Thermal Expansion Converter
ScienceConvert coefficient of thermal expansion between per-Kelvin, per-Celsius, per-Fahrenheit, and ppm/°C — used for materials science and engineering design.
From
To
All conversionsfor 1 Parts per Million per °C (ppm/°C)
| Per Kelvin (1/K) | 0.000001 |
| Per Celsius (1/°C) | 0.000001 |
| Per Fahrenheit (1/°F) | 5.5556e-7 |
| Per Rankine (1/°R) | 5.5556e-7 |
| Parts per Million per °C (ppm/°C) | 1 |
What is a Thermal Expansion?
The Thermal Expansion Converter converts the coefficient of thermal expansion between per-Kelvin, per-Celsius, per-Fahrenheit, per-Rankine, and the materials-science-standard parts per million per °C (ppm/°C). This coefficient describes how much a material's dimensions change per degree of temperature change — a critical value in engineering design wherever materials experience temperature swings.
Enter a value in any supported unit and the converter calculates the equivalent instantly. For the underlying temperature-scale relationship this conversion depends on, see the Temperature Interval Converter.
How to use this Thermal Expansion calculator
- Choose your starting unit from the source dropdown — for example, "Parts per Million per °C (ppm/°C)".
- Enter the numeric coefficient value you want to convert in the input field.
- Choose your target unit from the destination dropdown — for example, "Per Kelvin (1/K)".
- Read the converted result, which updates instantly as you type or change units.
- Use the swap (⇅) button if you need to reverse the conversion direction.
- Use the copy button to grab the result for a materials comparison or engineering design calculation.
Formula & Methodology
The converter's base unit is per Kelvin (1/K), identical in scale to per-Celsius. Every supported unit has a fixed multiplier: - 1 per Celsius (1/°C) = 1 per K (identical degree size) - 1 per Fahrenheit (1/°F) = 1.8 per K (accounts for the smaller Fahrenheit degree size) - 1 per Rankine (1/°R) = 1.8 per K (identical to per °F) - 1 ppm/°C = 0.000001 per K Any conversion follows: Result = Input × (toBase of source unit ÷ toBase of target unit) Worked example — converting steel's typical CTE of 12 ppm/°C to per Kelvin: Result = 12 × 0.000001 = 0.000012 per K (1.2 × 10⁻⁵ /K) This matches the commonly cited value for steel's linear thermal expansion coefficient in SI units.
Frequently Asked Questions
The coefficient of thermal expansion (CTE) measures how much a material's dimensions change per degree of temperature change, expressed in units like per Kelvin (1/K) or parts per million per degree Celsius (ppm/°C). A higher CTE means the material expands or contracts more for a given temperature change.
Most solid materials have very small thermal expansion coefficients — a typical metal might expand by only a few thousandths of a percent per degree — so expressing the value in parts per million per °C keeps the numbers in a more readable range than using raw per-Kelvin fractions.
Divide the ppm/°C value by 1,000,000, since ppm means 'parts per million.' Enter your value with 'Parts per Million per °C (ppm/°C)' as the source and 'Per Kelvin (1/K)' as the target to apply this automatically.
Because a Fahrenheit degree interval is smaller than a Celsius/Kelvin interval (5/9 the size), the same physical expansion rate corresponds to a larger 'per °F' value — specifically 1.8 times larger — than the equivalent 'per K' or 'per °C' value, since expansion per smaller degree steps looks like a bigger number per step.
No — this converter handles unit conversion of whatever coefficient value you already have; it doesn't distinguish between linear expansion coefficient (length change) and volumetric expansion coefficient (volume change), which are different physical quantities related by roughly a factor of 3 for isotropic materials. Make sure you're comparing coefficients of the same type.
Steel has a CTE of roughly 12 ppm/°C, aluminium roughly 23 ppm/°C, and glass roughly 9 ppm/°C — these differences matter significantly in engineering design where dissimilar materials are joined and need to expand at compatible rates to avoid stress or failure.
When materials with different thermal expansion coefficients are bonded or fitted together (like a metal fitting in a different metal housing), temperature changes can create mechanical stress or gaps as the materials expand at different rates — engineers need accurate, correctly converted CTE values to predict and design around this.
Thermal expansion coefficients are defined per unit of temperature interval (not per absolute temperature), so understanding how temperature intervals convert between scales — covered by the [Temperature Interval Converter](/temperature-interval-converter/) — is the same underlying logic that determines how thermal expansion coefficients convert between per-Celsius and per-Fahrenheit.
The unit conversion math works the same regardless of whether you're converting a linear, area, or volumetric expansion coefficient, since the temperature-scale relationship is identical — just be careful not to mix a linear coefficient value with a volumetric one in the same comparison.
CTE is typically measured with a dilatometer, which precisely tracks a sample's dimensional change across a controlled temperature range, then calculates the coefficient from the observed expansion divided by the temperature interval applied.
Also known as