = 6.666667 µin/in·°F
12 µm/m·°C = 6.666667 µin/in·°F
26.67 ppm/°F → ppm/°C
6.67 µin/in·°F = 12.006 µm/m·°C
6.67 µin/in·°F = 12.006 µm/m·°C
30.000012 /°C → ppm/°C
0.000012 1/°C = 12 µm/m·°C
0.000012 1/°C = 12 µm/m·°C
423 ppm/°C (Al) → ppm/°F
23 µm/m·°C = 12.777778 µin/in·°F
23 µm/m·°C = 12.777778 µin/in·°F
50.012 mm/m·°C → ppm/°C
0.012 mm/m·°C = 12 µm/m·°C
0.012 mm/m·°C = 12 µm/m·°C
612 ppm/°C → 1/°F
12 µm/m·°C = 6.6667e-6 in/in·°F
12 µm/m·°C = 6.6667e-6 in/in·°F
ppm per °Cppm/°C
Micrometers of expansion per meter per degree Celsius. Identical to 10⁻⁶/K. The standard unit for linear expansion coefficients.
ppm per °Fppm/°F
Microinches per inch per degree Fahrenheit. Equal to ppm/°C ÷ 1.8, because a Fahrenheit degree is smaller.
10⁻⁶ per kelvin10⁻⁶/K
Identical to ppm/°C because kelvin and Celsius intervals are equal. Used in SI material tables.
mm per meter per °Cmm/m·°C
1,000 ppm/°C. Steel is about 0.012 mm/m·°C.
Thermal expansion conversion appears in structural, piping and precision engineering.
| Written as | Value for steel | Meaning |
|---|---|---|
| 1/°C or 1/K | 0.000012 | Per unit length, per degree |
| 10⁻⁶/°C or 10⁻⁶/K | 12 | The same, scaled by a million |
| ppm/°C | 12 | Identical to 10⁻⁶/°C |
| µm/m·°C | 12 | Identical to ppm/°C |
| mm/m·°C | 0.012 | 1,000 times larger unit |
| ppm/°F or µin/in·°F | 6.67 | Per degree Fahrenheit |
| 1/°F or in/in·°F | 0.00000667 | Per degree Fahrenheit, unscaled |
Pick the unit that matches how your number is written. If you enter 0.000012 with ppm/°C selected, the converter warns you, because that value is written as a plain coefficient. A kelvin and a Celsius degree are the same size, so /K and /°C give the same number. A Fahrenheit degree is smaller, so the coefficient per °F is smaller:
ppm/°F = ppm/°C ÷ 1.8
| Material | ppm/°C | ppm/°F |
|---|---|---|
| Invar | 1.5 | 0.83 |
| Gray cast iron | 10.8 | 6.0 |
| Carbon steel | 12 | 6.7 |
| Copper | 16.5 | 9.2 |
| 304 stainless steel | 17.3 | 9.6 |
| Brass | 18.5 | 10.3 |
| Aluminium | 23 | 12.8 |
These are means near room temperature. Exact values depend on the alloy and the temperature range. The engineering materials properties table gives other properties for the same metals.
Expansion depends on the change in temperature. A change of 20 °C equals a change of 36 °F, not 68 °F. The usual "add 32" applies to a reading on a thermometer, not to a difference between two readings.
Keep the units matched and the sum is short: ΔL = α × L × ΔT.
The thermal expansion calculator does this, and it also gives the stress if the part cannot move.
What thermal expansion is explains why materials grow when heated.
The ppm/°C to ppm/°F factor 1.8 is exact (1 °C = 1.8 °F). 10⁻⁶/K and ppm/°C are identical. FlowUtil computes with full precision and rounds only the displayed value.
Expansion coefficients vary with temperature range and alloy, so two significant figures normally reflect the material. State the temperature range for accurate expansion calculations.