Thermal Expansion Converter

The coefficient of thermal expansion (α) is how much a material grows for each degree it warms, as a fraction of its length. A steel bar with α = 12 × 10⁻⁶ /K gets 12 millionths longer for every kelvin.

The change in length is:

ΔL = α * L * ΔT

For example, a 10 m steel rail warming by 30 K grows 12 × 10⁻⁶ × 10 × 30 = 0.0036 m, or 3.6 mm.

How the units work

The unit is "per degree": a length divided by a length, divided by a temperature difference. The length units cancel, so m/(m·K), in/(in·K) and mm/(mm·K) are all the same as 1/K, also written K⁻¹.

• 1/K and 1/°C are the same number, since a difference of 1 K equals a difference of 1 °C.
• 1/°F and 1/°R are the same number, and smaller: a degree Fahrenheit is only 5/9 of a kelvin, so a coefficient per °F is 5/9 of the one per K.
• ppm/K, µm/(m·K) and 10⁻⁶/K are the same thing: steel's 12 × 10⁻⁶/K is 12 ppm/K, or 12 µm per meter per kelvin. Enter 12e-6 in the tool.

How to convert thermal expansion units

Type a value into any field, and every other unit is calculated at once. For example, steel's 12 × 10⁻⁶/K:

1. Per °C: the same number.

   12 × 10⁻⁶ /K = 12 × 10⁻⁶ /°C

2. Per °F: multiply by 5/9.

   12 × 10⁻⁶ × 5 / 9 = 6.67 × 10⁻⁶ /°F

Common conversions

Typical values, in 10⁻⁶/K: steel 12, aluminium 23, copper 17, concrete 12, glass 9, PVC 50–80.

Thermal expansion units

• Length / length / Kelvin (1/K): The unit of thermal expansion in terms of Kelvin is expressed as 1/K or K⁻¹. This unit measures the change in length per unit length per Kelvin change in temperature. The conversion factor from Kelvin to Celsius is 1:1, as both scales have the same magnitude for temperature changes.
  Conversion Factor: 1 K⁻¹ = 1 °C⁻¹

• Length / length / Celsius (1/°C): The Celsius scale is widely used for measuring temperature in everyday contexts. The unit for thermal expansion in Celsius is 1/°C or °C⁻¹. The conversion factor from Celsius to Kelvin is also 1:1.
  Conversion Factor: 1 °C⁻¹ = 1 K⁻¹

• Length / length / Fahrenheit (1/°F): The Fahrenheit scale is commonly used in the United States. The unit for thermal expansion in Fahrenheit is 1/°F or °F⁻¹.
  Conversion Factor: 1 °F⁻¹ = 1.8 K⁻¹

• Length / length / Rankine (1/°R): The Rankine scale is an absolute temperature scale, and the unit for thermal expansion in Rankine is 1/°R or °R⁻¹. Because the Rankine scale is based on the Fahrenheit scale, the conversion factor is the same.
  Conversion Factor: 1 °R⁻¹ = 1.8 K⁻¹

• Length / length / Réaumur (1/°Re): The Réaumur scale is an obsolete temperature scale, but it is still used in some contexts. The unit for thermal expansion in Réaumur is 1/°Re or °Re⁻¹.
  Conversion Factor: 1 °Re⁻¹ = 0.8 K⁻¹